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



PDF
Thumbnail PDF

File

LIPIcs.TIME.2024.7.pdf
  • Filesize: 0.77 MB
  • 16 pages

Document Identifiers

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

Cite AsGet BibTex

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

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. J. Allen. Maintaining knowledge about temporal intervals. Communications of the ACM, 26(11):832-843, 1983. URL: https://doi.org/10.1145/182.358434.
  2. M. Baaz, N. Preining, and R. Zach. First-order Gödel logics. Annals of Pure and Applied Logic, 147:23-47, 2007. URL: https://doi.org/10.1016/J.APAL.2007.03.001.
  3. U. Bodenhofer. Representations and constructions of similarity-based fuzzy orderings. Fuzzy Sets and Systems, 137(1):113-136, 2003. URL: https://doi.org/10.1016/S0165-0114(02)00436-0.
  4. G. E. Brancati, E. Vieta, J. M. Azorin, J. Angst, C. L. Bowden, S. Mosolov, A. H. Young, and G. Perugi. The role of overlapping excitatory symptoms in major depression: are they relevant for the diagnosis of mixed state? Journal of Psychiatric Research, 115:151-157, 2019. Google Scholar
  5. D. Bresolin, D. Della Monica, A. Montanari, and G. Sciavicco. A tableau system for right propositional neighborhood logic over finite linear orders: An implementation. In Proc. of the 22th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX), volume 8123 of LNCS, pages 74-80. Springer, 2013. URL: https://doi.org/10.1007/978-3-642-40537-2_8.
  6. A. Brunello, G. Sciavicco, and I. E. Stan. Interval temporal logic decision tree learning. In Proceedings of the 16th European Conference on Logics in Artificial Intelligence (JELIA), volume 11468 of LNCS, pages 778-793. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-19570-0_50.
  7. J. J. Buckley and Y. Hayashi. Fuzzy neural networks: A survey. Fuzzy Sets and Systems, 66:1-13, 1994. Google Scholar
  8. C. C. Chang. Algebraic analysis of many valued logics. Transactions of the American Mathematical society, 88(2):467-490, 1958. Google Scholar
  9. Y. Chen, T. Wang, B. Wang, and Z. Li. A survey of fuzzy decision tree classifier. Fuzzy Information and Engineering, 1(2):149-159, 2009. Google Scholar
  10. P. Cintula, P. Hájek, and C. Noguera, editors. Handbook of Mathematical Fuzzy Logic, volume 37-38 of Studies in Logic. Mathematical Logic and Foundation. College publications, 2011. Google Scholar
  11. W. Conradie, D. Della Monica, E. Muñoz-Velasco, and G. Sciavicco. An approach to fuzzy modal logic of time intervals. In Proc. of the 24th European Conference on Artificial Intelligence (ECAI), volume 325 of FAIA, pages 696-703. IOS Press, 2020. URL: https://doi.org/10.3233/FAIA200156.
  12. W. Conradie, D. Della Monica, E. Muñoz-Velasco, G. Sciavicco, and I. E. Stan. Fuzzy Halpern and Shoham’s interval temporal logics. Fuzzy Sets and Systems, 456:107-124, 2023. URL: https://doi.org/10.1016/J.FSS.2022.05.014.
  13. W. Conradie, R. Monego, E. Muñoz-Velasco, G. Sciavicco, and I. E. Stan. A sound and complete tableau system for fuzzy Halpern and Shoham’s interval temporal logic. In Proc. of the 30th International Symposium on Temporal Representation and Reasoning (TIME), volume 278 of LIPIcs, pages 9:1-9:14. Schloss Dagstuhl, 2023. URL: https://doi.org/10.4230/LIPICS.TIME.2023.9.
  14. S. Dutta. An event based fuzzy temporal logic. In Proc. of the 18th International Symposium on Multiple-Valued Logic, pages 64-71, 1988. Google Scholar
  15. L. Esakia, G. Bezhanishvili, W. H. Holliday, and A. Evseev. Heyting Algebras: Duality Theory. Springer, 2019. Google Scholar
  16. M. Fitting. Many-valued modal logics. Fundamenta Informaticae, 15(3-4):235-254, 1991. Google Scholar
  17. M. Fitting. Tableaus for many-valued modal logic. Studia Logica, 55(1):63-87, 1995. URL: https://doi.org/10.1007/BF01053032.
  18. A. Frigeri, L. Pasquale, and P. Spoletini. Fuzzy time in linear temporal logic. ACM Transactions on Computational Logic, 15:1-22, 2014. URL: https://doi.org/10.1145/2629606.
  19. V. Goranko, A. Montanari, P. Sala, and G. Sciavicco. A general tableau method for propositional interval temporal logics: Theory and implementation. Journal of Applied Logics, 4(3):305-330, 2006. URL: https://doi.org/10.1016/J.JAL.2005.06.012.
  20. V. Goranko, A. Montanari, and G. Sciavicco. Propositional interval neighborhood temporal logics. Journal of Universal Computer Science, 9(9):1137-1167, 2003. URL: https://doi.org/10.3217/JUCS-009-09-1137.
  21. V. Goranko, A. Montanari, and G. Sciavicco. A road map of interval temporal logics and duration calculi. Journal of Applied Non-Classical Logics, 14(1-2):9-54, 2004. URL: https://doi.org/10.3166/JANCL.14.9-54.
  22. P. Hájek. The Metamathematics of Fuzzy Logic. Kluwer, 1998. Google Scholar
  23. J. Y. Halpern and Y. Shoham. A Propositional Modal Logic of Time Intervals. Journal of the ACM, 38(4):935-962, 1991. URL: https://doi.org/10.1145/115234.115351.
  24. L. I. Kuncheva. Fuzzy Classifier Design, volume 49 of Studies in Fuzziness and Soft Computing. Springer, 2000. URL: https://doi.org/10.1007/978-3-7908-1850-5.
  25. S. Kundu. Similarity relations, fuzzy linear orders, and fuzzy partial orders. Fuzzy Sets and Systems, 109(3):419-428, 2000. URL: https://doi.org/10.1016/S0165-0114(97)00370-9.
  26. K. B. Lamine and F. Kabanza. Using fuzzy temporal logic for monitoring behavior-based mobile robots. In Proc. of the IASTED International Conference, Robotics and Applications, pages 116-121, 2000. Google Scholar
  27. F. Manzella, G. Pagliarini, A. Paparella, G. Sciavicco, and I. E. Stan. Sole.jl - Symbolic Learning in Julia. https://github.com/aclai-lab/Sole.jl, 2024.
  28. F. Manzella, G. Pagliarini, G. Sciavicco, and I. E. Stan. Interval Temporal Random Forests with an Application to COVID-19 Diagnosis. In Proceedings of the 28th International Symposium on Temporal Representation and Reasoning (TIME), volume 206 of LIPIcs, pages 7:1-7:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPICS.TIME.2021.7.
  29. E. Muñoz-Velasco, M. Pelegrín-Garcí, P. Sala, G. Sciavicco, and I. E. Stan. On coarser interval temporal logics. Artificial Intelligence, 266:1-26, 2019. URL: https://doi.org/10.1016/J.ARTINT.2018.09.001.
  30. S. Ovchinnikov. Similarity relations, fuzzy partitions, and fuzzy orderings. Fuzzy Sets and Systems, 40(1):107-126, 1991. Google Scholar
  31. A. Rose. Formalisations of further ℵ₀-valued Łukasiewicz propositional calculi. Journal of Symbolic Logic, 43(2):207-210, 1978. URL: https://doi.org/10.2307/2272818.
  32. G. Sciavicco and I. E. Stan. Knowledge extraction with interval temporal logic decision trees. In Proceedings of the 27th International Symposium on Temporal Representation and Reasoning (TIME), volume 178 of LIPIcs, pages 9:1-9:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPICS.TIME.2020.9.
  33. H. Thiele and S. Kalenka. On fuzzy temporal logic. In Proc. of the 2nd International Conference on Fuzzy Systems, pages 1027-1032. IEEE, 1993. Google Scholar
  34. L. A. Zadeh. Similarity relations and fuzzy orderings. Information Sciences, 3(2):177-200, 1971. URL: https://doi.org/10.1016/S0020-0255(71)80005-1.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail