On centers and state spaces of logics
On central atoms of Archimedean atomic lattice effect algebras
If element of a lattice effect algebra is central, then the interval is a lattice effect algebra with the new top element and with inherited partial binary operation . It is a known fact that if the set of central elements of is an atomic Boolean algebra and the supremum of all atoms of in equals to the top element of , then is isomorphic to a direct product of irreducible effect algebras ([16]). In [10] Paseka and Riečanová published as open problem whether is a bifull sublattice...
On closed classes of quasilinear functions
On collections of almost disjoint families
On complete -algebras
On complete-cocomplete subspaces of an inner product space
In this note we give a measure-theoretic criterion for the completeness of an inner product space. We show that an inner product space is complete if and only if there exists a -additive state on , the orthomodular poset of complete-cocomplete subspaces of . We then consider the problem of whether every state on , the class of splitting subspaces of , can be extended to a Hilbertian state on ; we show that for the dense hyperplane (of a separable Hilbert space) constructed by P. Pták and...
On connections between information systems, rough sets and algebraic logic
In this note we remark upon some relationships between the ideas of an approximation space and rough sets due to Pawlak ([9] and [10]) and algebras related to the study of algebraic logic - namely, cylindric algebras, relation algebras, and Stone algebras. The paper consists of three separate observations. The first deals with the family of approximation spaces induced by the indiscernability relation for different sets of attributes of an information system. In [3] the family of closure operators...
On decidability of one class of boolean formulas
On effective presentations of formal concept lattices.
On Equational Classes of Algebraic Versions of Logic I.
On exact conditionals.
On extension properties for observables
On fields and ideals connected with notions of forcing
We investigate an algebraic notion of decidability which allows a uniform investigation of a large class of notions of forcing. Among other things, we show how to build σ-fields of sets connected with Laver and Miller notions of forcing and we show that these σ-fields are closed under the Suslin operation.
On free Boolean vectors.
On free -algebras
In the present paper we show that free -algebras can be constructed by applying free abelian lattice ordered groups.
On functions that cannot be mv-truth values in algebraic structures.
It is shown, in a general frame and playing with idempotency, that in order to have on a given lattice a Multiple Valued Logic preserving the lattice structure, the only t-norms and t-conorms allowing to modelize the truth values of a v b, a ^ b and a --> b are Min and Max, respectively, apart from ordinal sums.
On fuzzy -algebras
The fuzzification of (normal) -subalgebras is considered, and some related properties are investigated. A characterization of a fuzzy -algebra is given.
On fuzzy ideals in Hilbert algebras.
On generalizations of fuzzy metric spaces
The aim of the paper is to present three-variable generalizations of fuzzy metric spaces in sense of George and Veeramani from functional and topological points of view, respectively. From the viewpoint of functional generalization, we introduce a notion of generalized fuzzy 2-metric spaces, study their topological properties, and point out that it is also a common generalization of both tripled fuzzy metric spaces proposed by Tian et al. and -fuzzy metric spaces proposed by Sedghi and Shobe. Since...
On generating and concreteness in quantum logics