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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 , Ionel Eduard Stan

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Author Details

Willem Conradie
  • School of Mathematics, University of the Witwatersrand, Johannisburg, South Africa
Riccardo Monego
  • Department of Mathematics and Computer Science, University of Ferrara, Italy
Emilio Muñoz-Velasco
  • Department of Applied Mathematics, University of Málaga, Spain
Guido Sciavicco
  • Department of Mathematics and Computer Science, University of Ferrara, Italy
Ionel Eduard Stan
  • Faculty of Engineering, Free University of Bozen-Bolzano, Italy

Funding

We acknowledge the support of the INDAM-GNCS project Symbolic and Numerical Analysis of Cyberphysical Systems (code CUP_E53C22001930001), funded by INDAM, and of the FIRD project Symbolic Geometric Learning, funded by the University of Ferrara. Work is partially supported by the Spanish Project PID2022-140630NB-I00.

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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) https://doi.org/10.4230/LIPIcs.TIME.2023.9

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Theory and algorithms for application domains
Keywords
  • Interval temporal logic
  • many-valued logic
  • tableau system

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References

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