Probability logic on many-valued events: standard completeness and (a kind of) algebraic semantics

Abstract: Proving 'standard completeness', that is completeness with respect to a class of algebras based on the real unit interval, has been for a long time a central problem for t-norm based (fuzzy) logics. Elaborated techniques to prove this kind of result have been developed and most of them rely on the fact that totally ordered algebras can be embedded, or just partially embedded, into standard structures. However, when we move from t-norm based logics to probabilistic modal logics based on them, these methods are no longer applicable and it is necessary to consider new ideas to prove standard completeness. In this seminar, besides clarifying what ’standard completeness’ means in the probabilistic setting, we will present the logic FP(L, L), a formalisms that allows to reason about probabilistic statements on events represented as formulas of Lukasiewicz logic, and we prove it to be standard complete. Further elaborating on the standard completeness for FP(L, L) we will also present results from an ongoing research line that allow to regard a peculiar class of projective MV-algebras as a semantics for that probability logic.

logic

Audience: researchers in the topic

Nonclassical Logic Webinar