Abstract
Hintikka’s game theoretical approach to semantics has been successfully applied also to some non-classical logics. A recent example is Başkent (A game theoretical semantics for logics of nonsense, 2020. arXiv:2009.10878), where a game theoretical semantics based on three players and the notion of dominant winning strategy is devised to fit both Bochvar and Halldén’s logics of nonsense, which represent two basic systems of the family of weak Kleene logics. In this paper, we present and discuss a new game theoretic semantics for Bochvar and Halldén’s logics, GTS-2, and show how it generalizes to a broader family of logics of variable inclusions.
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Acknowledgements
An earlier version of the paper was presented at the XXII Trends in Logic workshop, entitled Strong & Weak Kleene Logics, (Cagliari, Italy—18–20 July 2022). Massimiliano Carrara and Michele Pra Baldi acknowledge the CARIPARO Foundation excellence project (2020–2024): Polarization of irrational collective beliefs in post-truth societies. Filippo Mancini’s research is supported by the DFG (Deutsche Forschungsgemeinschaft) funded research group Inductive Metaphysics (Grant No. FOR 2495). Wei Zhu was funded by the Postdoctoral Stipend from the Fritz Thyssen Foundation, Germany, for the project (Ref. 40.22.0.015PH) Suspension and Computational Errors in Paraconsistent Weak Kleene Belief Update. We would like to thank the anonymous referees for their precious comments and suggestions on earlier versions of the paper.
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Carrara, M., Mancini, F., Pra Baldi, M. et al. A New Game Theoretic Semantics (GTS-2) for Weak Kleene Logics. Stud Logica (2024). https://doi.org/10.1007/s11225-024-10113-5
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DOI: https://doi.org/10.1007/s11225-024-10113-5