A minimal logic for interactive epistemology

I will propose a minimal logic for interactive epistemology based on a qualitative representation of epistemic individual and group attitudes including knowledge, belief, strong belief, common knowledge and common belief. I will show that the logic is sufficiently expressive to provide an epistemic foundation for various game-theoretic notions and solution concepts such as strong and weak dominance, 1-round of deletion of weakly dominated strategies, followed by iterated deletion of strongly dominated strategies (DWDS1IDSDS) and 2-rounds of deletion of weakly dominated strategies, followed by iterated deletion of strongly dominated strategies (DWDS2-IDSDS). Two semantics for the logic will be given, a Kripkean possible-world semantics and a semantics based on the concept of type space. Equivalence results for two semantics as well as axiomatization and complexity results for the logic will be given.