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Documents authored by Diéguez, Martín

Document
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.
Cite as

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-dev.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.ICLP.2012.290
Paving the Way for Temporal Grounding

Authors: Felicidad Aguado, Pedro Cabalar, Martín Diéguez, Gilberto Pérez, and Concepción Vidal

Published in: LIPIcs, Volume 17, Technical Communications of the 28th International Conference on Logic Programming (ICLP'12) (2012)

Abstract
In this paper we consider the problem of introducing variables in temporal logic programs under the formalism of Temporal Equilibrium Logic (TEL), an extension of Answer Set Programming (ASP) for dealing with linear-time modal operators. We provide several fundamental contributions that pave the way for the implementation of a grounding process, that is, a method that allows replacing variables by ground instances in all the possible (or better, relevant) ways.
Cite as

Felicidad Aguado, Pedro Cabalar, Martín Diéguez, Gilberto Pérez, and Concepción Vidal. Paving the Way for Temporal Grounding. In Technical Communications of the 28th International Conference on Logic Programming (ICLP'12). Leibniz International Proceedings in Informatics (LIPIcs), Volume 17, pp. 290-300, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{aguado_et_al:LIPIcs.ICLP.2012.290,
  author =	{Aguado, Felicidad and Cabalar, Pedro and Di\'{e}guez, Mart{\'\i}n and P\'{e}rez, Gilberto and Vidal, Concepci\'{o}n},
  title =	{{Paving the Way for Temporal Grounding}},
  booktitle =	{Technical Communications of the 28th International Conference on Logic Programming (ICLP'12)},
  pages =	{290--300},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-43-9},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{17},
  editor =	{Dovier, Agostino and Santos Costa, V{\'\i}tor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICLP.2012.290},
  URN =		{urn:nbn:de:0030-drops-36301},
  doi =		{10.4230/LIPIcs.ICLP.2012.290},
  annote =	{Keywords: ASP, linear temporal logic, grounding, temporal equilibrium logic}
}
Document
DOI: 10.4230/LIPIcs.ICLP.2012.445
Temporal Answer Set Programming

Authors: Martín Diéguez

Published in: LIPIcs, Volume 17, Technical Communications of the 28th International Conference on Logic Programming (ICLP'12) (2012)

Abstract
Answer Set Programming (ASP) has become a popular way for representing different kinds of scenarios from knowledge representation in Artificial Intelligence. Frequently, these scenarios involve a temporal component which must be considered. In ASP, time is usually represented as a variable whose values are defined by an extensional predicate with a finite domain. Dealing with a finite temporal interval has some disadvantages. First, checking the existence of a plan is not possible and second, it also makes difficult to decide whether two programs are strongly equivalent. If we extend the syntax of Answer Set Programming by using temporal operators from temporal modal logics, then infinite time can be considered, so the aforementioned disadvantages can be overcome. This extension constitutes, in fact, a formalism called Temporal Equilibrium Logic, which is based on Equilibrium Logic (a logical characterisation of ASP). Although recent contributions have shown promising results, Temporal Equilibrium Logic is still a novel paradigm and there are many gaps to fill. Our goal is to keep developing this paradigm, filling those gaps and turning it into a suitable framework for temporal reasoning.
Cite as

Martín Diéguez. Temporal Answer Set Programming. In Technical Communications of the 28th International Conference on Logic Programming (ICLP'12). Leibniz International Proceedings in Informatics (LIPIcs), Volume 17, pp. 445-450, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{dieguez:LIPIcs.ICLP.2012.445,
  author =	{Di\'{e}guez, Mart{\'\i}n},
  title =	{{Temporal Answer Set Programming}},
  booktitle =	{Technical Communications of the 28th International Conference on Logic Programming (ICLP'12)},
  pages =	{445--450},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-43-9},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{17},
  editor =	{Dovier, Agostino and Santos Costa, V{\'\i}tor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICLP.2012.445},
  URN =		{urn:nbn:de:0030-drops-36444},
  doi =		{10.4230/LIPIcs.ICLP.2012.445},
  annote =	{Keywords: Answer Set Programming, Temporal Equilibrium Logic, Linear Temporal Logic}
}
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