Inference engines for rule-based systems attempt to match facts in working memory with rule antecedents. Rules for which matching can be performed are considered for execution (firing). Matching is well defined when the arguments of each proposition used in facts and rules can assume only a single value [Forgy 1982]. However, the matching of propositions whose arguments can assume interval values, interval-valued-argument propositions, requires expansion of the standard definition of pattern matching. The complexity of the problem is compounded by the fact that two intervals may be related in a number of ways. This paper describes a powerful knowledge representation which can be used for expressing interval-valued arguments. In addition, it specifies an approach for performing matching between interval-valued-argument propositions. This approach was inspired by the authors' need to perform matching on propositions whose arguments were ranges of real values and by J.F. Allen's work in temporal reasoning [Allen 1983]. It represents an expansion of current matching techniques. Several examples are provided to illustrate the power and utility of this approach. Many of these concepts have been implemented in a rule-based expert system shell called the Generalized Adaptive Learning Environment (GALE), a research tool being used to study machine learning in diagnostic expert systems.
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