Modal Multilattice Logic

Logica Universalis 11 (3):317-343 (2017)

Abstract

A modal extension of multilattice logic, called modal multilattice logic, is introduced as a Gentzen-type sequent calculus \. Theorems for embedding \ into a Gentzen-type sequent calculus S4C and vice versa are proved. The cut-elimination theorem for \ is shown. A Kripke semantics for \ is introduced, and the completeness theorem with respect to this semantics is proved. Moreover, the duality principle is proved as a characteristic property of \.

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Author's Profile

Yaroslav Shramko
Kryvyi Rih State Pedagogical University, Ukraine

References found in this work

A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Constructible Falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.

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