Justified Belief and the Topology of Evidence

Abstract

We introduce a new topological semantics for evidence, evidence-based justifications, belief and knowledge. This setting builds on the evidence model framework of van Benthem and Pacuit, as well as our own previous work on a topological semantics for Stalnaker's doxastic-epistemic axioms. We prove completeness, decidability and finite model property for the associated logics, and we apply this setting to analyze key issues in Epistemology: no false lemma Gettier examples, misleading defeaters, and undefeated justification versus undefeated belief.