Download PDFOpen PDF in browserA Simple Token Game and its Logic19 pages•Published: May 26, 2024AbstractWe introduce a simple game of resource-conscious reasoning. In this two-player game, players P and O place tokens of positive and negative polarity onto a game board according to certain rules. P wins if she manages to match every negative token with a corresponding positive token.We study this token game using methods from computational complexity and proof theory. Specifically, we show complexity results for various fragments of the game, in- cluding PSPACE-completeness of a finite restriction and undecidability of the full game featuring non-terminating plays. Moreover, we show that the finitary version of the game is axiomatisable and can be embedded into exponential-free linear logic. The full game is shown to satisfy the exponential rules of linear logic, but is not fully captured by it. Finally, we show determinacy of the game, that is the existence of a winning strategy for one of the players. Keyphrases: game semantics, linear logic, proof theory, resource logic In: Nikolaj Bjorner, Marijn Heule and Andrei Voronkov (editors). Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 100, pages 341--359
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