Dag Westerståhl: Logical constants and logical consequence

I will first briefly overview the problem of logical constants (what is it that makes a symbol logical?) and some approaches to it, in particular the invariance approach originating with Tarski. Then I present some recent joint work with Denis Bonnay on a new approach:
Given an interpreted language and a set of logical constants, Tarski's semantic definition of logical consequence yields a consequence relation. But given a consequence relation, is there a natural way to extract from it a set of logical constants? I compare two ways of doing so, one purely syntactical, based on the idea that an expression is logical if it is essential to the validity of at least one inference, and one semantical, based on the idea that an expression is logical if its interpretation is fully determined by the rules for its use. To describe these methods, Galois connections between consequence relations, sets of symbols, and sets of interpretations (all ordered under inclusion) play an important role.