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An extended variant of atoms loop check for positive logic programs

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Abstract

The Equality check and the Subsumption check are weakly sound, but are not complete even for function-free logic programs. Although the OverSize (OS) check is complete for positive logic programs, it is too general in the sense that it prunes SLD-derivations merely based on the depth-bound of repeated predicate symbols and the size of atoms, regardless of the inner structure of the atoms, so it may make wrong conclusions even for some simple programs. In this paper, we explore complete loop checking mechanisms for positive logic programs. We develop an extended Variant of Atoms (VA) check that has the following features: (1) it generalizes the concept of “variant” from “the same up to variable renaming” to “the same up to variable renaming except possibly with some arguments whose size recursively increases”, (2) it makes use of the depth-bound of repeated variants of atoms instead of depth-bound of repeated predicate symbols, (3) it combines the Equality/Subsumption check with the VA check, (4) it is complete w. r. t. the leftmost selection rule for positive logic programs, and (5) it is more sound than both the OS check and all the existing versions of the VA check.

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Authors and Affiliations

  1. Department of Computer Science, Chongqing University, 630044, Chongqing, P. R. China

    Yi -Dong Shen

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  1. Yi -Dong Shen
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Correspondence to Yi -Dong Shen.

Additional information

The research was completed when the author visited the University of Maryland Institute for Advanced Computer Studies.

Yi-Dong Shen, Ph. D: He is a professor of Computer Science at Chongqing University, China. He received the Ph. D degree in computer Science from Chongqing University in 1991. He was a visiting researcher at the University of Valenciennes, France (1992–1993) and the University of Maryland Institute for Advanced Computer Studies (UMIACS), U. S. A. (1995–1996), respectively. His present interests include: Artificial Intelligence, Deductive and Object-Oriented Databases, Logic Programming and Parallel Processing.

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Shen, Y.D. An extended variant of atoms loop check for positive logic programs. NGCO 15, 187–203 (1997). https://doi.org/10.1007/BF03037237

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  • DOI: https://doi.org/10.1007/BF03037237

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