UBC Theses and Dissertations

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UBC Theses and Dissertations

An approach to the organization of taxonomies Bishop, Graig David


The ISA hierarchy used by present day inferential database systems is deficient in that it does not represent a variety of domain relationships (type relationships). Such hierarchies associate explicitly defined sets with the leaves of a tree. Non-leaf nodes in the tree inherit members from their child nodes. In keeping with the use of sets, this paper gives motivation for having type relationships other than subset. Included are union, intersection and a disjointness condition. A formalism for the typed database (TDB) is given, using the monadic first order predicate calculus as its theoretical basis. Non-unit formulae represent intensional (general) information about the world being represented and unit ground clauses represent extensional (specific) information. Predicates represent types, and constant symbols represent set members. This is connected to the set concept via predicate extensions. The extension is that set of constant symbols which are provable as arguments to the given predicate. Given the so-called concreteness condition and consistency of the TDB, the desired set theoretic relationships (union, intersection and disjointness) of predicate extensions follow. This strengthens the link between the formalism of the predicate calculus and the more natural set representation. A canonical form of a TDB is shown that admits an appropriate machine representation. Using this is can be determined if a constant symbol as an argument to a given predicate is provable (domain membership) in constant time. An update algorithm is developed and is shown to be correct in that it maintains concreteness and consistency. Thus the TDB is shown to be a practical generalization of the ISA hierarchy but is considerably more expressive.

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