The talk will began remembering results on papers [22, 15, 16] where the authors model uncertainty measures as fuzzy modalities on a many-valued residuated logics. the basic idea is that uncertainty measures is not a truth degree but could be interpreted as a truth degree of the fuzzy sentence ”the probability of φ”. The main properties being that the language does not allow nested modalities a...

In this paper, we will develop an algebraic study of substructural propositional logics over FLew, i.e. the logic which is obtained from the intuitionistic logics by eliminating the contraction rule. Our main technical tool is to use residuated lattices as the algebraic semantics for them. This enables us to study different kinds of nonclassical logics, including intermediate logics, BCK-logics...

We consider first-order infinite-valued Łukasiewicz logic and its expansion, rational Pavelka RPL∀. From the viewpoint of provability, we compare several Gentzen-type hypersequent calculi for these logics with each other Hájek’s Hilbert-type same logics. To facilitate comparing previously known logics, define two new analytic RPL∀ include them in our comparison. The key part comparison is a den...

A filter of a sentential logic S is Leibniz when it is the smallest one among all the S-filters on the same algebra having the same Leibniz congruence. This paper studies these filters and the sentential logic S+ defined by the class of all S-matrices whose filter is Leibniz, which is called the strong version of S , in the context of protoalgebraic logics with theorems. Topics studied include ...

We consider propositional logic programs with negations. We deene notions of constructive transformation and constructive completion of a program. We use these notions to characterize SLDNF-resolution in classical, intuitionistic and intermediate logics, and also to derive a characterization in modal logics of knowledge. We show that the three-valued and four-valued x-point or declarative seman...

We look at extensions (i.e., stronger logics in the same language) of the Belnap-Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap-Dunn and do not coincide with any of the known extensions (Kleene’s logics, Priest’s logic of paradox). We characterize the reduced algebraic models of these new logics and prove a completeness result for the first ...

This paper presents an analysis of Gödel logics with countable truth value sets with respect to the topological and order theoretic structure of the underlying truth value set. Gödel logics have taken an important rôle in various areas of computer science, e.g. logic programming and foundations of parallel computing. As shown in a forthcoming paper all these logics are not recursively axiomatiz...