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DOI: 10.4230/LIPIcs.TIME.2023.9

A Sound and Complete Tableau System for Fuzzy Halpern and Shoham’s Interval Temporal Logic

Authors: Willem Conradie, Riccardo Monego, Emilio Muñoz-Velasco, Guido Sciavicco, and Ionel Eduard Stan

Published in: LIPIcs, Volume 278, 30th International Symposium on Temporal Representation and Reasoning (TIME 2023)

Abstract

Interval temporal logic plays a critical role in various applications, including planning, scheduling, and formal verification; recently, interval temporal logic has also been successfully applied to learning from temporal data. Halpern and Shoham’s interval temporal logic, in particular, stands out as a very intuitive, yet expressive, interval-based formalism. To address real-world scenarios involving uncertainty and imprecision, Halpern and Shoham’s logic has been recently generalized to the fuzzy (many-valued) case. The resulting language capitalizes on many-valued modal logics, allowing for a range of truth values that reflect multiple expert perspectives, but inherits the bad computational behaviour of its crisp counterpart. In this work, we investigate a sound and complete tableau system for fuzzy Halpern and Shoham’s logic, which, although possibly non-terminating, offers a semi-decision procedure for the finite case.

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Willem Conradie, Riccardo Monego, Emilio Muñoz-Velasco, Guido Sciavicco, and Ionel Eduard Stan. A Sound and Complete Tableau System for Fuzzy Halpern and Shoham’s Interval Temporal Logic. In 30th International Symposium on Temporal Representation and Reasoning (TIME 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 278, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{conradie_et_al:LIPIcs.TIME.2023.9,
  author =	{Conradie, Willem and Monego, Riccardo and Mu\~{n}oz-Velasco, Emilio and Sciavicco, Guido and Stan, Ionel Eduard},
  title =	{{A Sound and Complete Tableau System for Fuzzy Halpern and Shoham’s Interval Temporal Logic}},
  booktitle =	{30th International Symposium on Temporal Representation and Reasoning (TIME 2023)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-298-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{278},
  editor =	{Artikis, Alexander and Bruse, Florian and Hunsberger, Luke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2023.9},
  URN =		{urn:nbn:de:0030-drops-190996},
  doi =		{10.4230/LIPIcs.TIME.2023.9},
  annote =	{Keywords: Interval temporal logic, many-valued logic, tableau system}
}

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A Sound and Complete Tableau System for Fuzzy Halpern and Shoham’s Interval Temporal Logic

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