Modal logic began as the study of different sorts of modalities, or modes of truth: alethic (“necessarily”), epistemic (“it is known that”), deontic (“it ought to be the case that”), temporal (“it has been the case that”), among others. (See Roberta Ballarin's article
in the Stanford Encyclopedia of Philosophy for the "modern origins" of modal logic.) By now, it has become a broad area of research, forming a sort of lingua franca between many disciplines, especially philosophy, computer science, economics, and linguistics.
There are two main goals in this course. The first goal is to introduce the basic techniques and concepts in modal logic. We will focus on the basic systems of modal logic (both propositional and predicate) and their metatheory (e.g., issues of completeness/incompleteness, decidability, and definability). The second goal is to critically examine the many variations and philosophical interpretations of the basic systems of modal logic. Topics that may be discussed (the final choice of topics will depend on student interest) include (dynamic) epistemic/doxastic logic, conditional logic, non-normal modal logics, logics of action and agency, applications of modal logic in game theory, intuitionistic logic, among others.
Students will come away from this course with a working
knowledge of modal logic and its use in philosophy, computer science and game theory. The main objective
is that students should be able to confidently apply techniques from modal logic to problems in their area of research. They
should be able to apply existing modal logics where appropriate and design new logical systems when necessary, and rigorously
analyze their properties.
. For more information about the topics which may be discussed during the semester, you can consult the webpages of the following related courses that I have taught:
- Logic and Artificial Intelligence, Advanced undergraduate/graduate course focusing on (dynamic) epsitemic logic, belief revision and preference logic taught at the Department of Philosophy at Carnegie Mellon University.
- Logics of Rational Agency, Short course taught at the North American Summer School for Logic, Language and Information (NASSLLI 2010). Also, see the earlier version taught at the European Summer School for Logic, Language and Information (ESSLLI 2009).
- Introduction to Modal Logic, Introductory course on modal for Masters of Logic students at the Institute for Logic, Language and Information, University of Amsterdam.