On Closed World Data Bases

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 so-called 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.