Document Zbl 07410428

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Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12650, 247-267 (2021). </div> <div class="abstract">Summary: The logic of Bunched Implications (BI) freely combines additive and multiplicative connectives, including implications; however, despite its well-studied proof theory, proof-search in BI has always been a difficult problem. The focusing principle is a restriction of the proof-search space that can capture various goal-directed proof-search procedures. In this paper we show that focused proof-search is complete for BI by first reformulating the traditional bunched sequent calculus using the simpler data-structure of nested sequents, following with a polarised and focused variant that we show is sound and complete via a cut-elimination argument. This establishes an operational semantics for focused proof-search in the logic of Bunched Implications.<br class="zbmathjax-paragraph">For the entire collection see [<a href="/1471.68019">Zbl 1471.68019</a>].</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7410428">Cited in <strong>4</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A68Nxx" title="MSC2020">68Nxx</a> </td> <td class="space"> Theory of software </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68Qxx" title="MSC2020">68Qxx</a> </td> <td class="space"> Theory of computing </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Alogic">logic</a>; <a href="/?q=ut%3Aproof-search">proof-search</a>; <a href="/?q=ut%3Afocusing">focusing</a>; <a href="/?q=ut%3Abunched+implications">bunched implications</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 07410428" data-ciurl="/ci/07410428" data-biburl="/bibtex/07410428.bib" data-amsurl="/amsrefs/07410428.bib" data-xmlurl="/xml/07410428.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07410428.pdf" title="Zbl 07410428 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/10.1007/978-3-030-71995-1_13" aria-label="DOI for “Focused proof-search in the logic of bunched implications”" title="10.1007/978-3-030-71995-1_13">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2010.08352"title="Note: arXiv document may differ from published version">arXiv</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">Andreoli, J.: Logic programming with focusing proofs in linear logic. 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