Removing redundancy from a clause

doi:10.1016/0004-3702(93)90069-N

Artificial Intelligence

Volume 61, Issue 2, June 1993, Pages 263-289

https://doi.org/10.1016/0004-3702(93)90069-N Get rights and content

Abstract

This paper deals with the problem of removing redundant literals from a given clause. We first consider condensing, a weak type of redundancy elimination. A clause is condensed if it does not subsume any proper subset of itself. It is often useful (and sometimes necessary) to replace a non-condensed clause C by a condensation, i.e., by a condensed subset of C which is subsumed by C. After studying the complexity of an existing clause condensing algorithm, we present a more efficient algorithm and provide arguments for the optimality of the new method. We prove that testing whether a given clause is condensed is co-NP-complete and show that several problems related to clause condensing belong to complexity classes that are, probably, slightly harder than NP. We also consider a stronger version of redundancy elimination: a clause C is strongly condensed iff it does not contain any proper subset C′ such that C logically implies C′. We show that the problem of testing whether a clause is strongly condensed is undecidable.

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^☆: This paper improves and extends earlier results of the first author presented in [9]. The work has been carried out in the context of the Christian Doppler Research Laboratory for Expert Systems.

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Removing redundancy from a clause☆

Abstract

Inf. Process. Lett.

Theor. Comput. Sci.

J. Comput. Syst. Sci.

J. Comput. Syst. Sci.

J. Comput. Syst. Sci.

Theor. Comput. Sci.

The NP-completeness of subsumption

What you always wanted to know about datalog (and never dared to ask)

IEEE Trans. Knowl. Data Eng.

Surveys in Computer Science

On the complexity of clause condensing