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A Logical Characterization of Forward and Backward Chaining in the Inverse Method

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Abstract

The inverse method is a generalization of resolution that can be applied to non-classical logics. We have recently shown how Andreoli’s focusing strategy can be adapted for the inverse method in linear logic. In this paper we introduce the notion of focusing bias for atoms and show that it gives rise to forward and backward chaining, generalizing both hyperresolution (forward) and SLD resolution (backward) on the Horn fragment. A key feature of our characterization is the structural, rather than purely operational, explanation for forward and backward chaining. A search procedure like the inverse method is thus able to perform both operations as appropriate, even simultaneously. We also present experimental results and an evaluation of the practical benefits of biased atoms for a number of examples from different problem domains.

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Authors and Affiliations

  1. Laboratoire d’Informatique (LIX) École Polytechnique, Palaiseau, France

    Kaustuv Chaudhuri

  2. Department of Computer Science, Carnegie Mellon University, Pittsburg, PA, USA

    Frank Pfenning & Greg Price

Authors
  1. Kaustuv Chaudhuri
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  2. Frank Pfenning
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  3. Greg Price
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Correspondence to Frank Pfenning.

Additional information

This work has been partially supported by the Office of Naval Research (ONR) under grant MURI N00014-04-1-0724 and by the National Science Foundation (NSF) under grant CCR-0306313. The first author was partially supported by a post-doctoral fellowship from INRIA-Futurs/École Polytechnique.

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Chaudhuri, K., Pfenning, F. & Price, G. A Logical Characterization of Forward and Backward Chaining in the Inverse Method. J Autom Reasoning 40, 133–177 (2008). https://doi.org/10.1007/s10817-007-9091-0

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  • DOI: https://doi.org/10.1007/s10817-007-9091-0

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