Let $fM(X)$ be the  space of  all finite regular Borel measures on $X$. A general measure algebra is a subspace  of$fM(X)$,which is an $L$-space and has a multiplication preserving the probability measures. Let $cLsubseteqfM(X)$ be a general measure algebra on a locallycompact space $X$. In this paper, we investigate the relation between Arensregularity of $cL$ and the topology of $X$. We  find...

In a recent paper, De Baets et al. have characterized the fuzzytolerance and fuzzy equivalence relations that a given strict order relation iscompatible with. In this paper, we generalize this characterization by consideringan arbitrary (crisp) relation instead of a strict order relation, while payingattention to the particular cases of a reflexive or irreflexive relation. The reasoninglargely ...

In this report we examine results pertaining to Karl Abrahamson’s PDL‖, namely PDL with an interleaving operator, ‖, with respect to an agent programming point of view. We first establish its usefulness in such contexts, before defining a syntax and semantics for the logic, looking at its relation to the regular expression shuffle operator and to PDL itself. We also look at the practical implic...

2. An important concept will be that of a component of a family 2F. Consider the equivalence relation on / generated by the relation R defined by: i'RV'o Fv n Fr T* 0 . Let /* be any equivalence class. Then &* = is, by definition, a component of $F. If Fv and Fv> are in different components, then jp., n Fv> = 0 . This means that 0? has a transversal if and only if every component of ...

Rough sets are efficient for data pre-processing in data mining. Matroids are based on linear algebra and graph theory, and have a variety of applications in many fields. Both rough sets and matroids are closely related to lattices. For a serial and transitive relation on a universe, the collection of all the regular sets of the generalized rough set is a lattice. In this paper, we use the latt...

Coinductive abstract compilation is a novel technique, which has been recently introduced for defining precise type systems for objectoriented languages. In this approach, type inference consists in translating the program to be analyzed into a Horn formula f , and in resolving a certain goal w.r.t. the coinductive (that is, the greatest) Herbrand model of f . Type systems defined in this way a...

This paper is an overview of what the author has learned about the critical group of a graph, including some new results. In particular we discuss the critical group of a graph in relation to that of its line graph when the original graph is regular. We begin by introducing the critical group from various aspects. We then study the subdivision graph and line graph in relation to the critical gr...

Although concept maps have been found to be effective in science education research, these are critiqued for being informal due to informal usage of relation and attribute names thereby resulting in ambiguity. Refined concept mapping, a development over the regular concept mapping is an approach towards introducing rigor and parsimony in representing knowledge. The method proposed suggests to s...

In classical statistical mechanics there is a clear correlation between relaxation to equilibrium and chaos. In contrast, for isolated quantum systems this relation is--to say the least--fuzzy. In this work we try to unveil the intricate relation between the relaxation process and the transition from integrability to chaos. We study the approach to equilibrium in two different many-body quantum...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We study the frame $mathfrak{O}(Min(mathcal{R}L))$ of minimal prime ideals of $mathcal{R}L$ in relation to $beta L$. For $Iinbeta L$, denote by $textit{textbf{O}}^I$ the ideal ${alphainmathcal{R}Lmidcozalphain I}$ of $mathcal{R}L$. We show that sending $I$ to the set of minimal prime ...