@ARTICLE{BrinkSchmidt92,
AUTHOR = {Brink, C. and Schmidt, R. A.},
YEAR = {1992},
TITLE = {Subsumption Computed Algebraically},
JOURNAL = {Computers and Mathematics with Applications},
VOLUME = {23},
NUMBER = {2--5},
PAGES = {329--342},
NOTE = {Also in Lehmann, F. (ed.) (1992), {\em Semantic Networks in
Artificial Intelligence}, Modern Applied Mathematics and Computer
Science Series {\bf 24}, Pergamon Press, Oxford, UK. Also available as
Technical Report TR-ARP-3/90, Automated Reasoning Project, Research
School of Social Sciences, Australian National University, Canberra,
Australia.},
ABSTRACT = {This paper deals with terminological representation
languages for {\sc kl-one}-type knowledge representation systems. Such
languages are based on the two primitive syntactic types called concepts
and roles, which are usually represented model-theoretically as sets and
binary relations respectively. Rather than following the
model-theoretic route, we show that the semantics can be naturally
accommodated in the context of an equational algebra of relations
interacting with sets. Equational logic is then a natural vehicle for
computing subsumptions, both of concepts and of roles. We thus propose
the {\em algebraic} rather than model-theoretic computation of
subsumption. }
}