Logic is a very wide, culturally interesting and deeply transversal area of scientific research.
In very general terms it can be said that one of the main aims of logic is that of pointing out the relevant deductive dependences between informative judgements and studying them abstractly in a rigorous way. This often helps to make hidden structure manifest.
Among the deductive dependences, there are those that hold between judgements concerning intelligible objects of scientific interest. More precisely, those dependences that establish which judgements are deducible from which, in accordance with fixed rules of inference.
Mathematical logic represents an extremely important case in point. The kind of judgements which are of interest for this branch of logic concern mathematical objects. Within suitable formal deductive systems, mathematical logic studies the deductive dependences that link the kind of judgements at issue as mathematical objects themselves.
Within the framework of mathematical logic, some important mathematical results ever to be discovered turned out to have unexpected and surprising concrete applications in connection with fundamental mathematical questions on one side and in the realm of computer science on the other.
The research group in mathematical logic aims at focussing its research activity on
- the development of constructive methods obtained by means of universal constructions;
- the study of coherence problems, with applications to topology and the programming languages.
Moreover, it intends to
- deepen the strict connections between topology and computability;
- realize an interactive proof assistant to be managed by the user through an interface obtained by means of the software JAPE;
- apply the structural understanding of mathematics to educational questions.