2nd Semester 2019/20: Algebraic Logic
Tommaso Moraschini [local responsible: Nick Bezhanishvili]
If you are interested in this project, please contact Nick Bezhanishvili by email.
Registration until 31 May 2020
It is well known that modal and intuitionistic logics can be studied through the lenses of modal and Heyting algebras. This is made possible by the so-called algebraization process which allows to cross the mirror between logic and algebra, making possible to study purely logical problems with the powerful methods of universal algebra and Priestley-style dualities.
Starting from familiar examples, this project will present an overview of the theory of algebraizable logics, i.e., a framework in which the equivalence between logical and algebraic phenomena can be explained in full generality. As an exemplification, the algebraic counterpart of various forms of deduction theorems will be investigated, shedding light on the theory of Jankov formulas.
The project will be organized in six previously recorded video lectures, complemented by selfcontained course notes. Further bibliography will be also provided, but should not, in principle, be necessary to understand the material of the course. Students will be able to contact the teacher and ask questions or clarifications both by e-mail or via Zoom meetings.
The prerequisites of the project are essentially the material covered by the course "Mathematical structures in logic". As most examples will be taken from modal and intuitionistic logics, familiarity with these will be helpful.
At the end of the course, each student will be asked to give a short presentation via Zoom on a topic related to the project. The assessment will be based on these presentations.
In addition, the course notes contain many exercises. Even if the students are strongly suggested to do them, these will not be part of the evaluation.
- T. Moraschini. Algebraic Logic. Course notes. Soon accessible online.
- J. M. Font. Abstract Algebraic Logic. An Introductory Textbook. Vol. 60 of Studies in Logic - Mathematical Logic and Foundations. College Publications, London, 2016.
- W. Blok and D. Pigozzi. Algebraizable logics. Vol. 396 of the Memoirs of the AMS, Providence, 1989.
- J. Raftery. A perspective on the algebra of logic. Quaestiones Mathematicae, 34:275-325, 2011.
Further references can be found in the bibliography of the course notes.