A general construction of many-valued modal logic. Given any finite linearly ordered set of truth values and any propositional connectives specified by truth tables, mv-K is the many-valued counterpart of the minimal normal modal logic K, presented as a Gentzen-like sequent calculus on labelled formulas where necessity is the infimum and possibility the supremum of accessible values. Necessity and possibility are treated as independent connectives rather than defined from each other; the system is sound and strongly complete over many-valued Kripke models with the finite model property, and many-valued intuitionistic logic embeds into one of its extensions.
A unified framework for many-valued modal logic. Starting from any finite linearly ordered set of truth values and any propositional connectives given by truth tables, the paper defines mv-K, the man…