Dynamic epistemic logic with assignment

Abstract

We add assignment operators to languages for epistemic actions, so that change of knowledge and change of facts can be combined in specifications of multi-agent system dynamics. We make a distinction between 'public assignment' and 'atomic assignment'. Public assignment means that the entire group of agents is aware of the factual change. This operation combines well with public announcement. We propose semantics for the logic of public announcements and public assignments, and we give a relevant valid principle. Atomic assignment means that only facts are changed, so that it can be expressed independently in the language how agents are aware of this factual change. Atomic assignment and 'test' (the truth of a formula) are the two basic constructs in a logic of epistemic actions. We propose semantics for this logic of epistemic actions and atomic assignment. The logic of public announcements and public assignments is a special case of this logic. Examples include card games where cards change hands.