Abstract Algebraic Logic is a general theory of the algebraization of deductive systems arising as an abstraction of the well-known Lindenbaum-Tarski process. The notions of logical matrix and of Leibniz congruence are among its main building blocks. Its most successful part has been developed mainly by BLOK, PIGOZZI and CZELAKOWSKI, and obtains a deep theory and very nice and powerful results ...

We define the Łukasiewicz Transform by mean of the partition of unity defined in [4] and semimodules over the semiring reducts of an MV-algebra. Then we describe the “Łukasiewicz Transform Based” (ŁTB) algorithm for image processing, showing some results of its application.

Learning over multi-view data is a challenging problem with strong practical applications. Most related studies focus on the classification point of view and assume that all the views are available at any time. We consider an extension of this framework in two directions. First, based on the BiGAN model, the Multi-view BiGAN (MV-BiGAN) is able to perform density estimation from multi-view input...

The multi-valued exponential bidirectional associative memory (MV-eBAM) has been proposed and proved to be asymptotically stable under certain constraints. Although multi-valued eBAM has been verified to possess high capacity by thorough simulations, the capacity is still unable to be solved analytically. In this paper, an algorithm is proposed to derive the capacity. Some important characteris...

The tensor virial theorem for subsystems is formulated for threecomponent systems and further effort is devoted to a special case where the inner subsystems and the central region of the outer one are homogeneous, the last surrounded by an isothermal homeoid. The virial equations are explicitly written under the additional restrictions: (i) similar and similarly placed inner subsystems, and (ii...

A pseudo-addition in BL-algebras is a binary operation that is associative and non commutative. The aim of this paper is to use the notion of pseudo-addition to study the notion of ideal and fuzzy ideal as a natural generalization of that of ideal and fuzzy ideal in MV-algebras. Using a pseudo-addition, we characterize fuzzy ideals and also obtain a concrete description of the fuzzy ideals gene...

Abstract. A few things are known, and many are unknown, on the automorphism group of the free MV-algebra over n − 1 generators. In this paper we show that this group appears as the stabilizer of 1l in the larger group of all automorphisms of the free cancellative hoop over n generators. Both groups have a dual action on the same space, namely the (n − 1)-dimensional cube. The larger group has a...

In this paper, we introduce the notion of bi-Smarandache BL-algebra, bi-weak Smarandache BL-algebra, bi-Q-Smarandache ideal and bi-Q-Smarandache implicative filter, we obtain some related results and construct quotient of bi-Smarandache BL-algebras via MV-algebras (or briefly bi-Smarandache quotient BL-algebra) and prove some theorems. Finally, the notion of bi-strong Smarandache BL-algebra is ...

We represent every normal-valued GMV-algebra as a GMV-algebra of real-valued functions; we also describe the universal MV-algebras and universal normal-valued GMV-algebras with a prescribed set of components.

A Banach lattice algebra is a Banach lattice, an associative algebra with a sub-multiplicative norm and the product of positive elements should be positive. In this note we study the Arens regularity and cohomological properties of Banach lattice algebras.