Escola de Inverno de Matemática 

14/03/2024, 14:45 — 15:00 — Sala P3.10, Pavilhão de Matemática Online
Sérgio Marcelino, Instituto Superior Técnico

Infinite-Valued Logics and Applications

The growing developments of computer science and artificial intelligence, and their applications in critical areas, demand new formal methods (read logics) able to cope with the reasoning tasks involved in their analysis. To meet the needs of the applications it is fundamental to find balances between the expressivity of the considered logics and the complexity of their associated decision problems.

Many reasoning activities can be indirectly encoded into classically based logics and benefit from dedicated SAT- or SMT-solvers. However, this is not the only possible approach and non-classical logics provide a range of alternatives. For example, there are infinite-valued fuzzy logics, taking values in the real unit interval, whose computational complexity does not exceed the complexity of the propositional classical logic which is 2-valued. These logics are used to directly reason under ambiguity and uncertainty, and play an important role in many applied scenarios as in modern neuro-symbolic approaches to AI. We will discuss some possible dissertation topics combining the study of many-valued logics and their applications.

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14H45_SM_h.pdf