Games and Strategies inside Elementary Logic

1 Logic and Games Connections between logic and games go back to Antiquity, and the first systematic interest in rules of rational debate. Argumentation is a kind of game, and improving one’s skills in winning arguments draws many students to the lecture halls of logic. Well-defined ‘logic games’ have been around since the 1950s, when Paul Lorenzen gave his pioneering analysis of argumentation as a two-person game between the proponent and opponent of some thesis under discussion – where validity of a thesis means that its proponent has a winning strategy against any opponent. By now, there are many logic games, for purposes of proof, semantic evaluation (Hintikka), model comparison (Ehrenfeucht), or model construction (Hodges), and the literature on the subject is growing quickly. Moreover, games related to logic games have become wide-spread in computer science. Despite this growing interest, the game-theoretic approach has not become an established ‘perspective’ in logic, the way ‘semantics’ or ‘proof theory’ are considered major modes of viewing validity and other logical key notions. The received opinion has it that logic games are a didactic tool, a useful handmaiden to syntax and semantics without independent interest. Moreover, they are mostly a facon de parler, as there are no substantial connections with the deeper mathematics of game theory as developed by Von Neuman/Morgenstern and Nash.