...-... Algebras.
-model and distributivity in Boolean algebras
-theories of Boolean algebras
A Cantor-Bernstein theorem for -complete MV-algebras
The Cantor-Bernstein theorem was extended to -complete boolean algebras by Sikorski and Tarski. Chang’s MV-algebras are a nontrivial generalization of boolean algebras: they stand to the infinite-valued calculus of Łukasiewicz as boolean algebras stand to the classical two-valued calculus. In this paper we further generalize the Cantor-Bernstein theorem to -complete MV-algebras, and compare it to a related result proved by Jakubík for certain complete MV-algebras.
A categorical view at generalized concept lattices
We continue in the direction of the ideas from the Zhang’s paper [Z] about a relationship between Chu spaces and Formal Concept Analysis. We modify this categorical point of view at a classical concept lattice to a generalized concept lattice (in the sense of Krajči [K1]): We define generalized Chu spaces and show that they together with (a special type of) their morphisms form a category. Moreover we define corresponding modifications of the image / inverse image operator and show their commutativity...
A certain Galois connection and weak automorphisms
A characterization of commutative basic algebras
A basic algebra is an algebra of the same type as an MV-algebra and it is in a one-to-one correspondence to a bounded lattice having antitone involutions on its principal filters. We present a simple criterion for checking whether a basic algebra is commutative or even an MV-algebra.
A characterization of quantic quantifiers in orthomodular lattices.
A Complete Boolean Algebra without Homogeneous or Rigid Factors.
A constructive proof of the Tychonoff's theorem for locales
A duality between algebras of basic logic and bounded representable -monoids
-algebras, introduced by P. Hájek, form an algebraic counterpart of the basic fuzzy logic. In the paper it is shown that -algebras are the duals of bounded representable -monoids. This duality enables us to describe some structure properties of -algebras.
A glimpse of deductive systems in algebra
The concept of a deductive system has been intensively studied in algebraic logic, per se and in connection with various types of filters. In this paper we introduce an axiomatization which shows how several resembling theorems that had been separately proved for various algebras of logic can be given unique proofs within this axiomatic framework. We thus recapture theorems already known in the literature, as well as new ones. As a by-product we introduce the class of pre-BCK algebras.
A groupoid characterization of Boolean algebras
We present a groupoid which can be converted into a Boolean algebra with respect to term operations. Also conversely, every Boolean algebra can be reached in this way.
A logic of injectivity.
A Loomis-Sikorski theorem for logics
A measure theoretic approach to logical quantification
A new approach to representation of observables on fuzzy quantum posets
We give a representation of an observable on a fuzzy quantum poset of type II by a pointwise defined real-valued function. This method is inspired by that of Kolesárová [6] and Mesiar [7], and our results extend representations given by the author and Dvurečenskij [4]. Moreover, we show that in this model, the converse representation fails, in general.
A non-associative generalization of MV-algebras
A note on a function representation of orthomodular posets
A note on ...-categorical model-companions.