The most heavily used methods to answer conjunctive queries on binary relations (such as the one associating keywords with web pages) are based on inverted lists stored in sorted arrays and use variants of binary search. We show that a succinct representation of the binary relation permits much better results, while using space within a lower order term of the optimal. We apply our results not ...

Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation. We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy binary relation on a crisp topological space.

We consider n ary relative products jn on subsets of a re exive and symmetric binary relation and de ne a variety of weakly associative relation algebras with polyadic composi tion operations WA A theorem that any A WA is representable over a re exive and symmetric relation is proved We also show that the equational theory of WA is decidable

For simplicity we adopt the following convention: I, X denote sets, M denotes a many sorted set indexed by I, R1 denotes a binary relation on X, and E1, E2, E3 denote equivalence relations of X. We now state the proposition (1) (E1 ⊔ E2) ⊔ E3 = E1 ⊔ (E2 ⊔ E3). Let X be a set and let R be a binary relation on X. The functor EqCl(R) yielding an equivalence relation of X is defined as follows: (De...

Binary relation extraction methods have been widely studied in recent years. However, few methods have been developed for higher n-ary relation extraction. One limiting factor is the effort required to generate training data. For binary relations, one only has to provide a few dozen pairs of entities per relation, as training data. For ternary relations (n=3), each training instance is a triple...

In original rough set theory, the notion of set approximation has been introduced by using indiscernibility relation defined on the set of objects. In some cases, it is necessary to generalize indiscernibility relation by using some other binary relations. In this paper, we consider similarity relations and tolerance relations among objects. These binary relations are defined from some similari...

Old welfare economics, Pigou (1920), considered social welfare as a cardinal notion, while new welfare economics,1 Little (1950) and Graaff (1957), consider social welfare as an ordinal notion. An in depth introduction to welfare economics and a discussion of the transition from old to new welfare economics, is expounded quite well by Samuelson (1947, Chap. 8, pp. 203–219, and pp. 249–252). For...

In an important contribution to the problem of aggregating infinite utility streams, Svensson (1980) shows the existence of a social welfare relation—a reflexive, transitive and complete binary relation over all possible infinite utility streams—that accommodates the axioms of Pareto and intergenerational equity. This possibility result is in sharp contrast with the seminal contribution by Diam...

Different partial hypergroupoids are associated with binary relations defined on a set H. In this paper we find sufficient and necessary conditions for these hypergroupoids in order to be reduced hypergroups. Given two binary relations and on H we investigate when the hypergroups associated with the relations ∩ , ∪ and are reduced. We also determine when the cartesian product of two hypergroupo...

Many data models do not directly support -ary relationships. In most cases, they are either reduced to some of their binary projections or directly translated into an -ary “relationship relation” in the relational model. This paper addresses the reification of an -ary relationship into a new class with binary relationships and studies the preservation of semantics in the translation. It shows t...