Topological Models for Group Knowledge and Belief
Aldo Iván Ramírez Abarca

Abstract:
The advantage of using Topology in formal models of knowledge and belief comes from the spatial intuitions it endorses. In the possible-worlds framework, standard topological semantics for knowledge and belief are given in terms of the interior operator, and the interpretation is unavoidably connected with traditional Kripke semantics. A recent development in the field is the use of Topology to model evidence, and in turn evidence-based belief and knowledge. In contrast to the standard approach, the evidential one does not characterize knowledge in terms of interior. In both approaches, single-agent semantics are fairly consolidated. The present work inaugurates the use of the second approach -evidential in nature- to model epistemic group notions, and in particular distributed knowledge. We offer a sound and complete axiomatization of a topological logic of distributed knowledge that accounts for a notion of belief based on evidence.