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DOI: 10.4230/LIPIcs.CSL.2017.14

A Decidable Intuitionistic Temporal Logic

Authors: Joseph Boudou, Martín Diéguez, and David Fernández-Duque

Published in: LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

Abstract

We introduce the logic ITL^e, an intuitionistic temporal logic based on structures (W,R,S), where R is used to interpret intuitionistic implication and S is an R-monotone function used to interpret temporal modalities. Our main result is that the satisfiability and validity problems for ITL^e are decidable. We prove this by showing that the logic enjoys the strong finite model property. In contrast, we also consider a 'persistent' version of the logic, ITL^p, whose models are similar to Cartesian products. We prove that, unlike ITL^e, ITL^p does not have the finite model property.

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Joseph Boudou, Martín Diéguez, and David Fernández-Duque. A Decidable Intuitionistic Temporal Logic. In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{boudou_et_al:LIPIcs.CSL.2017.14,
  author =	{Boudou, Joseph and Di\'{e}guez, Mart{\'\i}n and Fern\'{a}ndez-Duque, David},
  title =	{{A Decidable Intuitionistic Temporal Logic}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Goranko, Valentin and Dam, Mads},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.14},
  URN =		{urn:nbn:de:0030-drops-77016},
  doi =		{10.4230/LIPIcs.CSL.2017.14},
  annote =	{Keywords: intuitionistic logic, temporal logic, products of modal logics}
}

Document

DOI: 10.4230/LIPIcs.CSL.2017.15

Decidable Logics with Associative Binary Modalities

Authors: Joseph Boudou

Published in: LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

Abstract

A new family of modal logics with an associative binary modality, called counting logics is proposed. These propositional logics allow to express finite cardinalities of sets and more generally to count the number of subsets satisfying some properties. We show that these logics can be seen both as specializations of the Boolean logic of bunched implications and as generalizations of the propositional dependence logic. Moreover, whereas most logics with an associative binary modality are undecidable, we prove that some counting logics are decidable, in particular the basic counting logic bCL. We conjecture that this interesting result is due to the valuation constraints in counting logics' semantics and prove that the logic corresponding to bCL without these constraints is undecidable. Finally, we give lower and upper bounds for the complexity of bCL's validity problem.

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Joseph Boudou. Decidable Logics with Associative Binary Modalities. In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{boudou:LIPIcs.CSL.2017.15,
  author =	{Boudou, Joseph},
  title =	{{Decidable Logics with Associative Binary Modalities}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{15:1--15:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Goranko, Valentin and Dam, Mads},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.15},
  URN =		{urn:nbn:de:0030-drops-76863},
  doi =		{10.4230/LIPIcs.CSL.2017.15},
  annote =	{Keywords: modal logics, abstract separation logics, team semantics, resource logics, substructural logics}
}

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Documents authored by Boudou, Joseph

A Decidable Intuitionistic Temporal Logic

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Decidable Logics with Associative Binary Modalities

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