Kevin Knight
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Abstract
The unification problem and several variants are presented. Various algorithms and data structures are discussed. Research on unification arising in several areas of computer science is surveyed; these areas include theorem proving, logic programming, and natural language processing. Sections of the paper include examples that highlight particular uses of unification and the special problems encountered. Other topics covered are resolution, higher order logic, the occur check, infinite terms, feature structures, equational theories, inheritance, parallel algorithms, generalization, lattices, and other applications of unification. The paper is intended for readers with a general computer science background—no specific knowledge of any of the above topics is assumed.
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Reviews
Alfs T. Berztiss
Surveys generally focus on a problem and examine various techniques for dealing with the problem. Much rarer, and requiring much greater erudition, is a survey that focuses on a technique and examines its uses in various application areas. This survey is of the latter type, and it can be taken as a model for such surveys. The reader will be particularly helped by the author's gift for exposition—he provides easily understood intuitive explanations for many of the harder aspects of unification. The bibliography is extensive (168 items) and, since most sections contain a discussion of current research, the survey can serve not only a novice, but also somebody experienced in one of the application domains who wants a broader appreciation of the topic. Unification is the technique of finding an object that fits two descriptions, and the primary concern with this technique has been in theorem proving by resolution. The successful application of the resolution principle requires a fast unification algorithm, and the first part of the survey deals with the history of unification algorithms, in which their complexity was reduced from exponential to linear time. The survey contains version of an early exponential algorithm and an almost linear algorithm. In all, 4 of the 13 sections of the survey deal with implementation. Seven sections consider applications. The standard applications in theorem proving and logic programming are, of course, covered. The author puts most emphasis on the use of unification in natural language processing (NLP), however. This emphasis is understandable because NLP is the author's research area, but one can question whether the merging of concept structures (view integration in database terminology, see Batini et al. [1]) is really unification. One of the remaining two sections examines unification in the framework of lattice theory, with generalization introduced as a dual of unification. The other section contains a list of the properties of unification and indicates research trends.
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