Propositional assignments, announcements, and their applications to logics of action and agency
Résumé
Assignments modify the world, while announcements modify the agents' knowledge. Their logic provides a simple but flexible tool for multi-agent systems. I will illustrate its applications by means of two examples. First, I will show how reasoning about the capabilities and powers of coalitions as done in coalition logic can be captured in the logic of assignments. Second, I will recast Reiter's famous solution to the frame problem in reasoning about actions in the same logic, and I will show that its extension to so-called knowledge-producing actions can be recast in the logic of assignments and announcements. I will then discuss decision procedures for several versions of the logic of assignments and announcements. I will show that (contrarily to standard PDL) the Kleene star can be eliminated from assignment programs in the dynamic logic of assignments and announcements. I will furthermore show how Lutz's rewriting procedure can be extended from public announcement logic to the logic of assignments and announcements.