Logics of Action and Time
Philippe Balbiani & Emiliano Lorini
Logic & Computation
Week Two - 11.00-12.30 - Level: I
By a "logic of action and time'', we mean any modal language for the logical description of phenomena such as action and tense. Today, logics of action and time constitute the heart of an active research area: the idea of associating with each program α of a programming language a modal connective [α] is at the root of many important propositional dynamic logics; several models of time have their modal counterparts in computational tree logics and linear temporal logics; the more recent dynamic epistemic logics offer new frameworks for integrating aspects of reasoning about knowledge and actions; applications to multi-agent systems have been considered within the context of the so-called ``Seeing To It That'' ($STIT$) logics. Nevertheless, much remains to be done, seeing that little is known about axiomatization/completeness, decidability/complexity and expressivity in several important logics of action and time. In this course, we will give a survey of the results on logics of action and time and we will present some of the open problems whose solution will have a great impact on the future of the area.