An algebraic semantics for possibilistic finite-valued Lukasiewicz logic

MARCOS, MIGUEL ANDRÉS

Milán

Seminario; Seminario Departamento de Informática, Università degli Studi di Milano Statale; 2023

Departamento de Informática, Università degli Studi di Milano Statale

Joint work with M.Busaniche, P.Cordero and R.O.RodriguezPossibility theory is an uncertainty theory devoted to the handling of incomplete informa-tion, and was originally introduced by Zadeh. However, only later on possibilistic logicemerges as a logic utilizing classical formulas associated with degrees of certainty.Possibilistic logic coincides with the modal logic KD45, which is associated to the first-order pseudomonadic fragment over Boolean algebras, that has been already studied by Bezhanishvili. More precisely, the classical possibilistic semantics are based on frames formed by a non-empty set W of possible worlds together with a function p:W?{0,1} known as a normalized possibility distribution. In this work we provide an algebraic semantics for a many valued logic that generalizes pseudomonadic Boolean algebras. When trying to extend the possibilistic logic to the non-classical setting, in order to present a modal many-valued system, the axiom of normality K is no longer valid and, as we shall see in the present work, the axioms D, 4and 5 are not enough to model the system.