Logic and Computation advanced course:
Dynamic Logics for Interactive Belief Revision.
This course is addressed to students and researchers interested in logics for reasoning about multi-agent belief revision, belief updates and knowledge updates induced by various forms of communication or interaction. It is a foundational course, designed to present to students and researchers from other fields the work done in recent years by a number of researchers on integrating ideas from Belief Revision Theory within the DEL (Dynamic-Epistemic Logic) paradigm. The course is self-contained, not assuming any background knowledge, but presupposing only some general experience or facility with using logical languages, the concepts of syntax and semantics etc. We start by presenting the main notions of "standard DEL", arguing that this logic is appropriate for updating "hard information" (unrevisable knowledge), but that it is inappropriate for "soft information" (possibly false beliefs or defeasible knowledge). We then present "belief-revision models", defining some important epistemic/doxastic notions, considering a number of logical languages for these models, and explaining the relevance of these notions to fundamental issues in contemporary Epistemology, in Computer Science and in the study of language and communication. We present various Belief Update operations and various belief-revision policies proposed by different authors, focusing on one particular proposal (the Action-Priority Update) of great generality and elegance. We present reduction laws (the "dynamic laws of Interactive Belief Revision"), complete axiomatizations, applications to dialogue games and communication strategies, connections with other research areas and open problems.