Dynamic Epistemic Logic with Topological Semantics

In this article we present dynamic epistemic logic in the content of topological semantics. Dynamic epistemic logic is a brunch of modern logic which close related to computer science. We show that the DEL under topological semantics is of highly similarity with that DEL under relational semantics. First we give some preliminary background of topological semantics. Then we introduce the concept of 2-topological space, by which we can study the knowledge and interaction between different agents. Finally, we define information update in topological model. Instead of the path" update as deleting worlds" used in relational semantics, here we view update as increasing open set. We prove the two ways of update is equivalent, show that the DEL in topological semantics as a nature extension of that DEL in relational semantics.