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Documents authored by Méry, Daniel

Document
DOI: 10.4230/LIPIcs.FSCD.2023.31
Labelled Tableaux for Linear Time Bunched Implication Logic

Authors: Didier Galmiche and Daniel Méry

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
In this paper, we define the logic of Linear Temporal Bunched Implications (LTBI), a temporal extension of the Bunched Implications logic BI that deals with resource evolution over time, by combining the BI separation connectives and the LTL temporal connectives. We first present the syntax and semantics of LTBI and illustrate its expressiveness with a significant example. Then we introduce a tableau calculus with labels and constraints, called TLTBI, and prove its soundness w.r.t. the Kripke-style semantics of LTBI. Finally we discuss and analyze the issues that make the completeness of the calculus not trivial in the general case of unbounded timelines and explain how to solve the issues in the more restricted case of bounded timelines.
Cite as

Didier Galmiche and Daniel Méry. Labelled Tableaux for Linear Time Bunched Implication Logic. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{galmiche_et_al:LIPIcs.FSCD.2023.31,
  author =	{Galmiche, Didier and M\'{e}ry, Daniel},
  title =	{{Labelled Tableaux for Linear Time Bunched Implication Logic}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{31:1--31:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.31},
  URN =		{urn:nbn:de:0030-drops-180159},
  doi =		{10.4230/LIPIcs.FSCD.2023.31},
  annote =	{Keywords: Temporal Logic, Bunched Implication Logic, Labelled Deduction, Tableaux}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2021.13
Beth Semantics and Labelled Deduction for Intuitionistic Sentential Calculus with Identity

Authors: Didier Galmiche, Marta Gawek, and Daniel Méry

Published in: LIPIcs, Volume 195, 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)

Abstract
In this paper we consider the intuitionistic sentential calculus with Suszko’s identity (ISCI). After recalling the basic concepts of the logic and its associated Hilbert proof system, we introduce a new sound and complete class of models for ISCI which can be viewed as algebraic counterparts (and extensions) of sheaf-theoretic topological models of intuitionistic logic. We use this new class of models, called Beth semantics for ISCI, to derive a first labelled sequent calculus and show its adequacy w.r.t. the standard Hilbert axiomatization of ISCI. This labelled proof system, like all other current proof systems for ISCI that we know of, does not enjoy the subformula property, which is problematic for achieving termination. We therefore introduce a second labelled sequent calculus in which the standard rules for identity are replaced with new special rules and show that this second calculus admits cut-elimination. Finally, using a key regularity property of the forcing relation in Beth models, we show that the eigenvariable condition can be dropped, thus leading to the termination and decidability results.
Cite as

Didier Galmiche, Marta Gawek, and Daniel Méry. Beth Semantics and Labelled Deduction for Intuitionistic Sentential Calculus with Identity. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 13:1-13:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{galmiche_et_al:LIPIcs.FSCD.2021.13,
  author =	{Galmiche, Didier and Gawek, Marta and M\'{e}ry, Daniel},
  title =	{{Beth Semantics and Labelled Deduction for Intuitionistic Sentential Calculus with Identity}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{13:1--13:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2021.13},
  URN =		{urn:nbn:de:0030-drops-142516},
  doi =		{10.4230/LIPIcs.FSCD.2021.13},
  annote =	{Keywords: Algebraic Semantics, Beth Models, Labelled Deduction, Intuitionistic Logic}
}
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