How game-theoretical semantics works: Classical first-order logic

Abstract

The structure of strategies for semantical games is studied by means of a new formalism developed for the purpose. Rigorous definitions of strategy, winning strategy, truth, and falsity are presented. Non-contradiction and bivalence are demonstrated for the truth-definition. The problem of the justification of deduction is examined from this perspective. The rules of a natural deduction system are justified: they are seen to guarantee existence of a winning strategy for the defender in the semantical game for the conclusion, given winning strategies for that player in the games for the premises. Finally, it is shown how semantical games and the truth-definition can be given for languages lacking individual constants. *** DIRECT SUPPORT *** AZ902009 00003