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

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

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Author Details

Guillermo Badia
  • School of Historical and Philosophical Inquiry, University of Queensland, Brisbane, Australia
Carles Noguera
  • Department of Information Engineering and Mathematics, University of Siena, Italy
Alberto Paparella
  • Department of Mathematics and Computer Science, University of Ferrara, Italy
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

This research has been partially funded by the Italian Ministry of University and Research through PNRR - M4C2 - Investimento 1.3 (Decreto Direttoriale MUR n. 341 del 15/03/2022), Partenariato Esteso PE00000013 - "FAIR - Future Artificial Intelligence Research" - Spoke 8 "Pervasive AI", funded by the European Union under the "NextGeneration EU programme". Moreover, this research has also been founded by the FIRD project Modal Geometric Symbolic Learning (University of Ferrara), and the Gruppo Nazionale Calcolo Scientifico-Istituto Nazionale di Alta Matematica (INDAM-GNCS) project Symbolic and Numerical Analysis of Cyberphysical Systems, CUP code E53C22001930001. Guido Sciavicco and Ionel Eduard Stan are GNCS-INdAM members; Carles Noguera is a GNSAGA-INdAM member.

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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) https://doi.org/10.4230/LIPIcs.TIME.2024.7

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.

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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