Two notes on locally finite cylindric algebras
Two-valued states on a concrete logic and the additivity problem
Über den Untergruppenverband der symmetrischen Gruppe, den Unterhalbgruppenver-band der symmetrischen Halbgruppe und den Unter-algebrenverband der Postchen Algebra.
Ueber die von drei Moduln erzeugte Dualgruppe
Ultra -ideals in lattice implication algebras
We define an ultra -ideal of a lattice implication algebra and give equivalent conditions for an -ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra -ideal.
Ultra -Ideals in lattice implication algebras and -algebras
A mistake concerning the ultra -ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an -ideal to be an ultra -ideal are given. Moreover, the notion of an -ideal is extended to -algebras, the notions of a (prime, ultra, obstinate, Boolean) -ideal and an -ideal of an -algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in -algebra: (1) prime proper -ideal and Boolean -ideal,...
Uncertainty relations and state spaces
Une Généralisation Du Théorème De Löwenheim Sur Les Équations De Boole
Une généralisation du théorème de Löwenheim sur les équations de Boole.
Une généralisation du théorème d'omission des types dans les algèbres polyadiques
Uniqueness of bounded observables
Using maximal ideals in the classification of MV-algebras
Utilisation des matrices booléennes pour l'étude des treillis de post
Vague ideals of implication groupoids
We introduce the concept of vague ideals in a distributive implication groupoid and investigate their properties. The vague ideals of a distributive implication groupoid are also characterized.
Validité dans les algèbres de Boole partielles.
Verification of the Formal Concept Analysis.
This paper is concerned with a formal verification of the Formal Concept Analysis framework. We use the PVS system to represent and formally verify some algorithms of this theory. We also develop a method to transform specifications of algorithms based on finite sets into other executable ones, preserving its correctness. We illustrate this method by constructing an executable algorithm to compute an implicational base of the system of implications between attributes of a finite formal context.
Very true operators on MTL-algebras
The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized...
Wajsberg algebras.
We present the basic theory of the most natural algebraic counterpart of the ℵ0-valued Lukasiewicz calculus, strictly logically formulated. After showing its lattice structure and its relation to C. C. Chang's MV-algebras we study the implicative filters and prove its equivalence to congruence relations. We present some properties of the variety of all Wajsberg algebras, among which there is a representation theorem. Finally we give some characterizations of linear, simple and semisimple algebras....
Weak cylindric probability algebras.
Weak products of universal algebras
Weak direct products of arbitrary universal algebras are introduced. The usual notion for groups and rings is a special case. Some universal algebraic properties are proved and applications to cylindric and polyadic algebras are considered.