A Decomposition Rule for Decision Procedures by Resolution-based Calculi

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A Decomposition Rule for Decision Procedures by Resolution-based Calculi (2004)

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by Ullrich Hustadt , Boris Motik , Ulrike Sattler

Venue:	In: Proc. 11th Int. Conf. on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR
Citations:	36 - 11 self

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@INPROCEEDINGS{Hustadt04adecomposition,
    author = {Ullrich Hustadt and Boris Motik and Ulrike Sattler},
    title = {A Decomposition Rule for Decision Procedures by Resolution-based Calculi},
    booktitle = {In: Proc. 11th Int. Conf. on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR},
    year = {2004},
    pages = {21--35},
    publisher = {Springer}
}

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Abstract

Abstract. Resolution-based calculi are among the most widely used calculi for theorem proving in first-order logic. Numerous refinements of resolution are nowadays available, such as e.g. basic superposition, a calculus highly optimized for theorem proving with equality. However, even such an advanced calculus does not restrict inferences enough to obtain decision procedures for complex logics, such as SHIQ. In this paper, we present a new decomposition inference rule, which can be combined with any resolution-based calculus compatible with the standard notion of redundancy. We combine decomposition with basic superposition to obtain three new decision procedures: (i) for the description logic SHIQ, (ii) for the description logic ALCHIQb, and (iii) for answering conjunctive queries over SHIQ knowledge bases. The first two procedures are worst-case optimal and, based on the vast experience in building efficient theorem provers, we expect them to be suitable for practical usage. 1

Keyphrases

resolution-based calculus decision procedure decomposition rule basic superposition theorem proving new decomposition inference rule numerous refinement standard notion first-order logic new decision procedure building efficient theorem provers shiq knowledge base vast experience complex logic conjunctive query description logic alchiqb description logic shiq advanced calculus practical usage

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