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Pseudo $\u2606$-autonomous lattices are non-commutative generalizations of $\u2606$-autonomous lattices. It is proved that the class of pseudo $\u2606$-autonomous lattices is a variety of algebras which is term equivalent to the class of dualizing residuated lattices. It is shown that the kernels of congruences of pseudo $\u2606$-autonomous lattices can be described as their normal ideals.

We present a new prover for propositional 3-valued logics, TAS-M3, which is an extension of the TAS-D prover for classical propositional logic. TAS-M3 uses the TAS methodology and, consequently, it is a reduction-based method. Thus, its power is based on the reductions of the size of the formula executed by the F transformation. This transformation dynamically filters the information contained in the syntactic structure of the formula to avoid as much distributions as possible, in order to improve...

Several transformation which enable implication functions in multivalued logics to be generated from conjunctions have been proposed in the literature. It is proved that for a rather general class of conjunctions modeled by triangular norms, the generation process is closed, thus shedding some light on the relationships between seemingly independent classes of implication functions.

We introduce Kleene's 3-valued logic in a language containing, besides the Boolean connectives, a constant $n$ for the undefined truth value, so in developing semantics we can switch from the usual treatment based on DM-algebras to the narrower class of DMF-algebras (De Morgan algebras with a single fixed point for negation). A sequent calculus for Kleene's logic is introduced and proved complete with respect to threevalent semantics. The completeness proof is based on a version of the prime ideal...

Motivation for this paper are classification problems in which data can not be clearly divided into positive and negative examples, especially data in which there is a monotone hierarchy (degree, preference) of more or less positive (negative) examples. We present a new formulation of a fuzzy inductive logic programming task in the framework of fuzzy logic in narrow sense. Our construction is based on a syntactical equivalence of fuzzy logic programs FLP and a restricted class of generalised annotated...

The present study aimed to introduce $n$-fold interval valued residuated lattice (IVRL for short) filters in triangle algebras. Initially, the notions of $n$-fold (positive) implicative IVRL-extended filters and $n$-fold (positive) implicative triangle algebras were defined. Afterwards, several characterizations of the algebras were presented, and the correlations between the $n$-fold IVRL-extended filters, $n$-fold (positive) implicative algebras, and the Gödel triangle algebra were discussed.

Logic and Probability, as theories, have been developed quite independently and, with a few exceptions (like Boole's), have largely ignored each other. And nevertheless they share a lot of similarities, as well a considerable common ground. The exploration of the shared concepts and their mathematical treatment and unification is here attempted following the lead of illustrious researchers (Reichenbach, Carnap, Popper, Gaifman, Scott & Krauss, Fenstad, Miller, David Lewis, Stalnaker, Hintikka...