Topological Models of Belief Logics
Rohit Parikh, Christopher Steinsvold · 2009
We explore the technical and philosophical aspects of topological models for modal logics of belief. We focus on K4, KD4, and KD45, interpreting the diamond as the derivative operator. Completeness proofs are presented for these logics, as well as for multi-agent KD45 with common belief. Special philosophical emphasis is given to the T1 condition, which we interpret to mean that the agent can never have a complete set of beliefs.