ESSLLI'09 Course on Dynamic Logics for Interactive Belief Revision
By Alexandru Baltag and Sonja Smets
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 an advanced 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 presupposes a background knowledge of the syntax and semantics of basic modal logic. Some familiarity with the standard modal logics for knowledge and belief, as well as with some basic issues of standard Belief Revision theory, would be most welcome (though not required) for an easier understanding of the material.
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, belief merge, communication strategies, connections with other research areas and open problems.