Algebras of Information States

Abstract

In this article, a non-standard informational semantics for superintuitionistic modal logics is introduced and studied. It is based on algebraic structures that are interpreted as algebras of information states. The proposed semantics combines into one framework various features of standard relational and algebraic semantics. Especially, the connection to the algebraic semantics is explored in detail. The framework can be viewed as a generalization of inquisitive semantics that enables us to add inquisitive disjunction to any superintuitionistic modal propositional logic.