TGTS Based Argumentation

Suppose two discussants hold opposite views about the level of pollution in Pinarella, and start arguing about that. Then, one of them says something like “The winner of the next UEFA Champions League final match will be Hellas Verona”, which is clearly out of topic with respect to the discussion topic. How do we model such a situation in an argumentation process? Our aim here is to provide a framework capable of handling such a phenomenon, namely a situation where one of the discussants in an argumentation process goes out of topic and gives rise to a certain reaction from the other. The ingredients of such a model are: a game-theoretical-semantics with a verifier and a falsifier, a discussion and a discussion topic. We develop our framework using a Paraconsistent Weak Kleene logic (PWK), with the off-topic reading of its non-classical value, and a topic-game-theoretical-semantics.