License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2023.31
URN: urn:nbn:de:0030-drops-180159
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18015/
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Galmiche, Didier ; Méry, Daniel

Labelled Tableaux for Linear Time Bunched Implication Logic

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LIPIcs-FSCD-2023-31.pdf (0.7 MB)

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.

BibTeX - Entry

@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/opus/volltexte/2023/18015},
  URN =		{urn:nbn:de:0030-drops-180159},
  doi =		{10.4230/LIPIcs.FSCD.2023.31},
  annote =	{Keywords: Temporal Logic, Bunched Implication Logic, Labelled Deduction, Tableaux}
}

Keywords: Temporal Logic, Bunched Implication Logic, Labelled Deduction, Tableaux
Collection: 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)
Issue Date: 2023
Date of publication: 28.06.2023

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