Logic of Assertability (2015)
(Vít Punčochář, Institute of Philosophy / Academy of Sciences of the Czech Republic, CZ)

In my talk, I will start with a nonstandard semantics for classical propositional logic which has an epistemic interpretation. It is not based on a relation of truth but on a relation of assertibility. While truth is relative to possible worlds, assertibility is relative to information states which are standardly modeled as sets of possible worlds. The semantics has several interesting and unusual properties. In particular, the framework is akin to relational semantics in the sense that it is based on a recursively defined relation between the elements of a given structure (information states) on one side and formulas on the other side. This relation is analogous to the relation of truth of standard relational semantics. However, the semantics is also closely related to algebraic semantics since the structures in question (algebras of information states) are algebraic structures typically used in algebraic semantics. I will show that this epistemic semantics can be generalized into a framework suitable for any superintuitionistic and normal modal logic. As a result, we obtain an alternative semantic approach which combines various features of algebraic and relational semantics into a new powerful framework.

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