Future event logic – axioms and complexity

In this paper we present a sound and complete axiomatization of future event logic. Future event logic is a logic that generalizes a number of dynamic epistemic logics, by using a new operator $\triangleright$ that acts as a quantifier over the set of all refinements of a given model. (A refinement is like a bisimulation except that from the three relational requirements only ‘atoms’ and ‘back’ need to be satisfied.) Thus the logic combines the simplicity of modal logic with some powers of monadic second order quantification. We prove the axiomatization is sound and complete and discuss some extensions to the result.