License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2016.16
URN: urn:nbn:de:0030-drops-59947
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5994/
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Chaudhuri, Kaustuv ; Marin, Sonia ; Straßburger, Lutz

Modular Focused Proof Systems for Intuitionistic Modal Logics

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LIPIcs-FSCD-2016-16.pdf (0.6 MB)

Abstract

Focusing is a general technique for syntactically compartmentalizing
the non-deterministic choices in a proof system, which not only
improves proof search but also has the representational benefit of
distilling sequent proofs into synthetic normal forms. However, since
focusing is usually specified as a restriction of the sequent
calculus, the technique has not been transferred to logics that lack a
(shallow) sequent presentation, as is the case for some of the logics
of the modal cube. We have recently extended the focusing technique
to classical nested sequents, a generalization of ordinary sequents.
In this work we further extend focusing to intuitionistic nested
sequents, which can capture all the logics of the intuitionistic S5
cube in a modular fashion. We present an internal cut-elimination
procedure for the focused system which in turn is used to show its
completeness.

BibTeX - Entry

@InProceedings{chaudhuri_et_al:LIPIcs:2016:5994,
  author =	{Kaustuv Chaudhuri and Sonia Marin and Lutz Stra{\ss}burger},
  title =	{{Modular Focused Proof Systems for Intuitionistic Modal Logics}},
  booktitle =	{1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-010-1},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{52},
  editor =	{Delia Kesner and Brigitte Pientka},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5994},
  URN =		{urn:nbn:de:0030-drops-59947},
  doi =		{10.4230/LIPIcs.FSCD.2016.16},
  annote =	{Keywords: intuitionistic modal logic, focusing, proof search, cut elimination, nested sequents}
}

Keywords: intuitionistic modal logic, focusing, proof search, cut elimination, nested sequents
Collection: 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)
Issue Date: 2016
Date of publication: 17.06.2016

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