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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 \.Author's Profile
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Citations of this work
On a multilattice analogue of a hypersequent S5 calculus.Oleg Grigoriev & Yaroslav Petrukhin - forthcoming - Logic and Logical Philosophy:1.
Modal and Intuitionistic Variants of Extended Belnap–Dunn Logic with Classical Negation.Norihiro Kamide - 2021 - Journal of Logic, Language and Information 30 (3):491-531.
Two proofs of the algebraic completeness theorem for multilattice logic.Oleg Grigoriev & Yaroslav Petrukhin - 2019 - Journal of Applied Non-Classical Logics 29 (4):358-381.
Modal extension of ideal paraconsistent four-valued logic and its subsystem.Norihiro Kamide & Yoni Zohar - 2020 - Annals of Pure and Applied Logic 171 (10):102830.
Falsification-Aware Calculi and Semantics for Normal Modal Logics Including S4 and S5.Norihiro Kamide - 2023 - Journal of Logic, Language and Information 32 (3):395-440.
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.
Intuitive semantics for first-degree entailments and 'coupled trees'.J. Michael Dunn - 1976 - Philosophical Studies 29 (3):149-168.
How a computer should think.Nuel Belnap - 1977 - In Gilbert Ryle (ed.), Contemporary aspects of philosophy. Boston: Oriel Press.
Some theorems about the sentential calculi of Lewis and Heyting.J. C. C. McKinsey & Alfred Tarski - 1948 - Journal of Symbolic Logic 13 (1):1-15.
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