Relation partition algebra : mathematical aspects of uses and part-of relations

L.M.G. Feijs, R.C. van Ommering

Research output: Contribution to journalArticleAcademicpeer-review

13 Citations (Scopus)

Abstract

Managing complexity in software engineering involves modularisation, grouping design objects into modules, subsystems, etc. This gives rise to new design objects with new ‘use relations’. The lower-level design objects relate to these in a ‘part-of’ relation. But how do ‘use relations’ at different levels of the ‘part-of hierarchy’ relate? We formalise our knowledge on uses and part-of relations, looking for mathematical laws about relations and partitions. A central role is played by an operator /. For a "uses" relation r on a set of objects X and a partitioning into modules viewed as an equivalence ¿, we form a relation r/¿ on the set X/¿. We adopt an axiomatic point of view and investigate a variety of models, corresponding to different abstraction mechanisms and different ways of relating high- and low-level uses relations.
Original languageEnglish
Pages (from-to)163-212
JournalScience of Computer Programming
Volume33
Issue number2
DOIs
Publication statusPublished - 1999

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