FAQ
logo of Jagiellonian University in Krakow

A semantical analysis of cut-free calculi for modal logics

Publication date: 06.09.2018

Reports on Mathematical Logic, 2018, Number 53, pp. 43 - 65

https://doi.org/10.4467/20842589RM.18.003.8836

Authors

Mitio Takano
Professor Emeritus, Niigata University Niigata 950-2181, Japan
All publications →

Titles

A semantical analysis of cut-free calculi for modal logics

Abstract

We analyze semantically the logical inference rules in cut-free sequent calculi for the modal logics hich 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 nite model property of the logics also follows.

Received 9 June 2017

AMS subject classification: 03B45, 03F05

References

[1] R. Gor´e, 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.

Information

Information: Reports on Mathematical Logic, 2018, Number 53, pp. 43 - 65

Article type: Original article

Titles:

Polish:

A semantical analysis of cut-free calculi for modal logics

English:

A semantical analysis of cut-free calculi for modal logics

Authors

Professor Emeritus, Niigata University Niigata 950-2181, Japan

Published at: 06.09.2018

Article status: Open

Licence: CC BY-NC-ND  licence icon

Percentage share of authors:

Mitio Takano (Author) - 100%

Article corrections:

-

Publication languages:

English

View count: 1760

Number of downloads: 1269

<p> A semantical analysis of cut-free calculi for modal logics</p>