# From consequence to meaning: the case of intuitionistic propositional logic (IPL)

## Dag Westerståhl, Stockholm University, Tsinghua University

One quarter of the talk presents background on how facts about entailments and non-entailments can single out the constants in a language, and in particular on an idea originating with Carnap that the standard relation of logical consequence in a formal language should fix the (model-theoretic) meaning of its logical constants. Carnap’s focus was classical propositional logic (CPL), but his question can be asked for any logical language. The rest of the talk gives a very general positive answer to this question for IPL: the usual IPL consequence relation does indeed determine the standard intuitionistic meaning of the propositional connectives, according to most well-known semantics for IPL, such as Kripke semantics, Beth semantics, Dragalin semantics, topological semantics, and algebraic semantics.