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The relationship between less detailed and more detailed versions of data is one of the major issues in processing geographic information. Fundamental to much work in model-oriented generalization, also called semantic generalization, is the notion of an equivalence relation. Given an equivalence relation on a set, the techniques of rough set theory can be applied to give generalized descriptio...

Based on the equivalence relation on a linear space, in this paper we introduce the definition of rough convex cones and rough convex fuzzy cones and discuss some of the fundamental properties of such rough convex cones.

In this paper there is proposed a method of partition the attributes of relation scheme in equivalence classes and in nonredundant equivalence classes. Several properties of these equivalence classes are proved. Their properties serve as the basis for an algorithm with a polynomial complexity, which determines the prime attributes of a database schema.

In [2] Lakoff and Nuñez develop a basis for the cognitive science of embodied mathematics. For them, the abstract concepts and reasonings of mathematics are grounded in the conceptual processes that we develop in our interaction with the physical world. Through the use of conceptual metaphor these cognitive devices are projected to the realm of mathematical reasoning. In this paper we employ th...

In this paper, we introduce the notion of N -graphs and describe methods of their construction. We prove that the isomorphism between N -graphs is an equivalence relation (resp. partial order relation). We then introduce the concept of N -line graphs and discuss some of their fundamental properties.

We introduce and study the notion of functorial Borel complexity for Polish groupoids. Such a notion aims at measuring the complexity of classifying the objects of a category in a constructive and functorial way. In the particular case of principal groupoids such a notion coincide with the usual Borel complexity of equivalence relations. Our main result is that on one hand for Polish groupoids ...

The purpose of this paper is to compute of fundamental relations of hypergroups. In this regards first we study some basic properties of fundamental relation of hypergroups, then we show that any given group is isomorphic to the fundamental group of a nontrivial hypergroup. Finally we study the connections between categories of hypergroups and groups via the fundam...

Baeten, Bergstra, and Klop (and later Caucal) have proved the remarkable result that bisimulation equivalence is decidable for irredundant context-free grammars. In this paper we provide a much simpler and much more direct proof of this result using a tableau decision method involving goal-directed rules. The decision procedure also provides the essential part of the bisimulation relation betwe...