Dipartimento di Matematica e informatica
Mathematical Logic
People
Faculty
PhD students and Post-Docs
- Gavin St. John
- Nicolò Zamperlin
- Giuseppe Zecchini
Students
- Marco Ferrara
Research Interests
Non-classical logics: our research focuses on various non-classical logical systems, like Kleene logics (which expand the set of truth-values beyond the binary truth and falsity), substructural logics (a large family of weak systems that generalize many well-known logics like classical and intuitionistic ones), quantum logic (a logic born from the theoretical considerations in quantum physics), modal logics (systems that deal with notions like necessity and possibility).
Figure 1: The algebra WK for Weak Kleene logics.
Abstract algebraic logic and algebras of logic: from the traditional relation between classical logic and Boolean algebras, abstract algebraic logic investigates the correspondence between logics and algebraic structures, providing rigorous definitions of what it means for a logic to be algebraizable and for a class of structures to be the counterpart of a logic.
Figure 2: Hasse diagram of the Leibniz hierarchy.
Universal algebra: the study of classes of structures provided with arbitrary operations at a general level, of which the most well-known algebraic structures (e.g., monoids, groups, rings) are particular cases. The results of universal algebra are an essential tool for algebraic logic.
Figure 3: Hasse diagram of the class operators H,S and P.
Quantum computing and quantum machine learning: the principles of quantum mechanics offer insights on how to (so far, theoretically) develop more efficient tools for computation, much quicker than the possibilities of traditional computers. Quantum computing is the study of such theory and its applications to machine learning.
Figure 4: Shor's factorization algorithm.
Seminars
The ALOPHIS (Applied Logic, Philosophy, and History of Science) seminars take place about twice a month. The detailed schedule is available at: Site
Events
- DeKLA workshop (October 17-18, 2024) ()
- Workshop on logics of variable inclusion (June 6 and 13, 2024)
- Trends in Logic (July 18-20, 2022) ()
Projects
- PRIN DeKLA (Devolopment of Kleene Logics and its Applications)
- Progetto Fondazione di Sardegna MAPS (Metric Algebras and their applications in Probability and Statistics)
- Progetto europeo MSCA-RISE MOSAIC (Modalities in Substructural Logics: Theory, Methods and Applications)
- Progetto UNICA Start-Up GraphNet
- PRIN Pnrr Qm4Np (Quantum Models for Logic, Computation and Natural Processes)
Research Collaborations
Selected Publications
- S. Bonzio and N. Zamperlin. Modal weak Kleene logics: axiomatizations and relational semantics, Journal of Logic and Computation, 2024.
- S. Bonzio and M. Pra Baldi. On the structure of Bochvar algebras, The Review of Symbolic Logic, 2024.
- S. Bonzio and A. Loi. Embeddings of metric Boolean algebras in R^N, Topology and its Applications, 2024.
- D. Fazio, A. Ledda, F. Paoli and G. St. John. A substructural Gentzen calculus for orthomodular quantum logic, The Review of Symbolic Logic, 2023.
- R. Giuntini, A.C. Granda Arango, H. Freytes, F. Holik and G. Sergioli. Multi-class classification based on quantum state discrimination. Fuzzy Sets and Systems, 2023.
- S. Bonzio, F. Paoli and M. Pra Baldi. Logics of variable inclusion, Trends in Logic, Springer, 2022.
- N. Galatos and G. St. John. Most simple extensions of FLe are undecidable, Journal of Symbolic Logic, 2022.
- S. Bonzio, T. Moraschini and M. Pra Baldi. Logics of left variables inclusion and Plonka sums of matrices, Archive for Mathematical Logic, 2021.
- H. Freytes. The Cantor-Bernstein-Schroeder theorem via universal algebra, Algebra Universalis, 2019.
- S. Bonzio, J. Gil-Férez, F. Paoli and L. Peruzzi. On Paraconsistent Weak Kleene Logic: Axiomatisation and Algebraic Analysis, Studia Logica, 2017.
- R. Giuntini, H. Freytes and G. Sergioli. Quantum logic associated to finite dimensional intervals of modular ortholattices, Journal of Symbolic Logic, 2016.