Hintikka-Style Semantic Games for Fuzzy Logics

Hintikka Style Game Rules for Semi-Fuzzy Quantifiers

“…Proof. (Sketch, relying on Theorems 1 and 2, as well as their generalizations to π and Π in [11] and [6], respectively.) Occurrences of ∀, ∃, and Π in G correspond to moves of type (A) for O, P, and N, respectively.…”

“…The aim of this paper is to explore the scope and limits of game rules for semi-fuzzy quantifiers that, in contrast to the G-game and the E-game, strictly adhere to 'Hintikka's principle': any state of the game is determined by a single (instance of a) subformula of the original formula and the information about which player acts as P and which as O. In [11], the first author has investigated such Hintikka-style games for propositional fuzzy logics. Moreover the focus there is on quite simple, binary branching rules.…”

“…As is customary in game theory, such (uniformly) random choices can be understood as those of an additional, nonstrategic player, called Nature (N for short). In particular it has been demonstrated in [11], that the expressivity of KZ is considerably extended already at the propositional level by introducing a new binary connective π given by the following H-game rule.…”

“…R H π : If the current formula is F πG then N decides randomly whether the game continues with F or G. As shown in [11], the corresponding truth function is given by…”