Comparative Remarks on Dialogical Logic and Game-Theoretical Semantics.
Tero Tulenheimo · HAL (Le Centre pour la Communication Scientifique Directe) · 2010
We turn attention to dialogical logic (henceforth DL) and game-theoretical semantics (or GTS), which both are game-based approaches to philosophical meaning theory. DL was first sketched by Paul Lorenzen in his 1958 talk ‘Logik und Agon’ [8]. Kuno Lorenz, starting from his 1961 doctoral thesis Arithmetik und Logik als Spiele [5], has further elaborated ideas which presently constitute the main body of DL. Jaakko Hintikka first expounded his ideas on GTS in his John Locke lectures at Oxford in 1964; the first publication, ‘Language-Games for Quantifiers’ [2], appeared in 1968. We will make formal comparisons between DL and GTS as applied to the characterization of material truth. Section 1 explains the basic ideas of DL and GTS. In Section 2 we recall Lorenz’s notion of strict dialogue [5] and formulate a related restricted variant of dialogues, the ‘memoryless dialogues.’ A formal comparison of memoryless dialogues and GTS is then presented for propositional logic with the connectives ∧,∨,¬. It is noted how the smooth correlations between the two approaches break down when→ is allowed as a syntactically given connective. Section 3 closes the paper by summarizing what was accomplished.