Game Theoretical Semantic for Relevant Logic

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V. L. Vasukov

Abstract

In 1979 D.E. Over proposed game theoretical semantics for first-degree entailment formulated by Anderson and Belnap. In order to extend this approach to include other systems of relevant logc (e.g., $\boldsymbol{R}$) we have two promoting facts. Firstly, there is Routley- Meyer’s situational semantic for system$\boldsymbol{R}$ of relevant logic. Secondly, this semantics shows some resemblance with W__ojcicki’s situational semantic of non-fregean logic for which the situational game semantics was developed by author exploiting essentially the notion of non-fregean games. In the paper an attempt is done to give a partial account of these results and some conception of situational games developed which laid down into foundation of the game theoretical semantics of relevant logic $\boldsymbol{R}$.

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References

Dishkant, H. “An Extension of the Lukasiewicz Logic to the Modal Logic of Quantum Mechanics”, Studia Logica, 1976, vol.37, no 2, pp. 149–155.
Dunn, M., Restall, G. “Relevance Logic”, Handbook of Philosophical Logic (2nd ed.) / ed. by D.M. Gabbay, F. Guenthner. Vol. 6. Dordrecht: Springer, 2005.
Mares, E. Relevance Logic: a Philosophical Interpretation. N.Y.: Cambridge University Press, 2004. 240 pp.
Over, D.E. “Game Theoretical Semantics and Entailment”, Studia Logica, 1979, vol.XL, no 1, pp. 68–74.
Vasyukov, V.L. “Scientific Discovery and the Context of Abduction”, Philosophy of Science, 2003, vol.9, pp. 180–205. (In Russian)
Vasyukov, V.L. “Dialogue Games for Dishkant’s Quantum Modal Logic”, Logical Investigations, 2013, vol.19, pp. 353–365. (In Russian)