Game Theoretical Semantic for Relevant Logic

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 $\boldsymbol{R}$.