Partiality II: Constructed relation algebras

That matrices of relations also obey the rules of relation algebra is well known. When the powerset ordering is considered, partialities may be conceived as lattice-continuous mappings — corresponding to existential images which are often studied independently. A partiality is suited to describe progress of yet partial information or availability. This has already been presented in Schmidt (2006) [11]. Matrices of partialities will considerably improve the possibility to study non-strictness, streams, partial evaluation, and net properties in a compact relation-algebraic form. They seem, however, to lead inevitably to some borderline cases as the Boolean lattice B0 and row-less matrices. It will be shown how these can be fruitfully applied concerning constructions with temporarily non-connected relation algebras.