# Some new directions in Epistemic Logic.

## Sergei Artemov

### The CUNY Graduate Center

We will review research avenues on which we will focus this semester.

1. Applications of Justification Logic: general theory of logical omniscience, new format of handling inconsistent information, argumentation theory, truth maintenance systems, tracking evidence and belief revision.

2. Syntactic Epistemic Logic. There is some well-known tension between a syntactic description of an epistemic scenario and its semantical analysis based on a specific model. Such analysis requires common knowledge of the model which does not usually follow from the assumptions. Syntactic Epistemic Logic offers an approach to epistemic situations which does not rely on the common knowledge of a model.

3. Generic Common Knowledge.The notion of common knowledge of F, as introduced by Lewis in 1969, refers to any situation in which each finite iteration of `agent 1 knows that agent 2 knows that … F’ holds. A similar approach has been offered by McCarthy and others. This situatuion is now called Generic Common Knowledge, GCK, of F. Now dominant notion of Common Knowledge CK was coined by Aumann in 1976 as the least of all GCK’s of F. Now there is a growing number of specific epistemic scenarios which require GCK rather than CK. We are developing the theory of GCK and applying GCK to CK in appropriate situations.

Professor Artemov holds a Distinguished Professor position at the Graduate Center of the City University of New York, in the Computer Science, Mathematics and Philosophy programs. He is also Professor of Mathematics at Moscow State University, the founder and the Head of the research laboratory Logical Problems in Computer Science. He conducts research in the areas of logic in computer science, mathematical logic and proof theory, knowledge representation and artificial intelligence, automated deduction and verification and optimal control and hybrid systems.