Tableaux approach for contact logics interpreted over intervals

• Autorzy: Özdemir Zafer

Identyfikatory

DOI

10.4467/20842589RM.23.001.18800

• Języki publikacji: EN

Abstrakty

EN

Contact logics are modal logic that is developed for reasoning about region-based theories of space. We develope a tableaux approach for contact logics interpreted over intervals (CLIOI) on the reals. For obtaining sound and complete tableaux-based decision procedures, the main technical tool is the semantic tableaux approach. We use intensively the following concepts: tableaux methods, termination of tableaux methods, saturated tableaux, termination theorem, soundness theorem, truth lemma, and completeness theorem.

Słowa kluczowe

EN

contact logics interpreted over intervals; tableaux approach; decision procedures

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2023
• Tom: Vol. 58
• Strony: 3--13
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Özdemir Zafer

• Industrial Engineering Department, Nişantaşı University, 34398, İstanbul, Turkey

Bibliografia

• 1] P. Balbiani, S. Kikot, Sahlqvist theorems for precontact logics, in: Advances in Modal Logic, Volume 9, College Publications 2012, pp. 55–70.
• [2] P. Balbiani, T. Tinchev, Definability and canonicity for Boolean logic with a binary relation, Fundamenta Informaticæ 129 (2014), 301–327.
• [3] P. Balbiani, T. Tinchev, D. Vakarelov, Modal logics for region-based theories of space, Fundamenta Informaticæ 81 (2007), 29–82.
• [4] P. Balbiani, T. Tinchev, D. Vakarelov, Dynamic logics of the region-based theory of discrete spaces, Journal of Applied Non-Classical Logics 17(1) (2007), 39–61.
• [5] P. Blackburn, M. de Rijke, Y. Venema, Modal Logic, Cambridge University Press 2001.
• [6] G. Dimov, D. Vakarelov, Contact algebras and region-based theory of space: a proximity approach — I, Fundamenta Informaticæ 74 (2006) 209–249.
• [7] I. Düntsch, M. Winter, A representation theorem for Boolean contact algebras, Theoretical Computer Science 347 (2005) 498–512.
• [8] M. Fitting, Tableau methods of proof for modal logics, Notre Dame Journal of Formal Logic 13 (1972) 237-247.
• [9] A. Galton, The mereotopology of discrete spaces, in Spatial Information Theory, Proceedings of the International Conference COSIT’99, Springer 1999, pp. 251–266.
• [10] A. Galton, Qualitative Spatial Change, Oxford University Press 2000.
• [11] R. Kontchakov, I. Pratt-Hartmann, F. Wolter, M. Zakharyaschev, Spatial logics with connectedness predicates, Logical Methods in Computer Science 6 (2010) 1–43.
• [12] D. Vakarelov, Region-based theory of space: algebras of regions, representation theory, and logics, in: Mathematical Problems from Applied Logic. Logics for the XXIst Century. II, Springer 2007, pp. 267–348.
• [13] J. Van Benthem, A note on modal formulas and relational properties, Journal of Symbolic Logic 40 (1975) 85–88.
• [14] F. Wolter, M. Zakharyaschev, Spatial representation and reasoning in RCC-8 with Boolean region terms, in: Proceedings of the 14th European Conference on Artificial Intelligence, IOS Press 2000, pp. 244–248.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).