Authors 
Title 
Status, Abstract 

Gunther Schmidt 
Relations and Partialities.pdf .bib 
Extended Abstractof an article to appear inJournal of Logic and Algebraic Programming,submitted for RelMiCS 8, Relational Methods in Computer ScienceFebruary 2226, 2005, St. Catharines, Ontario, Canada 

University of the Federal Armed Forces Munich 85577 Neubiberg, Germany schmidt@informatik.unibwmuenchen.de 

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 nonstrict
transfer of partialities in processes
are latticecontinuous
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. 