Stanford University PHIL 169: Modal Logic - Syllabus Winter 2003

Modal Logic

Instructors: Johan van Benthem and Darko Sarenac Office: 101B (5-0108) and 90-92K (3-2192) Office Hours: Wednesday 2:30-3:30 (in 92K) Email: johan@csli.stanford.edu and sarenac@stanford.edu Required Text: Notes by Professor van Benthem will be provided Recommended Text: Modal Logic. Patrick Blackburn , Maarten de Rijke, Yde Venema Overview: Introduction to the basics of modal logic, with an emphasis on action and information. Topics show the interdisciplinary nature of the field, lying in between philosophy, computer science, linguistics, mathematics, and economic game theory. The class is a preparation for Philosophy 269, a class on advanced modal logic Professor van Benthem teaches in the spring. Note: This class runs for seven weeks only. Course requirements: 6 or 7 exercise sets and a final project. The format of the project is negotiable. In the past, 3-5 page papers and programming assignments were the most common format. Prerequisite: 159 or a similar background in standard predicate logic. Schedule: Week 1 We introduce the basic modal language, and its evaluation in possible worlds models. This is a paradigm for studying the diverse modal languages used in practice. Expressive power is measured by the modern technique of bisimulation invariance, also found in computer science. We can think of bisimulation in terms of playing games, a topic that will return in this course. January 7: Basic language and semantics January 9: Bisimulation and expressive power Week 2 A look at the balance found in any logical system. Expressive power comes at a price in terms of complexity for the basic tasks a logical system is used for. These are semantic evaluation/model checking, valid reasoning/SAT-testing, and model comparison for language equivalence/structural similarity. This involves a brief excursion into computational complexity, a whole topic by itself. January 14: Valid reasoning and axiomatics January 16: Complexity of logical tasks Week 3 Our 'working analogy' between modal operators and quantifiers is turned into a systematic translation. This puts the basic modal language inside a spectrum of much stronger 'modal' languages, and we look at some modern versions, such as, for instance Hybrid Logic. January 21: Translation to classical logics January 23: Extended modal languages Week 4 We survey the landscape of modal logics, looking both along the path of reflexivity-friendly systems like T, S4, S5, up to 'Id', and the path leading up to the modal logic of endpoints, which contains Loeb's provability logic. We will develop some frame correspondence techniques to determine the semantic content of specific modal axioms. January 28: The landscape of modal logics January 30: Frame correspondence Weeks 5 and 6 Professor van Benthem introduces some of the following more advanced topics in Modal Logic: (1) epistemic logics of knowledge, (2) dynamic logics of action, (3) dynamic-epistemic logic of information update in communication, (4) logical analysis of games, equilibrium and rationality. February 4, 6, 11, 13 and possibly two or three additional sessions. Week 7 February 18: Logics of Space or Temporal Logics February 20: Review (last class)