Algebras of Information States V´ ıt Punˇ coch´ aˇ r Abstract In this paper, a novel informational semantics for superintuitionistic modal logics is introduced and studied. It is based on algebraic struc- tures that are interpreted as algebras of information states. The pro- posed semantics combines into one framework various features of stan- dard 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 proposi- tional logic. Key words: Information states, relational semantics, algebraic se- mantics, intuitionistic logic, inquisitive disjunction 1 Introduction In formal semantics of logical systems, one can identify two basic approaches, one of which might be called ontic or truth-conditional and the other epis- temic or informational. In an ontic semantics, the basic semantic concept is the concept of truth, which is modelled as a relation between sentences and complete states of affairs (possible worlds). In contrast, the informational approach is based on a relation between sentences and information states. The most basic example of the truth-conditional approach is the standard semantics of classical logic. An informational semantics was provided, for example, for intuitionistic logic (Kripke, 1965), for relevant logics (Urquhart, 1972), and for substructural subsystems of Nelson logics (Wansing, 1993). In this paper, we will propose an informational semantics for intuition- istic logic and its extensions which, however, differs significantly from the standard Kripke semantics. The main difference is in the behaviour of dis- junction. In our framework, it is possible that a disjunction holds in a state a even if none of the disjuncts holds in a. A similar framework was intro- duced in (Punˇ coch´ aˇ r, 2014, 2015). In the present paper, we will work with more general structures and the semantics will be studied from a different perspective. In (Punˇ coch´ aˇ r, 2015), the relation to Kripke semantics was explored. In the present paper, we will focus especially on the connections to algebraic semantics. It will turn out that, even though the semantics is relational, its connection to algebraic semantics is very strong. 1