Document Zbl 07628203

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Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 13385, 449-467 (2022). </div> <div class="abstract">Summary: Adding multi-modalities (called <span class="zbmathjax-textit">subexponentials</span>) to linear logic enhances its power as a logical framework, which has been extensively used in the specification of <span class="zbmathjax-textit">e.g.</span> proof systems, programming languages and bigraphs. Initially, subexponentials allowed for classical, linear, affine or relevant behaviors. Recently, this framework was enhanced so to allow for commutativity as well. In this work, we close the cycle by considering associativity. We show that the resulting system $( \mathsf{acLL}_\varSigma )$ admits the (multi)cut rule, and we prove two undecidability results for fragments/variations of $\mathsf{acLL}_\varSigma $.<br class="zbmathjax-paragraph">For the entire collection see [<a href="/1499.68012">Zbl 1499.68012</a>].</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A7628203">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A7628203">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A68V15" title="MSC2020">68V15</a> </td> <td class="space"> Theorem proving (automated and interactive theorem provers, deduction, resolution, etc.) </td> </tr></table> </div> <div class="software"> <h3>Software:</h3><a href="/software/29641">CatLog3</a>; <a href="/software/24229">Grail</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 07628203" data-ciurl="/ci/07628203" data-biburl="/bibtex/07628203.bib" data-amsurl="/amsrefs/07628203.bib" data-xmlurl="/xml/07628203.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07628203.pdf" title="Zbl 07628203 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/978-3-031-10769-6_27" aria-label="DOI for “Non-associative, non-commutative multi-modal linear logic”" title="10.1007/978-3-031-10769-6_27">DOI</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Aarts, E.; Trautwein, K., Non-associative Lambek categorial grammar in polynomial time, Math. Log. Q., 41, 4, 476-484 (1995) · <a href="/0837.03033" class="nowrap">Zbl 0837.03033</a> · <a href="https://doi.org/10.1002/malq.19950410405" class="nowrap">doi:10.1002/malq.19950410405</a></td> </tr><tr> <td>[2]</td> <td class="space">Abrusci, V.M.: A comparison between Lambek syntactic calculus and intuitionistic linear logic. Zeitschr. Math. Logik Grundl. Math. (Math. Logic Q.) 36, 11-15 (1990) · <a href="/0719.03005" class="nowrap">Zbl 0719.03005</a></td> </tr><tr> <td>[3]</td> <td class="space">Ajdukiewicz, K., Die syntaktische Konnexität, Studia Philosophica, 1, 1-27 (1935) · <a href="/62.1050.03" class="nowrap">JFM 62.1050.03</a></td> </tr><tr> <td>[4]</td> <td class="space">Bar-Hillel, Y., A quasi-arithmetical notation for syntactic description, Language, 29, 47-58 (1953) · <a href="/0156.25402" class="nowrap">Zbl 0156.25402</a> · <a href="https://doi.org/10.2307/410452" class="nowrap">doi:10.2307/410452</a></td> </tr><tr> <td>[5]</td> <td class="space">Belnap, N., Display logic, J. Philos. Log., 11, 4, 375-417 (1982) · <a href="/0509.03008" class="nowrap">Zbl 0509.03008</a> · <a href="https://doi.org/10.1007/BF00284976" class="nowrap">doi:10.1007/BF00284976</a></td> </tr><tr> <td>[6]</td> <td class="space">Bulinska, M., On the complexity of nonassociative Lambek calculus with unit, Stud. Logica, 93, 1, 1-14 (2009) · <a href="/1182.03041" class="nowrap">Zbl 1182.03041</a> · <a href="https://doi.org/10.1007/s11225-009-9205-2" class="nowrap">doi:10.1007/s11225-009-9205-2</a></td> </tr><tr> <td>[7]</td> <td class="space">Buszkowski, W.: Lambek calculus with nonlogical axioms. In: Language and Grammar, Studies in Mathematical Linguistics and Natural Language, pp. 77-93. CSLI Publications (2005) · <a href="/1137.03300" class="nowrap">Zbl 1137.03300</a></td> </tr><tr> <td>[8]</td> <td class="space">Buszkowski, W.; Farulewski, M.; Grumberg, O.; Kaminski, M.; Katz, S.; Wintner, S., Nonassociative Lambek calculus with additives and context-free languages, Languages: From Formal to Natural, 45-58 (2009), Heidelberg: Springer, Heidelberg · <a href="/1239.03016" class="nowrap">Zbl 1239.03016</a> · <a href="https://doi.org/10.1007/978-3-642-01748-3_4" class="nowrap">doi:10.1007/978-3-642-01748-3_4</a></td> </tr><tr> <td>[9]</td> <td class="space">Chaudhuri, K.: Undecidability of multiplicative subexponential logic. In: Alves, S., Cervesato, I. (eds.) Proceedings Third International Workshop on Linearity, LINEARITY 2014, Vienna, Austria, 13th July 2014. EPTCS, vol. 176, pp. 1-8 (2014). doi:10.4204/EPTCS.176.1 · <a href="/1486.03103" class="nowrap">Zbl 1486.03103</a></td> </tr><tr> <td>[10]</td> <td class="space">Chaudhuri, K., Marin, S., Straßburger, L.: Modular focused proof systems for intuitionistic modal logics. In: FSCD, pp. 16:1-16:18 (2016) · <a href="/1387.03016" class="nowrap">Zbl 1387.03016</a></td> </tr><tr> <td>[11]</td> <td class="space">Chvalovský, K., Undecidability of consequence relation in full non-associative Lambek calculus, J. Symb. Logic, 80, 2, 567-586 (2015) · <a href="/1373.03025" class="nowrap">Zbl 1373.03025</a> · <a href="https://doi.org/10.1017/jsl.2014.39" class="nowrap">doi:10.1017/jsl.2014.39</a></td> </tr><tr> <td>[12]</td> <td class="space">Clouston, R., Dawson, J., Goré, R., Tiu, A.: Annotation-free sequent calculi for full intuitionistic linear logic. In: Rocca, S.R.D. (ed.) Computer Science Logic 2013 (CSL 2013), CSL 2013, Torino, Italy, 2-5 September 2013. LIPIcs, vol. 23, pp. 197-214. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013). doi:10.4230/LIPIcs.CSL.2013.197 · <a href="/1356.03103" class="nowrap">Zbl 1356.03103</a></td> </tr><tr> <td>[13]</td> <td class="space">Danos, V.; Joinet, J-B; Schellinx, H.; Gottlob, G.; Leitsch, A.; Mundici, D., The structure of exponentials: uncovering the dynamics of linear logic proofs, Computational Logic and Proof Theory, 159-171 (1993), Heidelberg: Springer, Heidelberg · <a href="/0793.03061" class="nowrap">Zbl 0793.03061</a> · <a href="https://doi.org/10.1007/BFb0022564" class="nowrap">doi:10.1007/BFb0022564</a></td> </tr><tr> <td>[14]</td> <td class="space">de Groote, P.; Lamarche, F., Classical non-associative Lambek calculus, Stud. Logica, 71, 3, 355-388 (2002) · <a href="/1032.03014" class="nowrap">Zbl 1032.03014</a> · <a href="https://doi.org/10.1023/A:1020520915016" class="nowrap">doi:10.1023/A:1020520915016</a></td> </tr><tr> <td>[15]</td> <td class="space">Gheorghiu, A.; Marin, S., Focused proof-search in the logic of bunched implications, Foundations of Software Science and Computation Structures, 247-267 (2021), Cham: Springer, Cham · <a href="/07410428" class="nowrap">Zbl 07410428</a> · <a href="https://doi.org/10.1007/978-3-030-71995-1_13" class="nowrap">doi:10.1007/978-3-030-71995-1_13</a></td> </tr><tr> <td>[16]</td> <td class="space">Girard, J.-Y.: Linear logic. Theor. Comput. Sci. 50, 1-102 (1987). doi:10.1016/0304-3975(87)90045-4 · <a href="/0625.03037" class="nowrap">Zbl 0625.03037</a></td> </tr><tr> <td>[17]</td> <td class="space">Guglielmi, A.; Straßburger, L.; Fribourg, L., Non-commutativity and MELL in the calculus of structures, Computer Science Logic, 54-68 (2001), Heidelberg: Springer, Heidelberg · <a href="/0999.03054" class="nowrap">Zbl 0999.03054</a> · <a href="https://doi.org/10.1007/3-540-44802-0_5" class="nowrap">doi:10.1007/3-540-44802-0_5</a></td> </tr><tr> <td>[18]</td> <td class="space">Hepple, M.: A general framework for hybrid substructural categorial logics. Technical report 94-14, IRCS (1994)</td> </tr><tr> <td>[19]</td> <td class="space">Kanazawa, M., On the recognizing power of the Lambek calculus with brackets, J. Logic Lang. Inform., 27, 4, 295-312 (2018) · <a href="/1427.03040" class="nowrap">Zbl 1427.03040</a> · <a href="https://doi.org/10.1007/s10849-018-9269-3" class="nowrap">doi:10.1007/s10849-018-9269-3</a></td> </tr><tr> <td>[20]</td> <td class="space">Kanovich, M.; Kuznetsov, S.; Nigam, V.; Scedrov, A.; Galmiche, D.; Schulz, S.; Sebastiani, R., A logical framework with commutative and non-commutative subexponentials, Automated Reasoning, 228-245 (2018), Cham: Springer, Cham · <a href="/1508.03092" class="nowrap">Zbl 1508.03092</a> · <a href="https://doi.org/10.1007/978-3-319-94205-6_16" class="nowrap">doi:10.1007/978-3-319-94205-6_16</a></td> </tr><tr> <td>[21]</td> <td class="space">Kanovich, M.; Kuznetsov, S.; Nigam, V.; Scedrov, A., Subexponentials in non-commutative linear logic, Math. Struct. Comput. Sci., 29, 8, 1217-1249 (2019) · <a href="/1456.03099" class="nowrap">Zbl 1456.03099</a> · <a href="https://doi.org/10.1017/S0960129518000117" class="nowrap">doi:10.1017/S0960129518000117</a></td> </tr><tr> <td>[22]</td> <td class="space">Kanovich, M.; Kuznetsov, S.; Scedrov, A.; Foret, A.; Morrill, G.; Muskens, R.; Osswald, R.; Pogodalla, S., Undecidability of the Lambek calculus with a relevant modality, Formal Grammar, 240-256 (2016), Heidelberg: Springer, Heidelberg · <a href="/1478.03043" class="nowrap">Zbl 1478.03043</a> · <a href="https://doi.org/10.1007/978-3-662-53042-9_14" class="nowrap">doi:10.1007/978-3-662-53042-9_14</a></td> </tr><tr> <td>[23]</td> <td class="space">Kanovich, M.; Kuznetsov, S.; Scedrov, A., The multiplicative-additive Lambek calculus with subexponential and bracket modalities, J. Log. Lang. Inform., 30, 31-88 (2021) · <a href="/1496.03087" class="nowrap">Zbl 1496.03087</a> · <a href="https://doi.org/10.1007/s10849-020-09320-9" class="nowrap">doi:10.1007/s10849-020-09320-9</a></td> </tr><tr> <td>[24]</td> <td class="space">Kopylov, A., Decidability of linear affine logic, Inf. Comput., 164, 1, 173-198 (2001) · <a href="/1007.03053" class="nowrap">Zbl 1007.03053</a> · <a href="https://doi.org/10.1006/inco.1999.2834" class="nowrap">doi:10.1006/inco.1999.2834</a></td> </tr><tr> <td>[25]</td> <td class="space">Kozak, M., Cyclic involutive distributive full Lambek calculus is decidable, J. Log. Comput., 21, 2, 231-252 (2011) · <a href="/1225.03022" class="nowrap">Zbl 1225.03022</a> · <a href="https://doi.org/10.1093/logcom/exq021" class="nowrap">doi:10.1093/logcom/exq021</a></td> </tr><tr> <td>[26]</td> <td class="space">Kurtonina, N.: Frames and labels. A modal analysis of categorial inference. Ph.D. thesis, Universiteit Utrecht, ILLC (1995) · <a href="/0826.03004" class="nowrap">Zbl 0826.03004</a></td> </tr><tr> <td>[27]</td> <td class="space">Kurtonina, N., Moortgat, M.: Structural control. In: Blackburn, P., de Rijke, M. (eds.) Specifying Syntactic Structures, CSLI, Stanford, pp. 75-113 (1997)</td> </tr><tr> <td>[28]</td> <td class="space">Lamarche, F.: On the Algebra of Structural Contexts. Mathematical Structures in Computer Science, p. 51 (2003). Article dans revue scientifique avec comité de lecture. https://hal.inria.fr/inria-00099461</td> </tr><tr> <td>[29]</td> <td class="space">Lambek, J., The mathematics of sentence structure, Am. Math. Monthly, 65, 3, 154-170 (1958) · <a href="/0080.00702" class="nowrap">Zbl 0080.00702</a> · <a href="https://doi.org/10.1080/00029890.1958.11989160" class="nowrap">doi:10.1080/00029890.1958.11989160</a></td> </tr><tr> <td>[30]</td> <td class="space">Lambek, J.: On the calculus of syntactic types. In: Jakobson, R. (ed.) Structure of Language and Its Mathematical Aspects, pp. 166-178. American Mathematical Society (1961)</td> </tr><tr> <td>[31]</td> <td class="space">Lellmann, B., Olarte, C., Pimentel, E.: A uniform framework for substructural logics with modalities. In: LPAR-21, pp. 435-455 (2017) · <a href="/1402.03030" class="nowrap">Zbl 1402.03030</a></td> </tr><tr> <td>[32]</td> <td class="space">Lincoln, P.; Mitchell, J.; Scedrov, A.; Shankar, N., Decision problems for propositional linear logic, Ann. Pure Appl. Logic, 56, 1-3, 239-311 (1992) · <a href="/0768.03003" class="nowrap">Zbl 0768.03003</a> · <a href="https://doi.org/10.1016/0168-0072(92)90075-B" class="nowrap">doi:10.1016/0168-0072(92)90075-B</a></td> </tr><tr> <td>[33]</td> <td class="space">Moortgat, M., Multimodal linguistic inference, Log. J. IGPL, 3, 2-3, 371-401 (1995) · <a href="/0840.03022" class="nowrap">Zbl 0840.03022</a> · <a href="https://doi.org/10.1093/jigpal/3.2-3.371" class="nowrap">doi:10.1093/jigpal/3.2-3.371</a></td> </tr><tr> <td>[34]</td> <td class="space">Moortgat, M., Multimodal linguistic inference, J. Logic Lang. Inform., 5, 3-4, 349-385 (1996) · <a href="/0919.03023" class="nowrap">Zbl 0919.03023</a> · <a href="https://doi.org/10.1007/BF00159344" class="nowrap">doi:10.1007/BF00159344</a></td> </tr><tr> <td>[35]</td> <td class="space">Moortgat, M., Morrill, G.: Heads and phrases: type calculus for dependency and constituent structure. Technical report (1991)</td> </tr><tr> <td>[36]</td> <td class="space">Moortgat, M., Oehrle, R.: Logical parameters and linguistic variation. In: Fifth European Summer School in Logic, Language and Information. Lecture Notes on Categorial Grammar (1993)</td> </tr><tr> <td>[37]</td> <td class="space">Moot, R.: The grail theorem prover: type theory for syntax and semantics. CoRR, abs/1602.00812 (2016). arXiv:1602.00812</td> </tr><tr> <td>[38]</td> <td class="space">Moot, R.; Retoré, C., The Logic of Categorial Grammars (2012), Heidelberg: Springer, Heidelberg · <a href="/1261.03001" class="nowrap">Zbl 1261.03001</a> · <a href="https://doi.org/10.1007/978-3-642-31555-8" class="nowrap">doi:10.1007/978-3-642-31555-8</a></td> </tr><tr> <td>[39]</td> <td class="space">Morrill, G.: Categorial formalisation of relativisation: Pied piping, islands, and extraction sites. Technical report LSI-92-23-R, Universitat Politècnica de Catalunya (1992)</td> </tr><tr> <td>[40]</td> <td class="space">Morrill, G., Parsing/theorem-proving for logical grammar CatLog3, J. Log. Lang. Inf., 28, 2, 183-216 (2019) · <a href="/1478.68416" class="nowrap">Zbl 1478.68416</a> · <a href="https://doi.org/10.1007/s10849-018-09277-w" class="nowrap">doi:10.1007/s10849-018-09277-w</a></td> </tr><tr> <td>[41]</td> <td class="space">Morrill, G., Leslie, N., Hepple, M., Barry, G.: Categorial deductions and structural operations. In: Studies in Categorial Grammar, Edinburgh Working Paper in Cognitive Science, vol. 5, pp. 1-21 (1990)</td> </tr><tr> <td>[42]</td> <td class="space">Nigam, V.; Miller, D., A framework for proof systems, J. Autom. Reason., 45, 2, 157-188 (2010) · <a href="/1242.03057" class="nowrap">Zbl 1242.03057</a> · <a href="https://doi.org/10.1007/s10817-010-9182-1" class="nowrap">doi:10.1007/s10817-010-9182-1</a></td> </tr><tr> <td>[43]</td> <td class="space">Nigam, V.; Olarte, C.; Pimentel, E., On subexponentials, focusing and modalities in concurrent systems, Theor. Comput. Sci., 693, 35-58 (2017) · <a href="/1373.68298" class="nowrap">Zbl 1373.68298</a> · <a href="https://doi.org/10.1016/j.tcs.2017.06.009" class="nowrap">doi:10.1016/j.tcs.2017.06.009</a></td> </tr><tr> <td>[44]</td> <td class="space">Nigam, V.; Pimentel, E.; Reis, G., An extended framework for specifying and reasoning about proof systems, J. Log. Comput., 26, 2, 539-576 (2016) · <a href="/1403.03125" class="nowrap">Zbl 1403.03125</a> · <a href="https://doi.org/10.1093/logcom/exu029" class="nowrap">doi:10.1093/logcom/exu029</a></td> </tr><tr> <td>[45]</td> <td class="space">Oehrle, R., Zhang, S.: Lambek calculus and preposing of embedded subjects. Coyote Papers (1989). http://hdl.handle.net/10150/226572</td> </tr><tr> <td>[46]</td> <td class="space">Olarte, C.; Chiarugi, D.; Falaschi, M.; Hermith, D., A proof theoretic view of spatial and temporal dependencies in biochemical systems, Theor. Comput. Sci., 641, 25-42 (2016) · <a href="/1344.68140" class="nowrap">Zbl 1344.68140</a> · <a href="https://doi.org/10.1016/j.tcs.2016.03.029" class="nowrap">doi:10.1016/j.tcs.2016.03.029</a></td> </tr><tr> <td>[47]</td> <td class="space">Pentus, M., Lambek calculus is NP-complete, Theor. Comput. Sci., 357, 186-201 (2006) · <a href="/1104.03013" class="nowrap">Zbl 1104.03013</a> · <a href="https://doi.org/10.1016/j.tcs.2006.03.018" class="nowrap">doi:10.1016/j.tcs.2006.03.018</a></td> </tr><tr> <td>[48]</td> <td class="space">Pruiksma, K., Chargin, W., Pfenning, F., Reed, J.: Adjoint logic (2018, Unpublished manuscript)</td> </tr><tr> <td>[49]</td> <td class="space">Shieber, S., Evidence against the context-freeness of natural languages, Linguist. Philos., 8, 333-343 (1985) · <a href="https://doi.org/10.1007/BF00630917" class="nowrap">doi:10.1007/BF00630917</a></td> </tr><tr> <td>[50]</td> <td class="space">Straßburger, L., On the decision problem for MELL, Theor. Comput. Sci., 768, 91-98 (2019) · <a href="/1454.03084" class="nowrap">Zbl 1454.03084</a> · <a href="https://doi.org/10.1016/j.tcs.2019.02.022" class="nowrap">doi:10.1016/j.tcs.2019.02.022</a></td> </tr><tr> <td>[51]</td> <td class="space">Tanaka, H.: A note on undecidability of propositional non-associative linear logics (2019). arXiv preprint arXiv:1909.13444</td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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