Directory

Description

The purpose of mathematical logic is exploring the applications of formal logic to mathematics, with strong connections with metamathematics, the foundations of mathematics and theoretical informatics. The group's research activity ranges across several levels, involving both the aspects more closely linked with the expressive power of various formal systems, and areas closer to applications. In the proof-theoretical and semantic direction, there is the analysis of logics with partially defined terms, in particular for the development of mathematical theories and the semantic extension of the case of intuitionistic logic. The purpose is to achieve a theoretical framework that can grasp several aspects of the ordinary practice of mathematics, placing them within a general logical mathematical picture. Modal and temporal logics are special formal systems, widely employed for representing and studying the properties of processes. Within this scope, the group studies properties of expressiveness, decidability, hierarchy, modularity of various types of logics that are useful in informatic applications such as model checking and system verification. Finally, many formal systems are naturally suitable for translating in the algebraic language (for instance, the Boolean algebras theory is the algebraic counterpart of the classical propositional logic), and the study of the algebras and of the dual topological spaces thus achieved is both interesting in itself, and a source of information for the overlying logic.

Research subjects

Classical logic subsystems (including intuitionistic logic). Cut elimination. Logic with equality.
Fixed-point logics, graded logics, temporal and modal logics. Alternation hierarchies of fixed points, interpolation, modularisation.