UniCa - Università degli studi di Cagliari
Philosophy, Epistemology, Human Sciences Doctoral Course

Introduction to algebraic logic

PhD in Philosophy, Epistemology, and Human Sciences

University of Cagliari, Department of Pedagogy, Psychology, and Philosophy

Title of the course: Introduction to algebraic logic.

Hours no.: 16

Teacher: Nicolò Zamperlin (n.zamperlin@gmail.com, MAT/01, MFIL/02).

Short bio/bibliography: sono attualmente borsista di ricerca presso il Dipartimento di Pedagogia, psicologia e filosofia dell’Università di Cagliari, supervisionato dal Prof. Francesco Paoli. Sono inoltre dottorando presso i medesimi dipartimento e supervisore nel Dottorato in Filosofia, epistemologia e scienze umane (cosupervisionato inoltre dal Prof. Stefano Bonzio). Ho in precedenza ricoperto l’incarico di assegnista di ricerca presso il Dipartimento di Matematica e informatica sempre dell’Università di Cagliari, supervisionato dal Prof. Stefano Bonzio (luglio 2024-giugno 2025). I miei interessi di ricerca vertono su logica algebrica, logica modale, logiche di Kleene e semantiche per l’iperintensionalità.

Publications:

  • F. Paoli, G. Vergottini, N. Zamperlin, D. Fazio, “On Bochvar algebras and regular double Stone algebras”, submitted.
  • N. Zamperlin, “Generalized Epstein semantics for Parry systems”, Studia Logica, 2025, online: https://doi.org/10.1007/s11225-025-10183-z.1.
  • S. Bonzio, N. Zamperlin, “Modal weak Kleene logics: axiomatizations and relational semantics”, Journal of Logic and Computation 35(3), 2025: https://doi.org/10.1093/logcom/exae046.
  • T. Jarmuzek, J. Malinowski, A. Parol, N. Zamperlin, “Axiomatization of Boolean Connexive Logics with syncategorematic negation and modalities”, Logic Journal of the IGPL, 2024, online: https://doi.org/10.1093/jigpal/jzae120.

Delivery method: frontal lessons.

Meeting calendar:

  • January 2026
    • 14th: 15.00 – 17:00, classroom 10
    • 22nd: 10.00 – 12.00, classroom 10
    • 28th: 10.00 – 12.00, classroom 9
  • February 2026
    • 3rd: 10.00 – 12.00, classroom 9
    • 10th: 10.00 – 12.00, classroom 10
    • 17th: 10.00 – 12.00, classroom 9
    • 25th: 10.00 – 12.00, classroom 9
  • March 2026
    • 4th: time and room to be defined.

Aula e/o Link: see above.

Language: English, unless all students speak Italian, in which case Italian is the only language. All reference literature is in English.

Required preliminary knowledge:Proficiency in the metatheory of classical propositional logic (at the level of a full introductory logic course). Basic knowledge of algebra (particularly lattice theory) and universal algebra (definitions of varieties and quasi-varieties) is helpful. All of this material can be found in the first two chapters of Burris & Sankappanavar (see bibliography).

Short description of the course: The course is a quick introduction to the theory of algebraizability of Blok and Pigozzi. Through the study of the first chapters of Font’s handbook on abstract algebraic logic we will explore the necessary notions for any further investigation of the modern approach to algebraic logic. The goal of the course is to provide students with the minimal tools to access the current literature about abstract algebraic logic. We will review the basic notions (consequence relations and closure operators) that precisely specify the definition of logic we will be working with and we will adapt these notions to classes of algebras. We will then move to the core of the theory of algebraizability, introducing the fundamentals (algebraic semantics, Lindenbaum-Tarski process, definition of algebraizability), exploring equivalence results (syntactic characterization, Leibniz congruence and isomorphism theorem), concluding with a glimpse to the semantics of matrices (logical matrix, Leibniz-reduced model).

Internal structure of the seminar meetings: The lessons are intended to cover the content of the first three chapters of the Font manual (see bibliography).

Bibliographic references:

  • Blok, W., and Pigozzi, D., Algebraizable logics, vol. 396 of Memoirs of the American Mathematical Society, A.M.S., 1989.
  • Burris, S., and Sankappanavar, H.P., A course in Universal Algebra, freely available online: https://www.math.uwaterloo.ca/snburris/htdocs/ualg.html, 2012 update.
  • Czelakowski, J., Protoalgebraic logics, vol. 10 of Trends in Logic: Studia Logica Library, Kluwer Academic Publishers, Dordrecht, 2001.
  • Font, J.M., Abstract Algebraic Logic: An Introductory Textbook, College Publications, 2016.

Final evaluation: seminar lesson held by students on a topic related to the course and agreed upon with the teacher.

Other useful information: