A semantical analysis of cut-free calculi for modal logics

• Autorzy: Takano M.

Identyfikatory

DOI

10.4467/20842589RM.18.003.8836

• Języki publikacji: EN

Abstrakty

EN

We analyze semantically the logical inference rules in cut-free sequent calculi for the modal logics which are obtained from the least normal logic K by adding axioms from T, 4, 5, D and B. This implies Kripke completeness, as well as the cutelimination property or the subformula property of the calculi. By slightly modifying the arguments, the finite model property of the logics also follows.

Słowa kluczowe

EN

sequent calculus; Kripke completeness; finite model property; cut-elimination; subformula property

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2018
• Tom: Vol. 53
• Strony: 43--65
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Takano M.

• Niigata University Niigata 950-2181, Japan

Bibliografia

• [1] R. Gore, Tableau methods for modal and temporal logics, In: Handbook of Tableau Methods (eds. M. D’Agostino, D.M. Gabbay, R. H¨ahnle and J. Posegga), Kluwer,Dordrecht, 1999, pp. 297–396.
• [2] S. Maehara, A general theory of completeness proofs, Annals of the Japan Association for Philosophy of Science 3:5 (1970), 242–256.
• [3] G.F. Shvarts, Gentzen style systems for K45 and K45D, In: Logic at Botik ’89 (eds. A.R. Meyer and M.A. Taitslin), Lecture Notes in Computer Science 363, Springer, Berlin, 1989, pp. 245–256.
• [4] M. Takano, Subformula property as a substitute for cut-elimination in modal propositional logics, Mathematica Japonica 37 (1992), 1129–1145.
• [5] M. Takano, A modified subformula property for the modal logics K5 and K5D, Bulletin of the Section of Logic 30 (2001), 115–122.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).