We study the complexity of natural equivalence relations on classes of computable structures such as isomorphism and bi-embeddability. We use the notion of tc-reducibility to show completeness of the isomorphism relation on many familiar classes in the context of all Σ1 equivalence relations on hyperarithmetical subsets of ω. We also show that the bi-embeddability relation on an appropriate hyp...

Rough sets were originally proposed in the presence of an equivalence relation. An equivalence relation is sometimes difficult to be obtained in rearward problems due to the vagueness and incompleteness of human knowledge. The purpose of this paper is to introduce and discuss the concept of T -rough semiprime ideal, T -rough fuzzy semiprime ideal and T -rough quotient ideal in a commutative rin...

In practice, we are often interested in order relations (e.g., when we describe preferences) or equivalence relations (e.g., when we describe clustering). Often, we do not have a complete information about the corresponding relation; as a result, we have several relations consistent with our knowledge. In such situations, it is desirable to know which elements a and b are possibly connected by ...

There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown that if the uncertainty perception and the question of when an agent reports that two things are indistinguishable are both carefully modeled, the problems dis...

Given the classification of low dimensional manifolds up to equivalence relations such as diffeomorphism or homeomorphism, one would hope to be able to continue to classify higher dimensional manifolds. Unfortunately, this turns out to be difficult or impossible, and so one solution would be turn to some weaker equivalence relation. One such equivalence relation would be to consider manifolds u...

We introduce the notion of finitary computable reducibility on equivalence relations on the domain ω. This is a weakening of the usual notion of computable reducibility, and we show it to be distinct in several ways. In particular, whereas no equivalence relation can be Π n+2-complete under computable reducibility, we show that, for every n, there does exist a natural equivalence relation which...

Interpretationpartial equivalence relation semanticssemantics

Checking that a given finite state program satisfies a linear temporal logic property is suffering in many cases from a severe space and time explosion. One way to cope with this is to reduce the state graph used for model checking. We define an equivalence relation between infinite sequences, based on infinite traces such that for each equivalence class, either all or none of the sequences sat...

A pair of sentences in different newspaper articles on an event can have one of several relations. Of these, we have focused on two, i.e., equivalence and transition. Equivalence is the relation between two sentences that have the same information on an event. Transition is the relation between two sentences that have the same information except for values of numeric attributes. We propose meth...

The starting point of the paper is the (well-known)observation that the “classical” Rough Set Theory as introduced by PAWLAK is equivalent to the S5 Propositional Modal Logic where the reachability relation is an equivalence relation. By replacing this equivalence relation by an arbitrary binary relation (satisfying certain properties, for instance, reflexivity and transitivity) we shall obtain...