Tableau-based translation from first-order logic to modal logic

• Autorzy: Perkov Tin , Mikec Luka

Identyfikatory

DOI

10.4467/20842589RM.21.006.14375

• Języki publikacji: EN

Abstrakty

EN

We define a procedure for translating a given first-order formula to an equivalent modal formula, if one exists, by using tableau-based bisimulation invariance test. A previously developed tableau procedure tests bisimulation invariance of a given first-order formula, and therefore tests whether that formula is equivalent to the standard translation of some modal formula. Using a closed tableau as the starting point, we show how an equivalent modal formula can be effectively obtained.

Słowa kluczowe

EN

modal logic; bisimulation invariance; tableaux

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2021
• Tom: Vol. 56
• Strony: 57--74
• Opis fizyczny: Bibliogr. 7 poz., rys.

Twórcy

autor

Perkov Tin

• Chair of Mathematics and Statistics, Faculty of Teacher Education, University of Zagreb, Savska c. 77, HR-10000 Zagreb, Croatia

autor

Mikec Luka

• Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička c. 30, HR-10000 Zagreb, Croatia

Bibliografia

• [1] J. van Benthem, Exploring Logical Dynamics, Studies in Logic, Language and Information, CSLI Publications & FoLLI, Stanford, 1996.
• [2] P. Blackburn, M. de Rijke, Y. Venema, Modal Logic, Cambridge University Press, 2001.
• [3] G. Boolos, Trees and Finite Satisfiability: Proof of a Conjecture of Burgess, Notre Dame Journal of Formal Logic 25 (1984), 193–197.
• [4] T. Bra¨uner, Hybrid Logic and its Proof-Theory, Springer, 2011.
• [5] J. Harrison, Handbook of Practical Logic and Automated Reasoning, Cambridge University Press, 2009.
• [6] T. Perkov, Tableau-based bisimulation invariance testing, Reports on Mathematical Logic 48 (2013), 101–115.
• [7] R. M. Smullyan, First-Order Logic, Springer-Verlag, 1968.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).