In this paper we propose a semiring-theoretic approach to MV-algebras based on the connection between such algebras and idempotent semirings established in [11] and improved in [4] — such an approach naturally imposing the introduction and study of a suitable corresponding class of semimodules, called MV-semimodules. Besides some basic yet fundamental results of more general interest for semiri...

The interplay between topological hyperconvex spaces and sigma-finite measures in such gives rise to a set of analytical observations. This paper introduces the Noetherian class k-finite k-hyperconvex subspaces (NHCs) admitting countable finite covers. A measure is constructed sigma-semiring NHC under ordering NHCs. relation maintains irreflexive anti-symmetric algebraic properties while retain...

This paper constructs a logic of soft constraints where the set of degrees of preference forms a partially ordered set. When the partially ordered set is a distributive lattice, this reduces to the idempotent semiring-based CSP approach, and the lattice operations can be used to define a sound and complete proof theory. For the general case, it is shown how sound and complete deduction can be p...

In this paper, we attempt to investigate the connection between various types of ideals (for examples $(m, n)$-ideal, bi-ideal, interior ideal, quasi ideal, prime ideal and maximal ideal) of an ordered semigroup $(S,cdot ,leq)$ and the correspond hyperideals of its EL-hyperstructure $(S,*)$ (if exists). Moreover, we construct the class of EL-$Gamma$-semihypergroup associated to a partially orde...

One of the most well-known induction principles in computer science is the fixed point induction rule, or least pre-fixed point rule. Inductive ∗semirings are partially ordered semirings equipped with a star operation satisfying the fixed point equation and the fixed point induction rule for linear terms. Inductive ∗-semirings are extensions of continuous semirings and the Kleene algebras of Co...

Representing and reasoning with an agent’s preferences is important in many applications of constraints formalisms. Such preferences are often only partially ordered. One class of soft constraints formalisms, semiring-based CSPs, allows a partially ordered set of preference degrees, but this set must form a distributive lattice; whilst this is convenient computationally, it considerably restric...

Trust management systems support the provision of the required levels of assurance in a flexible and scalable manner by locally discriminating between the entities with which a principal should interact. However, there is a tension between the preservation of privacy and the controlled release of information when an entity submits credentials for establishing and verifying trust. Furthermore, t...

A *–k-semiring is an ordered semiring S equipped with a star operation such that for any a,b 2 S, a*b is the least fixed point of the linear mapping x # ax + b over S. The notion of *–k-semirings is a generalization of several important concepts such as continuous semirings, (weak) inductive *-semirings and the Kleene algebras of Conway and Kozen. We investigate several basic properties of *–k-...