On Semantic Gamification
The purpose of this essay is to study the extent in which the semantics for different logical systems can be represented game theoretically. I will begin by considering different definitions of what it means to gamify a semantics, and show completeness and limitative results. In particular, I will argue that under a proper definition of gamification, all finitely algebraizable logics can be gamified, as well as some infinitely algebraizable ones (like Łukasiewicz) and some non-algebraizable (like intuitionistic and van Fraassen supervaluation logic).
- 3.Fermüller, C.G.: On matrices, Nmatrices and Games. J. Logic Comput. (2013)Google Scholar
- 6.Hintikka, J., Sandu, G.: Game-Theoretical Semantics (1997)Google Scholar
- 9.Łukasiewicz, J., Borkowski, L.: Selected Works: Studies in Logic and the Foundations of Mathematics. North-Holland Publishing Co., Amsterdam (1970)Google Scholar
- 13.Parikh, R.: D-structures and their semantics. Not. AMS 19, A329 (1972)Google Scholar
- 19.van Fraassen, B.C.: Presuppositions: supervaluations and free logic. In: Lambert, K. (ed.) The Logical Way of doing Things, pp. 67–92. Yale University Press (1969)Google Scholar