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style="width: 100%;"><div class="u-taCenter"></div><div class="profile--tab_content_container js-tab-pane tab-pane active" id="all"><div class="profile--tab_heading_container js-section-heading" data-section="Papers" id="Papers"><h3 class="profile--tab_heading_container">Papers by Jan Paseka</h3></div><div class="js-work-strip profile--work_container" data-work-id="100206064"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206064/Atomicity_of_lattice_effect_algebras_and_their_sub_lattice_effect_algebras"><img alt="Research paper thumbnail of Atomicity of lattice effect algebras and their sub-lattice effect algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/101094897/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206064/Atomicity_of_lattice_effect_algebras_and_their_sub_lattice_effect_algebras">Atomicity of lattice effect algebras and their sub-lattice effect algebras</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">summary:We show some families of lattice effect algebras (a common generalization of orthomodular...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">summary:We show some families of lattice effect algebras (a common generalization of orthomodular lattices and MV-effect algebras) each element E of which has atomic center C(E) or the subset S(E) of all sharp elements, resp. the center of compatibility B(E) or every block M of E. The atomicity of E or its sub-lattice effect algebras C(E), S(E), B(E) and blocks M of E is very useful equipment for the investigations of its algebraic and topological properties, the existence or smearing of states on E, questions about isomorphisms and so. Namely we touch the families of complete lattice effect algebras, or lattice effect algebras with finitely many blocks, or complete atomic lattice effect algebra E with Hausdorff interval topology</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6525d2ed91437d03bd47f178ee8e21fb" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094897,"asset_id":100206064,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094897/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206064"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206064"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206064; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206063"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206063/Modularity_atomicity_and_states"><img alt="Research paper thumbnail of Modularity, atomicity and states" class="work-thumbnail" src="https://attachments.academia-assets.com/101094938/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206063/Modularity_atomicity_and_states">Modularity, atomicity and states</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Effect algebras are a generalization of many structures which arise in quantum physics and in mat...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra E that is not an orthomodular lattice there exists an (o)continuous state ω on E, which is subadditive. Moreover, we show properties of finite and compact elements of such lattice effect algebras.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b8fa5eb72589ad58dce15bb7dcc37347" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094938,"asset_id":100206063,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094938/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206063"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206063"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206063; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206062"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206062/Inherited_Properties_of_Effect_Algebras_Preserved_by_Isomorphisms"><img alt="Research paper thumbnail of Inherited Properties of Effect Algebras Preserved by Isomorphisms" class="work-thumbnail" src="https://attachments.academia-assets.com/101094896/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206062/Inherited_Properties_of_Effect_Algebras_Preserved_by_Isomorphisms">Inherited Properties of Effect Algebras Preserved by Isomorphisms</a></div><div class="wp-workCard_item"><span>Acta Polytechnica</span><span>, 2013</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We show that isomorphism of effect algebras preserves properties of effect algebras derived from ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We show that isomorphism of effect algebras preserves properties of effect algebras derived from effect algebraic sum ? of elements. These are partial order, order convergence, order topology, existence of states and other important properties. However, there are properties of effect algebras for which the preservation of the ?-operation is not substantial and they need not be preserved.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="24b6c4d9ad89a99969fc04a1dfb89051" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094896,"asset_id":100206062,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094896/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206062"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206062"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206062; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206061"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206061/Algebraic_Properties_of_Paraorthomodular_Posets"><img alt="Research paper thumbnail of Algebraic Properties of Paraorthomodular Posets" class="work-thumbnail" src="https://attachments.academia-assets.com/101094943/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206061/Algebraic_Properties_of_Paraorthomodular_Posets">Algebraic Properties of Paraorthomodular Posets</a></div><div class="wp-workCard_item"><span>Logic Journal of the IGPL</span><span>, 2021</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Paraorthomodular posets are bounded partially ordered sets with an antitone involution induced by...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Paraorthomodular posets are bounded partially ordered sets with an antitone involution induced by quantum structures arising from the logico-algebraic approach to quantum mechanics. The aim of the present work is starting a systematic inquiry into paraorthomodular posets theory both from algebraic and order-theoretic perspectives. On the one hand, we show that paraorthomodular posets are amenable of an algebraic treatment by means of a smooth representation in terms of bounded directoids with antitone involution. On the other, we investigate their order-theoretical features in terms of forbidden configurations. Moreover, sufficient and necessary conditions characterizing bounded posets with an antitone involution whose Dedekind–MacNeille completion is paraorthomodular are provided.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="80bf3e0868099d2bacc8e158dc1d5441" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094943,"asset_id":100206061,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094943/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206061"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206061"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206061; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206060"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206060/Dynamic_Logic_Assigned_to_Automata"><img alt="Research paper thumbnail of Dynamic Logic Assigned to Automata" class="work-thumbnail" src="https://attachments.academia-assets.com/101094893/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206060/Dynamic_Logic_Assigned_to_Automata">Dynamic Logic Assigned to Automata</a></div><div class="wp-workCard_item"><span>International Journal of Theoretical Physics</span><span>, Feb 22, 2017</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A dynamic logic B can be assigned to every automaton A without regard if A is deterministic or no...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">A dynamic logic B can be assigned to every automaton A without regard if A is deterministic or nondeterministic. This logic enables us to formulate observations on A in the form of composed propositions and, due to a transition functor T , it captures the dynamic behaviour of A. There are formulated conditions under which the automaton A can be recovered by means of B and T .</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9abb9921c5043b9e3405cf22a9f3187b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094893,"asset_id":100206060,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094893/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206060"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206060"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206060; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206059"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206059/A_Representation_Theorem_for_Quantale_Valued_sup_algebras"><img alt="Research paper thumbnail of A Representation Theorem for Quantale Valued sup-algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/101094892/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206059/A_Representation_Theorem_for_Quantale_Valued_sup_algebras">A Representation Theorem for Quantale Valued sup-algebras</a></div><div class="wp-workCard_item"><span>2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL)</span><span>, May 1, 2018</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">With this paper we hope to contribute to the theory of quantales and quantale-like structures. It...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">With this paper we hope to contribute to the theory of quantales and quantale-like structures. It considers the notion of Q-sup-algebra and shows a representation theorem for such structures generalizing the well-known representation theorems for quantales and sup-algebras. In addition, we present some important properties of the category of Q-sup-algebras.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="62bca1e6fb1c521db1dc4a6a31a5258f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094892,"asset_id":100206059,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094892/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206059"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206059"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206059; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206058"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206058/On_the_Coextension_of_Cut_Continuous_Pomonoids"><img alt="Research paper thumbnail of On the Coextension of Cut-Continuous Pomonoids" class="work-thumbnail" src="https://attachments.academia-assets.com/101094890/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206058/On_the_Coextension_of_Cut_Continuous_Pomonoids">On the Coextension of Cut-Continuous Pomonoids</a></div><div class="wp-workCard_item"><span>Order</span><span>, 2018</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We introduce cut-continuous pomonoids, which generalise residuated posets. The latter's defining ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We introduce cut-continuous pomonoids, which generalise residuated posets. The latter's defining condition is that the monoidal product is residuated in each argument; we define cut-continuous pomonoids by requiring that the monoidal product is in each argument just cut-continuous. In the case of a total order, the condition of cut-continuity means that multiplication distributes over existing suprema. Morphisms between cut-continuous pomonoids can be chosen either in analogy with unital quantales or with residuated lattices. Under the assumption of commutativity and integrality, congruences are in the latter case induced by filters, in the same way as known for residuated lattices. We are interested in the construction of coextensions: given cut-continuous pomonoids K and C, we raise the question how we can determine the cut-continuous pomonoids L such that C is a filter of L and the quotient of L induced by C is isomorphic to K. In this context, we are in particular concerned with tensor products of modules over cut-continuous pomonoids. Using results of M. Erné and J. Picado on closure spaces, we show that such tensor products exist. An application is the construction of residuated structures related to fuzzy logics, in particular left-continuous t-norms.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="f869809013c1be86eeba82d73fee2d4e" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094890,"asset_id":100206058,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094890/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206058"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206058"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206058; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206056"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206056/Categorical_foundations_of_variety_based_bornology"><img alt="Research paper thumbnail of Categorical foundations of variety-based bornology" class="work-thumbnail" src="https://attachments.academia-assets.com/101094933/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206056/Categorical_foundations_of_variety_based_bornology">Categorical foundations of variety-based bornology</a></div><div class="wp-workCard_item"><span>Fuzzy Sets and Systems</span><span>, 2016</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Following the concept of topological theory of S. E. Rodabaugh, this paper introduces a new appro...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Following the concept of topological theory of S. E. Rodabaugh, this paper introduces a new approach to (lattice-valued) bornology, which is based in bornological theories, and which is called variety-based bornology. In particular, motivated by the notion of topological system of S. Vickers, we introduce the concept of variety-based bornological system, and show that the category of variety-based bornological spaces is isomorphic to a full reflective subcategory of the category of variety-based bornological systems.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ae1118912c845ce8e823192002839ec7" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094933,"asset_id":100206056,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094933/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206056"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206056"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206056; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206055"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206055/Galois_connections_and_tense_operators_on_q_effect_algebras"><img alt="Research paper thumbnail of Galois connections and tense operators on q-effect algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/101094940/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206055/Galois_connections_and_tense_operators_on_q_effect_algebras">Galois connections and tense operators on q-effect algebras</a></div><div class="wp-workCard_item"><span>Fuzzy Sets and Systems</span><span>, 2016</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">For effect algebras, the so-called tense operators were already introduced by Chajda and Paseka. ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">For effect algebras, the so-called tense operators were already introduced by Chajda and Paseka. They presented also a canonical construction of them using the notion of a time frame. Tense operators express the quantifiers "it is always going to be the case that" and "it has always been the case that" and hence enable us to express the dimension of time both in the logic of quantum mechanics and in the many-valued logic. A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a time frame such that each of these operators can be obtained by the canonical construction. To approximate physical real systems as best as possible, we introduce the notion of a q-effect algebra and we solve this problem for q-tense operators on q-representable q-Jauch-Piron q-effect algebras.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="0837fecb1ea1691c9a8d3283fb55ac7d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094940,"asset_id":100206055,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094940/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206055"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206055"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206055; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206053"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206053/Filters_on_Some_Classes_of_Quantum_B_Algebras"><img alt="Research paper thumbnail of Filters on Some Classes of Quantum B-Algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/101094931/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206053/Filters_on_Some_Classes_of_Quantum_B_Algebras">Filters on Some Classes of Quantum B-Algebras</a></div><div class="wp-workCard_item"><span>International Journal of Theoretical Physics</span><span>, 2015</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper, we continue the study of quantum B-algebras with emphasis on filters on integral q...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper, we continue the study of quantum B-algebras with emphasis on filters on integral quantum B-algebras. We then study filters in the setting of pseudo-hoops. First, we establish an embedding of a cartesion product of polars of a pseudo-hoop into itself. Second, we give sufficient conditions for a pseudohoop to be subdirectly reducible. We also extend the result of Kondo and Turunen to the setting of noncommutative residuated ∨-semilattices that, if prime filters and ∨-prime filters of a residuated ∨-semilattice A coincide, then A must be a pseudo MTL-algebra.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="e4258935209f6a25ec1e49e128821930" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094931,"asset_id":100206053,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094931/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206053"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206053"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206053; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206052"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206052/Tense_Operators_and_Dynamic_De_Morgan_Algebras"><img alt="Research paper thumbnail of Tense Operators and Dynamic De Morgan Algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/101094934/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206052/Tense_Operators_and_Dynamic_De_Morgan_Algebras">Tense Operators and Dynamic De Morgan Algebras</a></div><div class="wp-workCard_item"><span>2013 IEEE 43rd International Symposium on Multiple-Valued Logic</span><span>, 2013</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">By a De Morgan algebra is meant a bounded poset equipped with an antitone involution considered a...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">By a De Morgan algebra is meant a bounded poset equipped with an antitone involution considered as negation. Such an algebra can be considered as an algebraic axiomatization of a propositional logic satisfying the double negation law. Our aim is to introduce the socalled tense operators in every De Morgan algebra for to get an algebraic counterpart of a tense logic with negation satisfying the double negation law which need not be Boolean. Following the standard construction of tense operators G and H by a frame we solve the following question: if a dynamic De Morgan algebra is given, how to find a frame such that its tense operators G and H can be reached by this construction. Index Terms-De Morgan lattice, De Morgan poset, semi-tense operators, tense operators, (partial) dynamic De Morgan algebra.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="140d68416d9c9c630e707bb7cbb9976c" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094934,"asset_id":100206052,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094934/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206052"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206052"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206052; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206051"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206051/Projective_sup_algebras_a_general_view"><img alt="Research paper thumbnail of Projective sup-algebras: a general view" class="work-thumbnail" src="https://attachments.academia-assets.com/101094935/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206051/Projective_sup_algebras_a_general_view">Projective sup-algebras: a general view</a></div><div class="wp-workCard_item"><span>Topology and its Applications</span><span>, 2008</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We begin with the notion of K-flat projectivity. For each sup-algebra L we then introduce a binar...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We begin with the notion of K-flat projectivity. For each sup-algebra L we then introduce a binary relation L on it. The K-flat projective sup-algebras are exactly such sup-algebras with each element a approximated by the element x, x L a and the relation L being stable with respect to the operations on L. Further on, we introduce the notion of a K-comonad and characterize K-flat projective sup-algebras as such sup-algebras having a coalgebra structure for the K-comonad.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="74ab5ea0822a27c8db5b332c67351265" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094935,"asset_id":100206051,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094935/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206051"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206051"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206051; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206049"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/100206049/On_tense_MV_algebras"><img alt="Research paper thumbnail of On tense MV-algebras" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/100206049/On_tense_MV_algebras">On tense MV-algebras</a></div><div class="wp-workCard_item"><span>Fuzzy Sets and Systems</span><span>, 2015</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206049"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206049"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206049; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=100206049]").text(description); $(".js-view-count[data-work-id=100206049]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 100206049; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='100206049']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=100206049]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":100206049,"title":"On tense MV-algebras","internal_url":"https://www.academia.edu/100206049/On_tense_MV_algebras","owner_id":241431338,"coauthors_can_edit":true,"owner":{"id":241431338,"first_name":"Jan","middle_initials":null,"last_name":"Paseka","page_name":"JPaseka","domain_name":"independent","created_at":"2022-10-20T23:38:14.667-07:00","display_name":"Jan Paseka","url":"https://independent.academia.edu/JPaseka"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206048"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206048/A_dynamic_Effect_Algebras_with_Dual_Operation"><img alt="Research paper thumbnail of A dynamic Effect Algebras with Dual Operation" class="work-thumbnail" src="https://attachments.academia-assets.com/101094939/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206048/A_dynamic_Effect_Algebras_with_Dual_Operation">A dynamic Effect Algebras with Dual Operation</a></div><div class="wp-workCard_item"><span>MATHEMATICS FOR APPLICATIONS</span><span>, 2012</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Tense operators for MV-algebras were introduced by Diaconescu and Georgescu. Based on their defin...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Tense operators for MV-algebras were introduced by Diaconescu and Georgescu. Based on their definition Chajda and Kolařík presented the definition of tense operators for lattice effect algebras. Chajda and Paseka tackled the problem of axiomatizing tense operators on an effect algebra by introducing the notion of a partial dynamic effect algebra. They also gave representation theorems for dynamic effect algebras. We continue to extend their work for partial S-dynamic effect algebras i.e. in the case when tense operators satisfy required conditions also for the dual effect algebraic operation •. We show that whenever tense operators are total our stronger notion coincides with their definition. We give also a representation theorem for partial S-dynamic effect algebras and its version for strict dynamic effect algebras.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="e6daf47988983a6a1a00118739d93715" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094939,"asset_id":100206048,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094939/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206048"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206048"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206048; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206047"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206047/Representations_of_zero_cancellative_pomonoids"><img alt="Research paper thumbnail of Representations of zero-cancellative pomonoids" class="work-thumbnail" src="https://attachments.academia-assets.com/101094936/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206047/Representations_of_zero_cancellative_pomonoids">Representations of zero-cancellative pomonoids</a></div><div class="wp-workCard_item"><span>Mathematica Slovaca</span><span>, 2014</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Several familiar results on representations of MV-algebras shape the idea that the use of solving...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Several familiar results on representations of MV-algebras shape the idea that the use of solving systems of linear equations can be studied also in the setting of zero-cancellative commutative pomonoids. This paper investigates this idea and shows that for the class of linearly representable zero-cancellative commutative pomonoids the respective results apply as well.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="a428cb8ad801521eb28853bca05347a0" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094936,"asset_id":100206047,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094936/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206047"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206047"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206047; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206046"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206046/Note_on_distributive_posets"><img alt="Research paper thumbnail of Note on distributive posets" class="work-thumbnail" src="https://attachments.academia-assets.com/101094887/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206046/Note_on_distributive_posets">Note on distributive posets</a></div><div class="wp-workCard_item"><span>MATHEMATICS FOR APPLICATIONS</span><span>, 2012</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this note we study distributive posets. We discuss several notions of distributivity in posets...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this note we study distributive posets. We discuss several notions of distributivity in posets and show their equivalence. Moreover, the Prime Ideal Theorem for Distributive Posets is shown to be equivalent with the famous Prime Ideal Theorem for Distributive Lattices using distributive ideal approach. n i=1 X i we put U(X 1 ,. .. , X n) = U(X) (L(X 1 ,. .. , X n) = L(X)). If, moreover, for some i, 1 ≤ i ≤ n, X i = {a i }, we substitute X i by a i as follows U(X</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="45a0c783acdd9ced5deae6e07cae84ba" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094887,"asset_id":100206046,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094887/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206046"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206046"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206046; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206044"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206044/Modularity_Atomicity_and_States_in_Archimedean_Lattice_Effect_Algebras"><img alt="Research paper thumbnail of Modularity, Atomicity and States in Archimedean Lattice Effect Algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/101094932/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206044/Modularity_Atomicity_and_States_in_Archimedean_Lattice_Effect_Algebras">Modularity, Atomicity and States in Archimedean Lattice Effect Algebras</a></div><div class="wp-workCard_item"><span>Symmetry, Integrability and Geometry: Methods and Applications</span><span>, 2010</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Effect algebras are a generalization of many structures which arise in quantum physics and in mat...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra E that is not an orthomodular lattice there exists an (o)continuous state ω on E, which is subadditive. Moreover, we show properties of finite and compact elements of such lattice effect algebras.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="5c49a2b3ef8452afd74a175ae9a9b91d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094932,"asset_id":100206044,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094932/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206044"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206044"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206044; 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We develop the notions of Rieffel induc...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we consider m-regular involutive quantales. We develop the notions of Rieffel induction and strong Morita equivalence for this category analogously to the situation for C *-algebras.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="00096a191dc96d6fd4102ed8dc6c48a0" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094930,"asset_id":100206043,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094930/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206043"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206043"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206043; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206042"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206042/On_Realization_of_Generalized_Effect_Algebras"><img alt="Research paper thumbnail of On Realization of Generalized Effect Algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/101094924/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206042/On_Realization_of_Generalized_Effect_Algebras">On Realization of Generalized Effect Algebras</a></div><div class="wp-workCard_item"><span>Reports on Mathematical Physics</span><span>, 2012</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A well known fact is that there is a finite orthomodular lattice with an order determining set of...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">A well known fact is that there is a finite orthomodular lattice with an order determining set of states which is not representable in the standard quantum logic, the lattice L(H) of all closed subspaces of a separable complex Hilbert space. We show that a generalized effect algebra is representable in the operator generalized effect algebra G D (H) of effects of a complex Hilbert space H iff it has an order determining set of generalized states. This extends the corresponding results for effect algebras of Riečanová and Zajac. Further, any operator generalized effect algebra G D (H) possesses an order determining set of generalized states MSC: 03G12; 06D35; 06F25; 81P10</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="605e51e60ac48294dbc8373f4af92fbc" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094924,"asset_id":100206042,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094924/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206042"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206042"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206042; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="16125946" id="papers"><div class="js-work-strip profile--work_container" data-work-id="100206064"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206064/Atomicity_of_lattice_effect_algebras_and_their_sub_lattice_effect_algebras"><img alt="Research paper thumbnail of Atomicity of lattice effect algebras and their sub-lattice effect algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/101094897/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206064/Atomicity_of_lattice_effect_algebras_and_their_sub_lattice_effect_algebras">Atomicity of lattice effect algebras and their sub-lattice effect algebras</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">summary:We show some families of lattice effect algebras (a common generalization of orthomodular...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">summary:We show some families of lattice effect algebras (a common generalization of orthomodular lattices and MV-effect algebras) each element E of which has atomic center C(E) or the subset S(E) of all sharp elements, resp. the center of compatibility B(E) or every block M of E. The atomicity of E or its sub-lattice effect algebras C(E), S(E), B(E) and blocks M of E is very useful equipment for the investigations of its algebraic and topological properties, the existence or smearing of states on E, questions about isomorphisms and so. Namely we touch the families of complete lattice effect algebras, or lattice effect algebras with finitely many blocks, or complete atomic lattice effect algebra E with Hausdorff interval topology</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6525d2ed91437d03bd47f178ee8e21fb" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094897,"asset_id":100206064,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094897/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206064"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206064"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206064; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206063"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206063/Modularity_atomicity_and_states"><img alt="Research paper thumbnail of Modularity, atomicity and states" class="work-thumbnail" src="https://attachments.academia-assets.com/101094938/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206063/Modularity_atomicity_and_states">Modularity, atomicity and states</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Effect algebras are a generalization of many structures which arise in quantum physics and in mat...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra E that is not an orthomodular lattice there exists an (o)continuous state ω on E, which is subadditive. Moreover, we show properties of finite and compact elements of such lattice effect algebras.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b8fa5eb72589ad58dce15bb7dcc37347" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094938,"asset_id":100206063,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094938/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206063"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206063"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206063; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206062"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206062/Inherited_Properties_of_Effect_Algebras_Preserved_by_Isomorphisms"><img alt="Research paper thumbnail of Inherited Properties of Effect Algebras Preserved by Isomorphisms" class="work-thumbnail" src="https://attachments.academia-assets.com/101094896/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206062/Inherited_Properties_of_Effect_Algebras_Preserved_by_Isomorphisms">Inherited Properties of Effect Algebras Preserved by Isomorphisms</a></div><div class="wp-workCard_item"><span>Acta Polytechnica</span><span>, 2013</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We show that isomorphism of effect algebras preserves properties of effect algebras derived from ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We show that isomorphism of effect algebras preserves properties of effect algebras derived from effect algebraic sum ? of elements. These are partial order, order convergence, order topology, existence of states and other important properties. However, there are properties of effect algebras for which the preservation of the ?-operation is not substantial and they need not be preserved.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="24b6c4d9ad89a99969fc04a1dfb89051" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094896,"asset_id":100206062,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094896/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206062"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206062"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206062; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206061"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206061/Algebraic_Properties_of_Paraorthomodular_Posets"><img alt="Research paper thumbnail of Algebraic Properties of Paraorthomodular Posets" class="work-thumbnail" src="https://attachments.academia-assets.com/101094943/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206061/Algebraic_Properties_of_Paraorthomodular_Posets">Algebraic Properties of Paraorthomodular Posets</a></div><div class="wp-workCard_item"><span>Logic Journal of the IGPL</span><span>, 2021</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Paraorthomodular posets are bounded partially ordered sets with an antitone involution induced by...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Paraorthomodular posets are bounded partially ordered sets with an antitone involution induced by quantum structures arising from the logico-algebraic approach to quantum mechanics. The aim of the present work is starting a systematic inquiry into paraorthomodular posets theory both from algebraic and order-theoretic perspectives. On the one hand, we show that paraorthomodular posets are amenable of an algebraic treatment by means of a smooth representation in terms of bounded directoids with antitone involution. On the other, we investigate their order-theoretical features in terms of forbidden configurations. Moreover, sufficient and necessary conditions characterizing bounded posets with an antitone involution whose Dedekind–MacNeille completion is paraorthomodular are provided.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="80bf3e0868099d2bacc8e158dc1d5441" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094943,"asset_id":100206061,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094943/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206061"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206061"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206061; 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This logic enables us to formulate observations on A in the form of composed propositions and, due to a transition functor T , it captures the dynamic behaviour of A. There are formulated conditions under which the automaton A can be recovered by means of B and T .</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9abb9921c5043b9e3405cf22a9f3187b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094893,"asset_id":100206060,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094893/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206060"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206060"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206060; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206059"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206059/A_Representation_Theorem_for_Quantale_Valued_sup_algebras"><img alt="Research paper thumbnail of A Representation Theorem for Quantale Valued sup-algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/101094892/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206059/A_Representation_Theorem_for_Quantale_Valued_sup_algebras">A Representation Theorem for Quantale Valued sup-algebras</a></div><div class="wp-workCard_item"><span>2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL)</span><span>, May 1, 2018</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">With this paper we hope to contribute to the theory of quantales and quantale-like structures. It...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">With this paper we hope to contribute to the theory of quantales and quantale-like structures. It considers the notion of Q-sup-algebra and shows a representation theorem for such structures generalizing the well-known representation theorems for quantales and sup-algebras. In addition, we present some important properties of the category of Q-sup-algebras.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="62bca1e6fb1c521db1dc4a6a31a5258f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094892,"asset_id":100206059,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094892/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206059"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206059"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206059; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206058"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206058/On_the_Coextension_of_Cut_Continuous_Pomonoids"><img alt="Research paper thumbnail of On the Coextension of Cut-Continuous Pomonoids" class="work-thumbnail" src="https://attachments.academia-assets.com/101094890/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206058/On_the_Coextension_of_Cut_Continuous_Pomonoids">On the Coextension of Cut-Continuous Pomonoids</a></div><div class="wp-workCard_item"><span>Order</span><span>, 2018</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We introduce cut-continuous pomonoids, which generalise residuated posets. The latter's defining ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We introduce cut-continuous pomonoids, which generalise residuated posets. The latter's defining condition is that the monoidal product is residuated in each argument; we define cut-continuous pomonoids by requiring that the monoidal product is in each argument just cut-continuous. In the case of a total order, the condition of cut-continuity means that multiplication distributes over existing suprema. Morphisms between cut-continuous pomonoids can be chosen either in analogy with unital quantales or with residuated lattices. Under the assumption of commutativity and integrality, congruences are in the latter case induced by filters, in the same way as known for residuated lattices. We are interested in the construction of coextensions: given cut-continuous pomonoids K and C, we raise the question how we can determine the cut-continuous pomonoids L such that C is a filter of L and the quotient of L induced by C is isomorphic to K. In this context, we are in particular concerned with tensor products of modules over cut-continuous pomonoids. Using results of M. Erné and J. Picado on closure spaces, we show that such tensor products exist. An application is the construction of residuated structures related to fuzzy logics, in particular left-continuous t-norms.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="f869809013c1be86eeba82d73fee2d4e" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094890,"asset_id":100206058,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094890/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206058"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206058"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206058; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206056"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206056/Categorical_foundations_of_variety_based_bornology"><img alt="Research paper thumbnail of Categorical foundations of variety-based bornology" class="work-thumbnail" src="https://attachments.academia-assets.com/101094933/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206056/Categorical_foundations_of_variety_based_bornology">Categorical foundations of variety-based bornology</a></div><div class="wp-workCard_item"><span>Fuzzy Sets and Systems</span><span>, 2016</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Following the concept of topological theory of S. E. Rodabaugh, this paper introduces a new appro...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Following the concept of topological theory of S. E. Rodabaugh, this paper introduces a new approach to (lattice-valued) bornology, which is based in bornological theories, and which is called variety-based bornology. In particular, motivated by the notion of topological system of S. Vickers, we introduce the concept of variety-based bornological system, and show that the category of variety-based bornological spaces is isomorphic to a full reflective subcategory of the category of variety-based bornological systems.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ae1118912c845ce8e823192002839ec7" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094933,"asset_id":100206056,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094933/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206056"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206056"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206056; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206055"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206055/Galois_connections_and_tense_operators_on_q_effect_algebras"><img alt="Research paper thumbnail of Galois connections and tense operators on q-effect algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/101094940/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206055/Galois_connections_and_tense_operators_on_q_effect_algebras">Galois connections and tense operators on q-effect algebras</a></div><div class="wp-workCard_item"><span>Fuzzy Sets and Systems</span><span>, 2016</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">For effect algebras, the so-called tense operators were already introduced by Chajda and Paseka. ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">For effect algebras, the so-called tense operators were already introduced by Chajda and Paseka. They presented also a canonical construction of them using the notion of a time frame. Tense operators express the quantifiers "it is always going to be the case that" and "it has always been the case that" and hence enable us to express the dimension of time both in the logic of quantum mechanics and in the many-valued logic. A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a time frame such that each of these operators can be obtained by the canonical construction. To approximate physical real systems as best as possible, we introduce the notion of a q-effect algebra and we solve this problem for q-tense operators on q-representable q-Jauch-Piron q-effect algebras.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="0837fecb1ea1691c9a8d3283fb55ac7d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094940,"asset_id":100206055,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094940/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206055"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206055"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206055; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206053"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206053/Filters_on_Some_Classes_of_Quantum_B_Algebras"><img alt="Research paper thumbnail of Filters on Some Classes of Quantum B-Algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/101094931/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206053/Filters_on_Some_Classes_of_Quantum_B_Algebras">Filters on Some Classes of Quantum B-Algebras</a></div><div class="wp-workCard_item"><span>International Journal of Theoretical Physics</span><span>, 2015</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper, we continue the study of quantum B-algebras with emphasis on filters on integral q...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper, we continue the study of quantum B-algebras with emphasis on filters on integral quantum B-algebras. We then study filters in the setting of pseudo-hoops. First, we establish an embedding of a cartesion product of polars of a pseudo-hoop into itself. Second, we give sufficient conditions for a pseudohoop to be subdirectly reducible. We also extend the result of Kondo and Turunen to the setting of noncommutative residuated ∨-semilattices that, if prime filters and ∨-prime filters of a residuated ∨-semilattice A coincide, then A must be a pseudo MTL-algebra.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="e4258935209f6a25ec1e49e128821930" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094931,"asset_id":100206053,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094931/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206053"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206053"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206053; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206052"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206052/Tense_Operators_and_Dynamic_De_Morgan_Algebras"><img alt="Research paper thumbnail of Tense Operators and Dynamic De Morgan Algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/101094934/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206052/Tense_Operators_and_Dynamic_De_Morgan_Algebras">Tense Operators and Dynamic De Morgan Algebras</a></div><div class="wp-workCard_item"><span>2013 IEEE 43rd International Symposium on Multiple-Valued Logic</span><span>, 2013</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">By a De Morgan algebra is meant a bounded poset equipped with an antitone involution considered a...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">By a De Morgan algebra is meant a bounded poset equipped with an antitone involution considered as negation. Such an algebra can be considered as an algebraic axiomatization of a propositional logic satisfying the double negation law. Our aim is to introduce the socalled tense operators in every De Morgan algebra for to get an algebraic counterpart of a tense logic with negation satisfying the double negation law which need not be Boolean. Following the standard construction of tense operators G and H by a frame we solve the following question: if a dynamic De Morgan algebra is given, how to find a frame such that its tense operators G and H can be reached by this construction. Index Terms-De Morgan lattice, De Morgan poset, semi-tense operators, tense operators, (partial) dynamic De Morgan algebra.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="140d68416d9c9c630e707bb7cbb9976c" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094934,"asset_id":100206052,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094934/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206052"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206052"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206052; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206051"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206051/Projective_sup_algebras_a_general_view"><img alt="Research paper thumbnail of Projective sup-algebras: a general view" class="work-thumbnail" src="https://attachments.academia-assets.com/101094935/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206051/Projective_sup_algebras_a_general_view">Projective sup-algebras: a general view</a></div><div class="wp-workCard_item"><span>Topology and its Applications</span><span>, 2008</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We begin with the notion of K-flat projectivity. For each sup-algebra L we then introduce a binar...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We begin with the notion of K-flat projectivity. For each sup-algebra L we then introduce a binary relation L on it. The K-flat projective sup-algebras are exactly such sup-algebras with each element a approximated by the element x, x L a and the relation L being stable with respect to the operations on L. Further on, we introduce the notion of a K-comonad and characterize K-flat projective sup-algebras as such sup-algebras having a coalgebra structure for the K-comonad.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="74ab5ea0822a27c8db5b332c67351265" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094935,"asset_id":100206051,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094935/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206051"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206051"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206051; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206049"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/100206049/On_tense_MV_algebras"><img alt="Research paper thumbnail of On tense MV-algebras" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/100206049/On_tense_MV_algebras">On tense MV-algebras</a></div><div class="wp-workCard_item"><span>Fuzzy Sets and Systems</span><span>, 2015</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206049"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206049"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206049; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=100206049]").text(description); $(".js-view-count[data-work-id=100206049]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 100206049; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='100206049']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=100206049]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":100206049,"title":"On tense MV-algebras","internal_url":"https://www.academia.edu/100206049/On_tense_MV_algebras","owner_id":241431338,"coauthors_can_edit":true,"owner":{"id":241431338,"first_name":"Jan","middle_initials":null,"last_name":"Paseka","page_name":"JPaseka","domain_name":"independent","created_at":"2022-10-20T23:38:14.667-07:00","display_name":"Jan Paseka","url":"https://independent.academia.edu/JPaseka"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206048"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206048/A_dynamic_Effect_Algebras_with_Dual_Operation"><img alt="Research paper thumbnail of A dynamic Effect Algebras with Dual Operation" class="work-thumbnail" src="https://attachments.academia-assets.com/101094939/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206048/A_dynamic_Effect_Algebras_with_Dual_Operation">A dynamic Effect Algebras with Dual Operation</a></div><div class="wp-workCard_item"><span>MATHEMATICS FOR APPLICATIONS</span><span>, 2012</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Tense operators for MV-algebras were introduced by Diaconescu and Georgescu. Based on their defin...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Tense operators for MV-algebras were introduced by Diaconescu and Georgescu. Based on their definition Chajda and Kolařík presented the definition of tense operators for lattice effect algebras. Chajda and Paseka tackled the problem of axiomatizing tense operators on an effect algebra by introducing the notion of a partial dynamic effect algebra. They also gave representation theorems for dynamic effect algebras. We continue to extend their work for partial S-dynamic effect algebras i.e. in the case when tense operators satisfy required conditions also for the dual effect algebraic operation •. We show that whenever tense operators are total our stronger notion coincides with their definition. We give also a representation theorem for partial S-dynamic effect algebras and its version for strict dynamic effect algebras.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="e6daf47988983a6a1a00118739d93715" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094939,"asset_id":100206048,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094939/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206048"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206048"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206048; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206047"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206047/Representations_of_zero_cancellative_pomonoids"><img alt="Research paper thumbnail of Representations of zero-cancellative pomonoids" class="work-thumbnail" src="https://attachments.academia-assets.com/101094936/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206047/Representations_of_zero_cancellative_pomonoids">Representations of zero-cancellative pomonoids</a></div><div class="wp-workCard_item"><span>Mathematica Slovaca</span><span>, 2014</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Several familiar results on representations of MV-algebras shape the idea that the use of solving...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Several familiar results on representations of MV-algebras shape the idea that the use of solving systems of linear equations can be studied also in the setting of zero-cancellative commutative pomonoids. This paper investigates this idea and shows that for the class of linearly representable zero-cancellative commutative pomonoids the respective results apply as well.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="a428cb8ad801521eb28853bca05347a0" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094936,"asset_id":100206047,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094936/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206047"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206047"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206047; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206046"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206046/Note_on_distributive_posets"><img alt="Research paper thumbnail of Note on distributive posets" class="work-thumbnail" src="https://attachments.academia-assets.com/101094887/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206046/Note_on_distributive_posets">Note on distributive posets</a></div><div class="wp-workCard_item"><span>MATHEMATICS FOR APPLICATIONS</span><span>, 2012</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this note we study distributive posets. We discuss several notions of distributivity in posets...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this note we study distributive posets. We discuss several notions of distributivity in posets and show their equivalence. Moreover, the Prime Ideal Theorem for Distributive Posets is shown to be equivalent with the famous Prime Ideal Theorem for Distributive Lattices using distributive ideal approach. n i=1 X i we put U(X 1 ,. .. , X n) = U(X) (L(X 1 ,. .. , X n) = L(X)). If, moreover, for some i, 1 ≤ i ≤ n, X i = {a i }, we substitute X i by a i as follows U(X</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="45a0c783acdd9ced5deae6e07cae84ba" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094887,"asset_id":100206046,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094887/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206046"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206046"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206046; 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We show that, in every modular Archimedean atomic lattice effect algebra E that is not an orthomodular lattice there exists an (o)continuous state ω on E, which is subadditive. Moreover, we show properties of finite and compact elements of such lattice effect algebras.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="5c49a2b3ef8452afd74a175ae9a9b91d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094932,"asset_id":100206044,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094932/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206044"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206044"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206044; 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We develop the notions of Rieffel induc...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we consider m-regular involutive quantales. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100206042"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100206042/On_Realization_of_Generalized_Effect_Algebras"><img alt="Research paper thumbnail of On Realization of Generalized Effect Algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/101094924/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100206042/On_Realization_of_Generalized_Effect_Algebras">On Realization of Generalized Effect Algebras</a></div><div class="wp-workCard_item"><span>Reports on Mathematical Physics</span><span>, 2012</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A well known fact is that there is a finite orthomodular lattice with an order determining set of...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">A well known fact is that there is a finite orthomodular lattice with an order determining set of states which is not representable in the standard quantum logic, the lattice L(H) of all closed subspaces of a separable complex Hilbert space. We show that a generalized effect algebra is representable in the operator generalized effect algebra G D (H) of effects of a complex Hilbert space H iff it has an order determining set of generalized states. This extends the corresponding results for effect algebras of Riečanová and Zajac. Further, any operator generalized effect algebra G D (H) possesses an order determining set of generalized states MSC: 03G12; 06D35; 06F25; 81P10</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="605e51e60ac48294dbc8373f4af92fbc" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101094924,"asset_id":100206042,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101094924/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100206042"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100206042"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100206042; 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