Séminaire Paris-Nancy en logique et philosophie des mathématiques PANALM

Nous aurons le plaisir d'écouter : Aybüke Özgün (ILLC, Univ. d'Amsterdam)

"Refining Epistemic Logic via Topology"

Epistemic logic is an umbrella term for a variety of modal logics whose main objects of study are knowledge and belief. As a field of study, epistemic logic uses mathematical tools to formalize, clarify, and address the questions that drive (formal) epistemology, and its applications extend not only to philosophy, but also to theoretical computer science, artificial intelligence, and eco- nomics. Research in epistemic logic has widely advanced based on the formal ground of normal modal logics and standard possible worlds semantics on relational structures as they provide a relatively easy way of modeling knowledge and belief. However, this mainstream approach is subject to well-known conceptual objections and open to extensions to better handle informa- tion. In this talk, I will focus on features of the standard (relational) possible worlds semantics that call for refinement/enrichment and provide an overview of topological approaches to epis- temic logic. In particular, I will argue that topological spaces emerge naturally as information structures if one not only seeks an easy way of modeling knowledge and belief, but also aims at representing evidence and its relationship to these notions. Based on some of the topological semantics proposed in [1, 2], I will show that the topological approach enables fine-grained and refined representations of the aforementioned epistemic notions, highlighting several variations and extensions in the literature, and (time-permitting) applications in mathematical logic, formal epistemology, and formal learning theory.
References
[1] Baltag, A., Bezhanishvili, N., Özgün, A., and Smets, S. (2022) Justified belief, knowledge, and the topology of evidence. Synthese, 200, 1–51. [2] Özgün, A. (2017) Evidence in Epistemic Logic: A Topological Perspective. Ph.D. thesis, ILLC, Univerisity of Amsterdam.