Date and Time: Monday, September 4th 2017, 13:00-14:30
Venue: ILLC Seminar Room F1.15, Science Park 107.
Title: Topo-Logic as a dynamic-epistemic logic (toward a logic for Learning Theory).
Abstract. In this talk, we investigate a natural extension of Topo-Logic of Moss and Parikh (1992), obtained by adding to it dynamic modalities for ‘topological public announcements’ in the style of Bjorndahl (2017). In other words, we revisit Topo-Logic as a dynamic epistemic logic with public announcements. The resulting “Dynamic Topo-Logic” forms a logic of evidence-based knowledge, knowability, learning of new evidence, and stability (of some truth φ) under any further (true) evidence-acquisition. Moreover, we also talk about a topological arbitrary announcement modality studied by van Ditmarsch et al. (2015), and investigate its interplay with the effort modality. We therefore develop a formal, topological framework that clarifies the intuitively obvious, yet formally elusive connection between the dynamic notions effort and its seemingly special instances: public and arbitrary announcements.
We give a complete axiomatization for this Dynamic Topo-Logic, which is — we argue — epistemically more intuitive and, in a sense, simpler than the standard axioms of Topo-Logic. Our completeness proof is also more direct, making use of a standard canonical model construction. Moreover, we study the relations between this extension and other known logical formalisms, showing in particular that it is co-expressive with the simpler and older logic of interior and global modality, which immediately provides an easy decidability proof both for the original Topo-Logic and for our extension. In turn, the effort modality also helps to simplify and streamline the axiomatization of the topological arbitrary announcement logic.
If time permits, we also discuss a variant of the Dynamic Topo-Logic as a Dynamic Logic for Learning Theory, and use it to characterize various notions of knowledge, belief, and learning.
The first part of the talk is joint work with Alexandru Baltag, and the second part is joint work with Alexandru Baltag, Nina Gierasimczuk, and Sonja Smets.