The recent development of abstract algebraic logic has led to a reconsideration of the universal algebraic theory of ordered algebras from a new perspective. The familiar equational logic of Birkhoff can be naturally viewed as one of the deductive systems that constitute the main object of study in abstract algebraic logic; technically it is a deductive system of dimension two. Large parts of u...

This paper introduces a temporal relational algebra as a query language for temporal deductive databases, i.e., Temporal Datalog programs. In Temporal Datalog programs, temporal relationships among data are formalized through temporal operators, not by an explicit reference to time. The minimum model of a given Temporal Datalog program is regarded as the temporal database the program models int...

We offer a new definition of $varepsilon$-orthogonality in normed spaces, and we try to explain some properties of which. Also we introduce some types of $varepsilon$-orthogonality in an arbitrary  $C^ast$-algebra $mathcal{A}$, as a Hilbert $C^ast$-module over itself, and investigate some of its properties in such spaces. We state some results relating range-kernel orthogonality in $C^*$-algebras.

in this note, we characterize chebyshev subalgebras of unital jb-algebras. we exhibit that if b is chebyshev subalgebra of a unital jb-algebra a, then either b is a trivial subalgebra of a or a= h r .l, where h is a hilbert space

Hilbert algebras are important tools for certain investigations in algebraic logic since they can be considered as fragments of any propositional logic containing a logical connective implication and the constant 1 which is considered as the logical value “true”. The concept of Hilbert algebras was introduced in the 50-ties by L. Henkin and T. Skolem (under the name implicative models) for inve...

‎Let $mathscr{L}$ be a commutative subspace lattice generated by finite many commuting independent nests on a complex separable Hilbert space $mathbf{H}$ with ${rm dim}hspace{2pt}mathbf{H}geq 3$‎, ‎${rm Alg}mathscr{L}$‎ ‎the CSL algebra associated with $mathscr{L}$ and $mathscr{M}$ be an algebra containing ${rm Alg}mathscr{L}$‎. ‎This article is aimed at describing the form of‎ ‎additive mapppi...

B. Magajna and J. Schweizer showed in 1997 and 1999, respectively, that C*-algebras of compact operators can be characterized by the property that every norm-closed (and coinciding with its biorthogonal complement, resp.) submodule of every Hilbert C*-module over them is automatically an orthogonal summand. We find out further generic properties of the category of Hilbert C*-modules over C*-alg...