...-... Algebras.
[0,1]-Valued Logic: A Natural Generalization of Boolean Logic
A certain Galois connection and weak automorphisms
A Kalmár-style completeness proof for the logics of the hierarchy
The logics of the family := are formally defined by means of finite matrices, as a simultaneous generalization of the weakly-intuitionistic logic and of the paraconsistent logic . It is proved that this family can be naturally ordered, and it is shown a sound and complete axiomatics for each logic of the form . The involved completeness proof showed here is obtained by means of a generalization of the well-known Kalmár’s method, usually applied for many-valued logics.
A new Proof of Prešić's Theorem on Finite Equations
A non commutative generalization of -autonomous lattices
Pseudo -autonomous lattices are non-commutative generalizations of -autonomous lattices. It is proved that the class of pseudo -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 -autonomous lattices can be described as their normal ideals.
A reduction-based theorem prover for 3-valued logic.
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...
A theorem on implication functions defined from triangular norms.
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.
Algebraic closure in continuous logic.
Algèbre du calcul propositionnel trivalent de Heyting
Algèbres de Lukasiewicz symétriques
All General Solutions of Finite Equations
All reproductive solutions of finite equations.
An algebraic completeness proof for Kleene's 3-valued logic
We introduce Kleene's 3-valued logic in a language containing, besides the Boolean connectives, a constant 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...
An ILP model for a monotone graded classification problem
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...
An investigation on the -fold IVRL-filters in triangle algebras
The present study aimed to introduce -fold interval valued residuated lattice (IVRL for short) filters in triangle algebras. Initially, the notions of -fold (positive) implicative IVRL-extended filters and -fold (positive) implicative triangle algebras were defined. Afterwards, several characterizations of the algebras were presented, and the correlations between the -fold IVRL-extended filters, -fold (positive) implicative algebras, and the Gödel triangle algebra were discussed.
Between logic and probability.
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...
Boolean part of BL-algebras
Calcul des séquents et déduction naturelle pour la logique trivalente de Lukasiewicz
Classification of Maps by Their Membership in Maximal Clones That Contain Minimum and Complement