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...

The notion of soft BCI-implicative ideals and BCI-implicative idealistic soft BCI-algebras is introduced and their basic properties are discussed. Relations between soft ideals and soft BCI-implicative ideals of soft BCI-algebras are provided. Also idealistic soft BCI-algebras and BCI-implicative idealistic soft BCI-algebras are being related. The intersection, union, “AND” operation and “OR” o...

The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. Bounded residuated lattice ordered monoids (Rl-monoids) are common generalizations of BL-algebras, i.e., algebras of the propositional basic fuzzy logic, and Heyting algebras, i.e., algebras of the propositional intuitionistic logic. From the point of view of uncertain i...

We study conditions on a sequence of probability measures {µ n } n on a commutative hyper-group K, which ensure that, for any representation π of K on a Hilbert space Ᏼ π and for any ξ ∈ Ᏼ π , (K π x (ξ)dµ n (x)) n converges to a π-invariant member of Ᏼ π. 1. Introduction. The mean ergodic theorem was originally formulated by von Neu-mann [13] for one-parameter unitary groups in Hilbert space. ...

In this paper, we deal with soft lattice implication algebras based on fuzzy sets. Using the concepts of fuzzy (implicative) filters, (∈,∈∨q)fuzzy (implicative) filters and (∈,∈∨q)-fuzzy (implicative) filters, some characterizations for ∈-soft sets and q-soft sets to be (implicative) filteristic soft lattice implication algebras are established.

a polynomial   1 2 ( , , , ) n f x x x is called multilinear if it is homogeneous and linear in every one of its variables. in the present paper our objective is to prove the following result: let   r be a prime k-algebra over a commutative ring   k with unity and let 1 2 ( , , , ) n f x x x be a multilinear polynomial over k. suppose that   d is a nonzero derivation on r such that ...

Based on the falling shadow theory, the concept of falling fuzzy (implicative) ideals as a generalization of that of a T ∧-fuzzy (implicative) ideal is proposed in MV-algebras. The relationships between falling fuzzy (implicative) ideals and T-fuzzy (implicative) ideals are discussed, and conditions for a falling fuzzy (implicative) ideal to be a T ∧-fuzzy (implicative) ideal are provided. Some...

Let Ω be a multiply Leibniz isometry equipped with a solvable, analytically natural graph. Recent developments in commutative analysis [5, 16] have raised the question of whether every hyper-partial graph is Noetherian and smoothly Poncelet. We show that