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DOI: 10.4230/LIPIcs.TIME.2024.7

Fitting’s Style Many-Valued Interval Temporal Logic Tableau System: Theory and Implementation

Authors: Guillermo Badia, Carles Noguera, Alberto Paparella, Guido Sciavicco, and Ionel Eduard Stan

Published in: LIPIcs, Volume 318, 31st International Symposium on Temporal Representation and Reasoning (TIME 2024)

Abstract

Many-valued logics, often referred to as fuzzy logics, are a fundamental tool for reasoning about uncertainty, and are based on truth value algebras that generalize the Boolean one; the same logic can be interpreted on algebras from different varieties, for different purposes and pose different challenges. Although temporal many-valued logics, that is, the many-valued counterpart of popular temporal logics, have received little attention in the literature, the many-valued generalization of Halpern and Shoham’s interval temporal logic has been recently introduced and studied, and a sound and complete tableau system for it has been presented for the case in which it is interpreted on some finite Heyting algebra. In this paper, we take a step further in this inquiry by exploring a tableau system for Halpern and Shoham’s interval temporal logic interpreted on some finite {FL_{ew}}-algebra, therefore generalizing the Heyting case, and by providing its open-source implementation.

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Guillermo Badia, Carles Noguera, Alberto Paparella, Guido Sciavicco, and Ionel Eduard Stan. Fitting’s Style Many-Valued Interval Temporal Logic Tableau System: Theory and Implementation. In 31st International Symposium on Temporal Representation and Reasoning (TIME 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 318, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{badia_et_al:LIPIcs.TIME.2024.7,
  author =	{Badia, Guillermo and Noguera, Carles and Paparella, Alberto and Sciavicco, Guido and Stan, Ionel Eduard},
  title =	{{Fitting’s Style Many-Valued Interval Temporal Logic Tableau System: Theory and Implementation}},
  booktitle =	{31st International Symposium on Temporal Representation and Reasoning (TIME 2024)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-349-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{318},
  editor =	{Sala, Pietro and Sioutis, Michael and Wang, Fusheng},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2024.7},
  URN =		{urn:nbn:de:0030-drops-212145},
  doi =		{10.4230/LIPIcs.TIME.2024.7},
  annote =	{Keywords: Interval temporal logic, many-valued logic, tableau system}
}

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Fitting’s Style Many-Valued Interval Temporal Logic Tableau System: Theory and Implementation

Abstract

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