Cool Logic

Aybüke Özgün (LORIA, CNRS - Université de Lorraine)

Relational vs. Neighbourhood Semantics for Epistemic Logic

November 28th at 17:30, in ILLC Seminar Room (F1.15)

Since Hintikka (1962, if not earlier) interpreted knowledge and belief in terms of standard relational (Kripke) semantics, the properties of knowledge and belief have come to be formulated as axioms in the language of basic modal logic. As this semantics provides a natural and relatively easy way of modelling epistemic logics, it has become one of the most commonly used tools for formal epistemologists and research in this area has been widely advanced based on the formal ground of Kripke semantics. However, it has also been acknowledged that Kripke semantics has some features that make the notions of knowledge and belief it implements too strong and is lacking some ingredients that make it possible to talk about the nature of acquired knowledge. On the other hand, a more general semantics, namely neighbourhood semantics, can be used in order to overcome the problems possessed by the relational formalism. In particular, topological semantics provides a deeper insight into the (evidence-based) nature of knowledge while generalizing Kripke semantics. In this talk, we will focus on the topological interpretation of knowledge in comparison to the relational interpretation and argue in favour of the former.