Gunther Schmidt: RATH-Paper

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Title

Status, Abstract

Gunther Schmidt

Rectangles, Fringes, and Inverses
.pdf .bib

Relational Methods in Computer Science, RelMiCS 10
April 6--12, 2008, Frauenwörth, Germany

Proceedings appeared as Lect. Notes in Comput. Sci. 4988 (352--366)

Fakultät für Informatik
Universität der Bundeswehr München
85577 Neubiberg, Germany
Gunther.Schmidt@UniBw.de August 2007 Relations and graphs are widely used as modeling tools. Relational composition is an associative operation; therefore semigroup considerations often help in relational algebra. We study here some less known such effects and relate them with non-enlargable rectangles inside the relation, i.e., with the basis of concept lattice considerations. The set of points contained in precisely one non-enlargable rectangle makes up the fringe. We show that the fringe sometimes acts as a generalized inverse of a relation. Regular relations have a generalized inverse. They may be characterized by an algebraic formula.

Authors	Title	Status, Abstract
Gunther Schmidt	Rectangles, Fringes, and Inverses .pdf .bib	Relational Methods in Computer Science, RelMiCS 10 April 6--12, 2008, Frauenwörth, Germany Proceedings appeared as Lect. Notes in Comput. Sci. 4988 (352--366)
Fakultät für Informatik Universität der Bundeswehr München 85577 Neubiberg, Germany Gunther.Schmidt@UniBw.de	August 2007	Relations and graphs are widely used as modeling tools. Relational composition is an associative operation; therefore semigroup considerations often help in relational algebra. We study here some less known such effects and relate them with non-enlargable rectangles inside the relation, i.e., with the basis of concept lattice considerations. The set of points contained in precisely one non-enlargable rectangle makes up the fringe. We show that the fringe sometimes acts as a generalized inverse of a relation. Regular relations have a generalized inverse. They may be characterized by an algebraic formula.