Complexity and Cautiousness Results for Reasoning from Partially Preordered Belief Bases

  • Authors:

  • Salem Benferhat;Safa Yahi

  • Affiliations:

  • Université Lille-Nord de France,Artois, F-62307 Lens, CRIL, F-62307 Lens, CNRS UMR 8188, F-62307 Lens,;Université Lille-Nord de France,Artois, F-62307 Lens, CRIL, F-62307 Lens, CNRS UMR 8188, F-62307 Lens,

  • Venue:
  • ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
  • Year:
  • 2009

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Abstract

Partially preordered belief bases are very convenient for an efficient representation of incomplete knowledge. They offer flexibility and avoid to compare unrelated pieces of information. A number of inference relations for reasoning from partially preordered belief bases have been proposed. This paper sheds light on the following approaches: the partial binary lexicographic inference, the compatible-based lexicographic inference, the democratic inference, the compatible-based inclusion inference, the strong possibilistic inference and the weak possibilistic inference. In particular, we propose to analyse these inference relations according to two key dimensions: the computational complexity and the cautiousness. It turns out that almost all the corresponding decision problems are located at most at the second level of the polynomial hierarchy. As for the cautiousness results, they genereally extend those obtained in the particular case of totally preordered belief bases.