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Transformation of binary relations
Proceedings of the Sixth International Conference on Computer Supported Cooperative Work in Design (IEEE Cat. No.01EX472), 2002In the object-oriented paradigm, as complexity rises, the cost of developing and maintaining software systems grows exponentially. This complexity emerges from the continuous evolution of software systems to cope with changing requirements. This crucial problem can be dealt with by performing an active transformation of the elements (i.e.
Jamal Said, Eric Steegmans
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Compact binary relation representations with rich functionality
Information and Computation, 2013 Binary relations are an important abstraction arising in many data representation problems. The data structures proposed so far to represent them support just a few basic operations required to fit one particular application.
Gonzalo Navarro +2 more
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Binary Relations and Permutation Groups
Mathematical Logic Quarterly, 1995AbstractWe discuss some new properties of the natural Galois connection among set relation algebras, permutation groups, and first order logic. In particular, we exhibit infinitely many permutational relation algebras without a Galois closed representation, and we also show that every relation algebra on a set with at most six elements is Galois closed
Hajnal Andréka +2 more
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1974
A binary relation defined on a set containing n elements can be interpreted as an n × n incidence matrix. Such matrix may be taken either over the two element boolean algebra or over the field Z2 . The main purpose of this paper is to study the incidence subgroups and the collineation subgroups of semigroups of binary relations.
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A binary relation defined on a set containing n elements can be interpreted as an n × n incidence matrix. Such matrix may be taken either over the two element boolean algebra or over the field Z2 . The main purpose of this paper is to study the incidence subgroups and the collineation subgroups of semigroups of binary relations.
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On a binary relation inference network
[1991] Proceedings. The Fifth International Parallel Processing Symposium, 2002Many human and machine reasoning tasks require complicated inferences between objects and events, in which the constituting inference processes depend in turn on successive inferences on more basic binary relations. Given a set of n binary relations between m different objects or events, it is possible to infer other consistent binary relations, to ...
Kai-Pui Lam, Crystal J. Su
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An algebraic approach to binary relations
Asian-European Journal of Mathematics, 2015Several attempts were made to assign to a given binary relation a certain binary operation in order to allow an algebraic approach for investigating binary relations. However, the previous attempts by the first two authors were restricted to the case of so-called directed binary relations.
Chajda, Ivan +2 more
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STRUCTURE OF FUZZY BINARY RELATIONS
Fuzzy Sets and Systems, 1981The structure of fuzzy binary relations of indifference and preference is studied. The full description of fuzzy equivalence relations in terms of fuzzy partitions is given. All possible logical relations between various transitivity properties of fuzzy preferences are established.
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On binary operators and their derived relations
BIT, 1988Considering a list of abstract binary operations and relations, the author gives a sequence of seven simple to prove, but interesting and very useful theorems, which appear frequently in algebra and other fields. All results are known, but the approach is nice and appropriate for teaching, with a good generality.
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The second calculus of binary relations
1993We view the Chu space interpretation of linear logic as an alternative interpretation of the language of the Peirce calculus of binary relations. Chu spaces amount to K-valued binary relations, which for K=2n we show generalize n-ary relational structures.
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Postulates for the calculus of binary relations
Journal of Symbolic Logic, 1940The theory of relations was discussed, along with the theory of classes, by Peirce and Schröder. While the calculus of classes has subsequently been presented (by Couturat, and by Huntington) as an abstract mathematical system, no similar formulation has been published of the calculus of relations.
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