Derived relations with exceptions

Abstract

Generalization rules are a powerful and versatile tool to represent knowledge at a high level of abstraction--as opposed to conventional data base systems which use data to represent specific facts. A generalization rule used in conjunction with a relational data base system serves two purposes: first, it represents knowledge of a general nature, and second, it defines the subset of a population of tuples that satisfy the conditions defined in the rule. As a generalization, the knowledge being represented does not depend on any specific facts, but rather it describes information of a general nature about an organization or a phenomenon; as a subset of a population, it describes all those individuals that fall into the generalization given by the rule. A major issue that had not been fully addressed in the literature is the problem of exceptions to generalizations. Exceptions arise naturally in the real world because, by definition, a generalization implies a loss of detail, and because even if it were feasible it is probably not desirable nor convenient to define every possible case in a generalization rule. This dissertation has identified the problems in dealing with exceptions, characterized the types of exceptions, analyzed the issues in storing generalization rules and exceptions, studied the possible conflicts in stored data, and proposed definite solutions. These solutions are given in a mathematical, axiomatic form. A mathematical entity called DRE-algebra has been defined that allows the formal specification of generalization rules, exceptions and data base operations on exceptions. In addition, an implementation has been given as an extension to the SQL data base language.