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Applied Intelligence

, Volume 36, Issue 2, pp 472–497 | Cite as

On the combination of logical and probabilistic models for information analysis

  • Jingsong Wang
  • John Byrnes
  • Marco ValtortaEmail author
  • Michael Huhns
Article

Abstract

Formal logical tools are able to provide some amount of reasoning support for information analysis, but are unable to represent uncertainty. Bayesian network tools represent probabilistic and causal information, but in the worst case scale as poorly as some formal logical systems and require specialized expertise to use effectively. We describe a framework for systems that incorporate the advantages of both Bayesian and logical systems. We define a formalism for the conversion of automatically generated natural deduction proof trees into Bayesian networks. We then demonstrate that the merging of such networks with domain-specific causal models forms a consistent Bayesian network with correct values for the formulas derived in the proof. In particular, we show that hard evidential updates in which the premises of a proof are found to be true force the conclusions of the proof to be true with probability one, regardless of any dependencies and prior probability values assumed for the causal model. We provide several examples that demonstrate the generality of the natural deduction system by using inference schemes not supportable directly in Horn clause logic. We compare our approach to other ones, including some that use non-standard logics.

Keywords

Reasoning Uncertainty Probabilistic reasoning Bayesian networks Natural deduction proofs Logic for knowledge representation 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Jingsong Wang
    • 1
  • John Byrnes
    • 2
  • Marco Valtorta
    • 1
    Email author
  • Michael Huhns
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity of South CarolinaColumbiaUSA
  2. 2.SRI InternationalSan DiegoUSA

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