Game theoretical semantics for some non-classical logics

Abstract

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A Game Theoretical Semantics for Logics of Nonsense

“…We define semantic games following the terminology given in [19,3]. First, we consider the language L of propositional logic given as follows in the Backus-Naur form for a set of countable propositional variables P:…”

“…Notice that what Definition 2.3 describes is rather different than what most readers may be familiar in classical game theory about strategy dominance. 3 The standard game theoretical definitions discuss pay-offs and higher pay-offs, whereas we focus on determining truth-values [18]. There is, however, a philosophical connection.…”

“…In an earlier work, a game theoretical semantics for Graham Priest's Logic of Paradox (LP, for short) was given [3]. In that work, the semantic games employed concurrent plays.…”

“…The logic of paradox introduces a third truth value which was intended to represent paradoxical statements. The third truth value P is called paradoxical and requires its own player, which was called Astrolabe [3]. Astrolabe forces the game to an end with the truth value P, so he is the paradoxifier.…”

“…In the context of dialogical logic, which can be seen as a variant of game semantics, the connection between semantic games and paraconsistency was explored in [20]. A recent work focused on the connection between various well-known paraconsistent logics and game semantics and offered various modifications for the games based on different logics [3,4]. The current work attempts at following the same path yet puts more emphasis on strategies.…”