Aim Introduction to the themes of information, computation, agency, and games in logic. Each week new skills will be trained, and outlooks will be given to mathematics, computer science, philosophy, etc. Also, students will be pointed to current research problems and directions.
Reading materials (course notes, parts of textbooks, additional papers) will be posted on the course website as we proceed, as well as powerpoint slides of on-line presentations after each class. It is best to skim the material lightly before class, and read again afterwards. Many readings come from the course text “Logic in Action” (LiA), but we add some more advanced background from the books “Logical Dynamics of Information and Interaction”(LDII) and “Logic in Games” (LiG).
Brief explanation. Our running theme in this course is basic features of information-driven agency. First we look at semantic information, knowledge, and the laws governing its upda- ting (Week 1,2), then we study more nuanced information spaces with plausibility orderings that support qualitative beliefs and belief revision (Week 3,4). In Week 5,6, we contrast this with the major quantitative approach to information update and belief, namely: probability, and raise questions about how the two perspectives, qualitative and quantitative, connect. A further important fact is that information can flow thanks to correlations or dependencies between different locations. In Week 7,8, we present a recent analysis of abstract dependence, as an example of new logics in the making. In Week 9,10, we turn to topology, a mathematical theory originally developed in the analysis of space and Analysis, but now also widely used to analyze basic structures in information and computation. We present modal logics of topology, partly in the format of games, and show how generalized topological spaces can also analyze powers of players in games. Games are a natural continuation of agency to social settings where in addition to pure information, preferences and goals play a crucial role. In Weeks 11-14, we will study the interface of logic and games in various directions, using logics to analyze games (Week 11,12), but also games to analyze logic (Week 13,14).
Please note: The official content of the course are only the topics presented in class, and defined by the slides to be posted: in principle, you should only study the passages corresponding to those topics.
