Algebraic Logic And Its Applications To Computer Science
Prof.
Paolo Aglianò
University of Siena - Dipartimento di Ingegneria dell'Informazione e Scienze Matematiche Stefano Fioravanti
Charles University - Praga
Course Type
Type B
Calendar
15-26/6/2026
Room
Program
This course provides an in-depth introduction to the field of algebraic logic, which studies logical systems via algebraic structures. The course focuses on the classical correspondence between propositional logics and varieties of algebras (like Boolean algebras, Heyting algebras, MV-algebras), along with duality theory, completeness, representation theorems, and algebraizable logics in the sense of Blok and Pigozzi. Students will explore how algebra can illuminate syntactic and semantic features of logics and will be introduced to modern perspectives in abstract algebraic logic. Special emphasis is given to applications in artificial intelligence, particularly in areas such as fuzzy logic, knowledge representation, reasoning under uncertainty, and non-monotonic inference. Algebraic semantics underpin many logic-based AI systems, offering a formal basis for interpretability, consistency, and efficient symbolic reasoning. The course explores how algebraic logic contributes to designing more robust AI frameworks, especially in explainable AI (XAI), logic programming, and automated reasoning systems. The course will cover the following topics (i) an introduction to the fundamental concepts of Universal Algebra needed for the remaining of the course; (ii) introduction to fuzzy logics and their algebrization, BL-logic; (iii) Lukasiewicz Logic and their algebrization MV-Algebras; (iv) Residuated la-ces; (v) finally, we will outline some current applications of fuzzy logic in the field of computer science.
