2nd Semester 2012/13: Algebraic Modal Logic
- Sumit Sourabh
If you are interested in this project, please contact the instructor by email.
- Algebraic logic is a discipline which uses tools and techniques from Universal algebra to study logic. Modal logic which is usually interpreted over relation structures or Kripke frames can also be seen as a Boolean algebra with operators (BAOs). The algebraic perspective adds a new dimension to the theory of modal logic. Starting from the seminal work of Jónsson and Tarski on representation of BAOs (1952), algebraic techniques have played an important role in modal logic.
This project is an introduction to algebraic modal logic. After the basics on BAOs and their representation, we'll see how duality theory unifies the relational and algebraic approaches to modal logic. As an application we shall see proofs of some important results in modal logic, using algebraic techniques.
- < A basic knowledge of Modal logic is required. Familiarity with basic algebras such as groups, partial orders and lattices will be helpful.
- This course is worth 6EC. Students will work on exercise problems and submit homework every week. In the final week, they will give presentations and/or submit a paper on a topic related to the course. Participation in class discussion will also be assessed.
- The main text for the course is Chapter 5 of Modal Logic, Cambridge University Press, Cambridge, 2001 by P. Blackburn, M. de Rijke and Y. Venema. An additional reference will be the chapter on Algebra and Coalgebra by Yde Venema in the Handbook of Modal Logic, which is available online. A list of papers and additional material will be posted on the project webpage.