## Section: New Results

### Game semantics for proof search with multiplicative connectives

Participants : Olivier Delande, Dale Miller.

There appears to be a very close connection between focusing proof systems and certain kinds of game semantics for proof search. The team has been working on understanding a “neutral approach to proof and refutation”. In [47] , Miller and Saurin attempted to use game semantics to provide a “neutral” approach to proof and refutation. Their approach worked well for additive games (which are essentially Hintikka games). If the nature of multiplicatives were greatly restricted (to simple “guards”), then this game theoretic approach worked well again. It was unclear, however, how to extend that effort to handle general multiplicative connectives. This past year, Olivier Delande has been developing a solution to this problem that involves several innovations in the earlier notion of games. In particular, since games are no longer determinate (games might end in a draw), game playing must continue even after one player has failed (in order to find out if the other play wins or draws). A paper on this work is planned for the end of 2007.