Section: New Results

Paraconsistency and Inconsistency-Friendly Logics

Paraconsistent logic is a family of formal systems in which the law of contradiction fails. In such systems, from an inconsistent set, not everything follows.

Can Baskent has studied such logical systems and their connections to formal linguistics within the framework of game theory. First, he observed how a game theoretical semantics can be given for some paraconsistent logics [43] . The advantage of game semantics is that it simply reflects the parsing tree of logic, and furthermore presents a semantical structure that uses elements from game theory. Such a study also requires an in-depth study of various paraconsistent logics, and their semantical structures [13] . Such a study requires some understanding of point-set topology, and its relation to logic.

Moreover, paraconsistent logics relate to dynamic logics as well. The logical model defines characterises how dynamic epistemic modalities, which are familiar from multi-agent systems, work [13] . This helps us understand how multi-agent interactions in an inconsistent model work in a sound way.

Another interesting way of seeing how inconsistency-friendly logics work is to consider them within the framework of game theory [37] . Game theory, similar to multi-agent systems, studies the intelligent and rational interaction of decision makers/agents. Yet, it suffers from various paradoxes. Such paradoxes are important from a computational semantical point of view. If paraconsistency is the most suitable tool to analyse paradoxes, then game theoretical paradoxes are not exceptions [37] .

The technical work always needs to be supplemented by some conceptual work. Granted, paraconsistent logics find their ways in various philosophical and semantical issues, yet their computational analysis usually falls short. In [44] , we discussed the connection between paraconsistent logics and Hintikka's interrogative models. These models have been developed by Hintikka, a pioneer of epistemic logic, and have been properly analysed from paraconsistent perspectives. If inquiry and questioning needs to be accounted for computationally, a paraconsistent approach will be an appropriate tool as well. Similarly, [39] discusses paraconsistency and its connection to social software. Social Software is a field conceived by Rohit Parikh, and it studies the computational and logical analysis of social protocols and policies. It lies in the intersection of social choice theory and game theory, and is a subset of logic.

Such results have been presented in various talks including, World Congress of Paraconsistency in Kolkata and Logic and the Foundations of Game and Decision Theory in Bergen, and warmly received.