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A Tractability Result for Reasoning with Incomplete First-Order Knowledge Bases

In previous work, Levesque proposed an extension to classical databases that would allow for a certain form of incomplete first-order knowledge. Since this extension was sufficient to make full logical deduction undecidable, he also proposed an alternative reasoning scheme with desirable logical properties. He also claimed (without proof) that this reasoning could be implemented efficiently using database techniques such as projections and joins. In this paper, we substantiate this claim and show how to adapt a bottom-up database query evaluation algorithm for this purpose, thus obtaining a tractability result comparable to those that exist for databases.