Epistemic modal logic

Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition dating back to Ancient Greece, epistemic logic is a much more recent development with applications in many fields, including philosophy, theoretical computer science, artificial intelligence, economics and linguistics. While philosophers since Aristotle have discussed modal logic, and Medieval philosophers such as Ockham and Duns Scotus developed many of their observations, it was C. I. Lewis who created the first symbolic and systematic approach to the topic, in 1912. It continued to mature as a field, reaching its modern form in 1963 with the work of Kripke.

Many papers were written in the fifties that spoke of a logic of knowledge in passing, but it was Finnish philosopher von Wright's paper An Essay in Modal Logic from 1951 that is seen as a founding document. It was not until 1962 that another Finn, Hintikka, would write Knowledge and Belief, the first book-length work to suggest using modalities to capture the semantics of knowledge rather than the alethic statements typically discussed in modal logic. This work laid much of the groundwork for the subject, but a great deal of research has taken place since that time. For example, epistemic logic has been combined recently with some ideas from dynamic logic to create dynamic epistemic logic, which can be used to specify and reason about information change and exchange of information in multi-agent systems. The seminal works in this field are by Plaza, Van Benthem, and Baltag, Moss, and Solecki.

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