POLY−MODAL LOGIC S5nC

Pavel A. Alexeev; Mikhail I. Golovanov

doi:10.55937/sut/1262184422

January 1997 POLY−MODAL LOGIC

S{5_n}C

Pavel A. Alexeev, Mikhail I. Golovanov

Author Affiliations +

SUT J. Math. 33(1): 1-9 (January 1997). DOI: 10.55937/sut/1262184422

Abstract

We investigate a poly-modal logic $S{5_n}C$ which has $n$ -modalities $(n > 1)$ satisfying the axioms of $S5$ and has axioms expressing permutability of modalities. We show that the logic $S{5_n}C$ is complete concerning Kripke semantics, has the finite model property and is decidable, however we prove $S{5_n}C$ is not locally finite. A main result consists of an algorithmic criterion for recognizing the admissibility of inference rules in $S{5_n}C$ , i.e. the logic $S{5_n}C$ is decidable with respect to the admissibility.

Funding Statement

The investigation was supported by Grant Center of Novosibirsk State University, Krasnoyarsk Regional Fund of Science, RFFI grant 96-01-00228.

Citation

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Pavel A. Alexeev. Mikhail I. Golovanov. "POLY−MODAL LOGIC $S{5_n}C$ ." SUT J. Math. 33 (1) 1 - 9, January 1997. https://doi.org/10.55937/sut/1262184422