Relations and Partialities

Authors

Title

Status, Abstract

Gunther Schmidt

Relations and Partialities

.pdf .bib
Extended Abstract
of an article to appear in
Journal of Logic and Algebraic Programming,
submitted for
RelMiCS 8, Relational Methods in Computer Science
February 22-26, 2005, St. Catharines, Ontario, Canada

Department of Computing Science
University of the Federal Armed Forces Munich
85577 Neubiberg, Germany
schmidt@informatik.unibw-muenchen.de
October 2004 We define the concept of partiality to cope with partial availability of arguments and results of program steps. To this end, relation algebras are investigated for which, in addition to the identity I, a specific type of an ordering E is given in order to model increasing degrees of availability. It turns out that functions regulating non-strict transfer of partialities in processes are lattice-continuous with respect to such orderings.
One may also consider partialities with regard to their "atomic" constituents. We exhibit how relations between the atomic constituents before and after a process step are represented by such continuous partiality transfer functions. Our result is that they are images of a multiplicative embedding into a larger relation algebra.

Authors	Title	Status, Abstract
Gunther Schmidt	Relations and Partialities .pdf .bib	Extended Abstract of an article to appear in Journal of Logic and Algebraic Programming, submitted for RelMiCS 8, Relational Methods in Computer Science February 22-26, 2005, St. Catharines, Ontario, Canada
Department of Computing Science University of the Federal Armed Forces Munich 85577 Neubiberg, Germany schmidt@informatik.unibw-muenchen.de	October 2004	We define the concept of partiality to cope with partial availability of arguments and results of program steps. To this end, relation algebras are investigated for which, in addition to the identity I, a specific type of an ordering E is given in order to model increasing degrees of availability. It turns out that functions regulating non-strict transfer of partialities in processes are lattice-continuous with respect to such orderings. One may also consider partialities with regard to their "atomic" constituents. We exhibit how relations between the atomic constituents before and after a process step are represented by such continuous partiality transfer functions. Our result is that they are images of a multiplicative embedding into a larger relation algebra.