Tommaso Flaminio: Local reduction of probabilistic reasoning to Lukasiewicz logic and MV-algebras
We will present proof-theoretical and algebraic properties for the probability logics FP(C,L) and FP(L,L), meant for reasoning on the uncertainty of Classical and Lukasiewicz events, respectively. Methodologically speaking, we will consider a translation function between formulas of these logics to the propositional language of Lukasiewicz calculus that allows us to apply the latter and the well developed theory of MV-algebras directly to probabilistic reasoning. More precisely, leveraging on such translation map, we will show proof-theoretical properties for FP(L,L) and introduce a class of algebras with respect to which FP(C,L) and FP(L,L) are proved to be locally sound and complete.
Tommaso Flaminio is Tenured Scientist (Científico Titular) at the Artificial Research Institute (IIIA) of the Spanish National Research Council (CSIC), Barcelona, Spain.