From Closure Games to Generalized Strong Kleene Theories of Truth
In this paper, we present the Method of Closure Games (MCG), which is a game theoretic framework to construct theories of truth. In particular, we will illustrate that -as a consequence of our first and second stable judgement theorem- MCG is a powerful tool to study three and four valued Strong Kleene theories of truth in a uniform manner. The uniform approach allows us to combine suitably related three and four valued Strong Kleene theories of truth into so called Generalized Strong Kleene theories of truth (GSK theories). We illustrate the notion of a GSK theory by means of V8+, an eight valued GSK theory which is defined in terms of one four valued and two three valued Strong Kleene theories.