


Mathematical Logic and Foundations 


The area of Mathematical Logic and Foundations of Mathematics includes several research topics, and in particular:
(1) Theory of Computability.
(2) NonClassical Logics, in particular, ManyValued Logic, Linear Logic and Provability Logic.
(3) Applications of Algebra to Logic.
(4) Harmonic theory in the Foundations of Arithmetic.
More specifically, in computablity theory, emphasis is given to research on models of relative computability, with a restricted and limited access to external databases (enumeration reducibility, computing with positive information, etc.); and to the theory of numberings, with a special interest in computations in the Ershov hierarchy, and in the arithmetical hierarchy.
The research on nonclassical logic is devoted to some logics which are relevant in Computer Science. For instance, manyvalued logic is very useful in the treatment of uncertain information (Ulam game with lies, with applications to error correcting codes, fuzzy control) and in de Finetti's approach to probability in terms of bets.
Linear logic is one of the most prominent logics in the last twenty years, and has deep applications in the theory of computations for providing: (1) geometrical abstraction in both proofs and algorithms, (2) resourcemanaged calculus machines with polynomial and elementary upper bounds, (3) extensions of the CurryHoward correspondence in the theory of calculations.
Modal logic is an extension of classical logic by a modality which may have various interpretations, among them, necessity or provability.
The interplay between algebra and logic is a longstanding research topic, which started in Siena in the seventies under the leadership of Roberto Magari. The research then expanded to algebras for nonclassical logics, abstract algebraic logic, universal algebra and categorical algebra.
Finally, the connection, at the origins of mathematics, between number theory and harmonic science has deeply influenced the formation of fundamental arithmetic concepts. These relate in particular to the theory of proportions and means, in connection with the problem of consonance, and the definition of logical and numerical algorithms for the formation of musical scales. People
Full Professors:
Fabio Bellissima, Andrea Sorbi
Assistant Professors:
Duccio Pianigiani, Giulia Simi
PhD Students:
Francesco Giannini, Cyrille Sandry Simeu 
Harmonic theory in the Foundations of Arithmetic 


Linear Logic 


Logic of provability and of interpretability 


ManyValued Logic, Algebraic Logic 


Theory of Computability 


Theory of Computability, Randomness 


Universal Algebra, Abstract Algebraic Logic, Categorical Algebra 


Universal Algebra, Categorical Algebra 






