Logical epistemology, also known as epistemic logic, proceeds axiomatically. ‘Ξ knows that A’ is formalized as a modal operator in a formal language that is interpreted using the standard apparatus of modal logic. This formal epistemological approach also pays homage to the forcing heuristics by limiting the scope of the knowledge operator through algebraic constraints imposed on the accessibility relation between possible worlds.

Logical epistemology dates back to Von Wright (1951) and especially to the work of Hintikka (1962) in the early 1960's. Epistemic logics have since then grown into powerful enterprises enjoying many important applications. The general epistemological significance of the logics of knowledge has to some extent been neglected by mainstreamers and formalists alike. The field is in a rather awkward position today. On the one hand, it is a discipline of importance for theoretical computer scientists, linguists and game theorists, for example, but they do not necessarily have epistemological ambitions in their use of epistemic logic. On the other hand, it is a discipline devoted to the logic of knowledge and belief but is alien to epistemologists and philosophers interested in the theory of knowledge.

Recent results and approaches have fortunately brought the logics of knowledge quite close to the theories of knowledge.