ABSTRACT Deductive question-answering systems generally evaluate queries under one of two possible assumptions which we in this paper refer to as the open and closed world assumptions. The open world assumption corresponds to the usual first order approach to query evaluation: Given a data base DB and a query Q, the only answers to Q are those which obtain from proofs of Q given DB as hypotheses. Under the closed world assumption, certain answers are admitted as a result of failure to find a proof. More specifically, if no proof of a positive ground literal exists, then the negation of that literal is assumed true. In this paper, we show that closed world evaluation of an arbitrary query may be reduced to open world evaluation of socalled atomic queries. We then show that the closed world assumption can lead to inconsistencies, but for Horn data bases no such inconsistencies can arise. Finally, we show how for Horn data bases under the closed world assumption purely negative clauses are irrelevant for deductive retrieval and function instead as integrity constraints. INTRODUCTION Deductive question-answering systems generally evaluate queries under one of two possible assumptions which we in this paper refer to as the open and closed world assumptions.

Artificial intelligence tasks which can be formulated as constraint satisfaction problems, with which this paper is for the most part concerned, are usually solved by backtracking.

We use the idea of a "dimension," how they are generated.

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The junction categories and link planting rules of SEE lyzed. That, however, is not the main point; it is merely typical of the way in which the program developed by a process of finding counter-examples that both invalidated old rules and hinted at new ones (Winston, 1973). The need to add and modify rules almost continuously to handle exceptions suggests that there is a basic flaw in the design. The flaw seems to be that Guzman used locally computed picture predicates as evidence for global scene-based properties. To avoid this one must ask what do the lines in the picture depict?

Artificial intelligence, long a topic of basic computer science research, is now being applied to problems of scientific, technical, and commercial interest. Some consultation programs, though limited in versatility, have achieved levels of performance rivaling those of human experts. A collateral benefit of this work is the systematization of previously unformalized knowledge in areas such as medical diagnosis and geo!ogy.