Reasoning with taxonomies
Verónica Dahl, Stewart Andrew Fall · 1996
Taxonomies are prevalent in a multitude of fields, including ecology, linguistics, programming languages, databases, and artificial intelligence. In this thesis, we focus on several aspects of reasoning with taxonomies, including the management of taxonomies in computers, extensions of partial orders to enhance the taxonomic information that can be represented, and novel uses of taxonomies in several applications. The first part of the thesis deals with theoretical and implementational aspects of representing, or encoding, taxonomies. our contributions include (i) a formal abstraction of encoding that encompasses all current techniques; (ii) a generalization of the technique of modulation that enhances the efficiency of this strategy for encoding and reduces its brittleness for dynamic taxonomies; (iii) the development of sparse logical terms as a universal implementation for encoding that is supported by a theoretical and empirical analysis demonstrating their efficiency and flexibility. The second part explores our contributions to the application and extension of taxonomic reasoning in knowledge representation, logic programming, conceptual structures and ecological modeling. We formalize extensions to partial orders that increase the ability of systems to express taxonomic knowledge. We develop a generalization of equality constraints among logic variables that induces a partial order among equivalence classes of variables. For graphic knowledge representation formalisms, we develop techniques for organizing the derived hierarchy among graphs in the knowledge base. Finally, we organize abstract models of landscapes in a taxonomy that provides a framework for systematically cataloging and analyzing landscape patterns.