Journal of Automated Reasoning

, Volume 40, Issue 2, pp 133–177

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


DOI: 10.1007/s10817-007-9091-0

Cite this article as:
Chaudhuri, K., Pfenning, F. & Price, G. J Autom Reasoning (2008) 40: 133. doi:10.1007/s10817-007-9091-0


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.


Inverse method Focusing SLD resolution Hyperresolution Intuitionistic linear logic 

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Laboratoire d’Informatique (LIX) École PolytechniquePalaiseauFrance
  2. 2.Department of Computer ScienceCarnegie Mellon UniversityPittsburgUSA

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