We prove “large associativity” of the partial sum in effect algebras and present an overview of distributivity-like properties of partial operations ⊕ and in effect algebras with respect to (possibly infinite) suprema and infima and vice versa generalizing several previous results.

The arithmetic on an extended set of proper and improper intervals presents algebraic completion of the conventional interval arithmetic allowing thus efficient solution of some interval algebraic problems. In this paper we summarize and present all distributive relations, known by now, on multiplication and addition of generalized (proper and improper) intervals.

In this paper we prove that the collection of all weakly distributive lattice ordered groups is a radical class and that it fails to be a torsion class.

E-unification problems are central in automated deduction. In this paper, we consider theories that are extensions of the well-known ACI or ACUI , obtained by adding finitely many homomorphism symbols, or a symbol ‘∗’ that distributes over the ACUIsymbol denoted ‘+’. We first show that when we adjoin a set of commuting homomorphisms to ACUI , unification is undecidable. We then consider the ACU...

This work deals with strong implications (S-implications in short) derived from uninorms continuous at ]0, 1[2. The general expression of such implications is found and several properties are studied. In particular, the distributivity of the Simplications over conjunctive and disjunctive uninorms is investigated.

Relational lattice reduces the set of six classic relational algebra operators to two binary lattice operations: natural join and inner union. We give an introduction to this theory with emphasis on formal algebraic laws. New results include Spight distributivity criteria and its applications to query transformations.

We show that if A is a stable basis algebra satisfying the distributivity condition, then B is a reduct of an independence algebra A having the same rank. If this rank is finite, then the endomorphism monoid of B is a left order in the endomorphism monoid of A.

We consider weighted tree automata over strong bimonoids which are, roughly speaking, semirings without distributivity. We prove sufficient and necessary conditions under which the initial algebra semantics and the run semantics of these automata coincide. We prove closure properties of the class of recognizable tree series, a determinization result, and a characterization of recognizable step ...

Examples of games between two partners with mixed strategies, calculated by the use of the probability amplitude as some vector in Hilbert space are given. The games are macroscopic ,no microscopic quantum agent is supposed. The reason for the use of the quantum formalism is in breaking of the distributivity property for the lattice of yes-no questions arising due to the special rules of games....