A Game Theoretical Semantics for Logics of Nonsense

TL;DR

This paper introduces a game semantics for logics of nonsense, providing a formal framework to understand how errors and nonsensical propositions are handled and propagated in logical systems.

Contribution

It develops a Hintikkan game semantics for logics of nonsense, relates it to game-theoretic solution methods, and extends the framework to new logics including Priest’s Logic of Paradox.

Findings

Proved correctness of the game semantics for logics of nonsense.

Connected semantic games with iterated elimination of dominated strategies.

Extended the semantics to develop a new logic of nonsense and Logic of Paradox.

Abstract

Logics of non-sense allow a third truth value to express propositions that are \emph{nonsense}. These logics are ideal formalisms to understand how errors are handled in programs and how they propagate throughout the programs once they appear. In this paper, we give a Hintikkan game semantics for logics of non-sense and prove its correctness. We also discuss how a known solution method in game theory, the iterated elimination of strictly dominated strategies, relates to semantic games for logics of nonsense. Finally, we extend the logics of nonsense only by means of semantic games, developing a new logic of nonsense, and propose a new game semantics for Priest's Logic of Paradox.