Editors' Introduction

Abstract

The idea of interpreting quantifiers in terms of a game between two players was first suggested at the end of the 19th century by one of the inventors of quantification theory, C. S. Peirce, but it laid buried in his papers until it was discovered in the 1980s. His idea was independently discovered in the 1950s, when Leon Henkin suggested a game semantics for infinitary languages. Paul Lorenzen introduced his Dialogspiele at the same time, while his student Kuno Lorenz introduced the vocabulary of game theory that led to our modern conception of game semantics shortly after. The idea is to provide an explanation of the meaning of the logical connectives and quantifiers in terms of rules for non-collaborative, zero-sum games between two agents, one of whom argues for the validity of the claim against moves from the other, and to define truth in terms of the existence of a winning strategy for the defender.