On Stratified Belief Base Compilation

  • Authors:

  • Sylvie Coste-Marquis;Pierre Marquis

  • Affiliations:

  • CRIL-CNRS, IUT de Lens, Université d'Artois, rue de l'Université, SP 16, 62307 Lens cedex, France e-mail: coste@cril.univ-artois.fr;CRIL-CNRS, Université d'Artois, rue de l'Université, SP 16, 62307 Lens cedex, France e-mail: marquis@cril.univ-artois.fr

  • Venue:
  • Annals of Mathematics and Artificial Intelligence
  • Year:
  • 2004

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Abstract

In this paper, we investigate the extent to which knowledge compilation can be used to circumvent the complexity of skeptical inference from a stratified belief base (SBB). We first analyze the compilability of skeptical inference from an SBB, under various requirements concerning both the selection policy under consideration, the possibility to make the stratification vary at the on-line query answering stage and the expected complexity of inference from the compiled form. Not surprisingly, the results are mainly negative. However, since they concern the worst case situation only, they do not prevent a compilation-based approach from being practically useful for some families of instances. While many approaches to compile an SBB can be designed, we are primarily interested in those which take advantage of existing knowledge compilation techniques for classical inference. Specifically, we present a general framework for compiling SBBs into so-called C-normal SBBs, where C is any tractable class for clausal entailment which is the target class of a compilation function. Another major advantage of the proposed approach lies in the flexibility of the C-normal belief bases obtained, which means that changing the stratification does not require to re-compile the SBB. For several families of compiled SBBs and several selection policies, the complexity of skeptical inference is identified. Some tractable restrictions are exhibited for each policy. Finally, some empirical results are presented.