Spatio-Epistemic Logics: When Knowledge Meets Geometry

Logic and Computation Courses

Introductory Course

Spatio-Epistemic Logics: When Knowledge Meets Geometry,
Philippe Balbiani (Toulouse Institute of Computer Science Research, France)

In the field of knowledge representation and reasoning, despite the fact that epistemic connectives are sometimes interpreted in concrete structures defined by means of runs and clock time functions, one of the things which strikes one when studying multi-agent epistemic logics is how abstract their semantics are. Contrasting this fact is the fact that real agents like robots in everyday life and virtual characters in video games have strong links with their spatial environment. In this course, we will introduce multi-agent epistemic logics which semantics can be defined by means either of purely geometrical notions, or of purely topological notions. In these logics, possible states are defined by considering the positions (points, regular closed subsets) in Rn occupied by agents and the sections (cone, regular closed subsets) of Rn seen by agents whereas accessibility relations are defined by means of the ability of agents to imagine possible states compatible with what they currently see.