Canonical Extensions and Kripke–Galois Semantics for Non-distributive Logics

This article presents an approach to the semantics of non-distributive propositional logics that is based on a lattice representation (and duality) theorem that delivers a canonical extension of the lattice. Our approach supports both a plain Kripke-style semantics and, by restriction, a general frame semantics. Unlike the framework of generalized Kripke frames (RS-frames), the semantic approach presented in this article is suitable for modeling applied logics (such as temporal, or dynamic), as it respects the intended interpretation of the logical operators. This is made possible by restricting admissible interpretations.

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