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

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.