Definability of Boolean Functions in Kripke Semantics

Abstract

A set $\mathcal{F}$ of Boolean functions is said to be functionally complete if every Boolean function is definable by combining functions in $\mathcal{F}$. Post clarified when a set of Boolean functions is functionally complete (with respect to classical semantics). In this paper, by extending Post’s theorem, we clarify when a set of Boolean functions is functionally complete with respect to Kripke semantics.