Course for international guest/part time students
- Faculty
- Faculty of Humanities
- Organization
- BTK Institute of Philosophy
- Code
- BMI-LOTD-325E.02
- Title
- Algebraic logic, category theory I: Algebraic logic
- Usual semester
- Autumn
- ECTS
- 4
- Language
- hu
- Learning outcomes
- Aim of the course: Starting from the 60-s of the 20th century, the development of theoretical computer science brought to the light a huge number of logical systems (e.g. several versions of dynamic logic of programs, lambda calculus etc.). After a while, it became apparent that, when checking some logical properties of these logical systems, certain patterns of ideas, concepts, proofs kept being repeated with only slight differences. It was time to develop appropriate abstract levels of the subject. Several schools have been formed. Some of these schools befenited from using universal algebraic methods. The most outstanding of these schools was led by Alfred Tarski. First, they concentrated on the algebraic counterpart of first order logic, developing this way the theories of cylindric-, polyadicand relation algebras. These studies naturally led to study the algebraic counterparts of other logics. This course provides an intensive introduction to algebraizing logical frameworks. Content of the course: We cover specific class(es) of algebras belonging to a given logic (e.g. Boolean algebras, Heyting algebras, Relational algebras, Cylindric algebras ); the algebraic counterparts of concrete logical properties. In this course we will look into this process of algebraization of logic. We will concentrate more on the semantical aspects than the syntactical ones. We show how to gain new knowledge in logic via algebraic methods and cover basics from universal algebra (subalgebras, homomorphic images, congruences, direct products varieties and quasi-varieties). We will study some famous techniques of algebraization and prove several ”Bridge theorems” between algebra and logic. Throughout our 1 approach will be in the spirit of the ”Budapest school” of algebraization. Grading criteria: Oral exam Literature: • H. Andréka, Z. Gyenis, I. Németi and I. Sain: Universal algebraic logic: Dedicated to the unity of science, Studies in Universal Logic, Birkhäuser Cham, Switzerland, 2022. • H. Andréka, I. Németi and I. Sain: Algebraic Logic. In: D. M. Gabbay and F. Guenther, editors, Handbook of Philosophical Logic Volume II, Second Edition, pages 133-247. Kluwer Academic Publishers, 2001.