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Some of Our Research Topics:
Members involved: Giuseppe Rosolini, Jacopo Emmenegger, Fabio Pasquali, Ruggero Pagnan, Greta Coraglia, Francesco Dagnino
Descriptive Set Theory
Descriptive set theory is commonly understood as the study of definability properties of subsets in Polish spaces.
The main recent contributions of the Genoa logic group to this subject concern classification problems for binary relations and the study of the Wadge hierarchies in various topological spaces.
Members involved: Riccardo Camerlo
Formal logic is a relatively young discipline, with classical first-order logic considered as the
`standard logic' (taking the place of other possible alternative systems); this is the logic of introductory (and even advanced) logic textbooks.
Classical logic had as main purpose the analysis of mathematical arguments and comes with a high level of idealization: every sentence is impersonal,
either true or false and refers just to facts, truth is permanent,
implication is non-causal. Temporal, modal, doxastic aspects are not important,
and should not be important in mathematical proofs. However, classical logic is not adequate in the analysis of scientific and everyday reasoning.
Even in mathematics, classical logic has been considered inadequate:
intuitionistic logic was born from the inadequacy of classical logic in representing the computationalcontent of deductive arguments.
Assumptions can be used ad libitum in a mathematical proof, but if assumptions represent entities with a price (that can be a concrete or a computational one) we need to take their multiplicity into account.
Linear logic and more generally substructural logics have been proposed as a more suitable tool for the investigation of problems in which
resources have a role. In a similar guise, conditional logics have been developed for the study of causation,
for which the standard material implication is not adequate.
Non-classical logics have applications in various fields, not just the traditional ones (philosophy, mathematics, computer science)
but also new ones in the social sciences, such as collective epistemology and formal ethics.
Even if non-classical logics are developed as alternatives to classical logic, they are often extensions of the latter, so the formal apparatus builds on the one of classical logic.
However, both the theory (models and deductive systems) and the metatheory (general results about them) have to be carefully re-built.
Non-classical logics provide a challenging field for the application and development of both semantical and proof-theoretical logical methods.
Members involved: Sara Negri, Riccardo Camerlo, Cosimo P. Brogi, Francesco Dagnino
Members involved: Sara Negri, Cosimo P. Brogi
Members involved: Giuseppe Rosolini, Fabio Pasquali, Greta Coraglia
Members involved: Giuseppe Rosolini, Jacopo Emmenegger, Cosimo P. Brogi