Towards a Dialogic Interpretation of Dynamic Proofs

The main result presented in this paper concerns a dialogic\index{dialogue} or game-theoretical interpretation of dynamic proofs. Dynamic proofs in themselves do not form a demonstration of the derivability of their last formula from a given premise set. Apart from the proof, such a demonstration requires a specific metalevel argument. In a natural and appealing form, the metalevel argument is phrased in terms of the existence of a winning strategy for the proponent. The aforementioned point is presented in terms of an approach that is in a sense Hilbertian and anti-Tarskian: the characterization of logical inference in terms of types of proofs, rather than in terms of properties of the consequence relation.