Representing Bayesian Networks Within Probabilistic Horn Abduction

This paper presents a simple framework for Horn clause abduction, with probabilities associated with hypotheses. It is shown how this representation can represent any probabilistic knowledge representable in a Bayesian belief network. The main contributions are in finding a relationship between logical and probabilistic notions of evidential reasoning. This can be used as a basis for a new way to implement Bayesian Networks that allows for approximations to the value of the posterior probabilities, and also points to a way that Bayesian networks can be extended beyond a propositional language.

[1]  J. Reggia,et al.  Abductive Inference Models for Diagnostic Problem-Solving , 1990, Symbolic Computation.

[2]  David Poole,et al.  A methodology for using a default and abductive reasoning system , 1989, Int. J. Intell. Syst..

[3]  O. Penrose.  The Direction of Time , 1962 .

[4]  Judea Pearl,et al.  Distributed Revision of Composite Beliefs , 1987, Artif. Intell..

[5]  Judea Pearl,et al.  Embracing Causality in Default Reasoning , 1988, Artif. Intell..

[6]  Gregory M. Provan,et al.  What is the most likely diagnosis? , 1990, UAI.

[7]  Solomon Eyal Shimony,et al.  A new algorithm for finding MAP assignments to belief networks , 1990, UAI.

[8]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[9]  Kathryn B. Laskey,et al.  Assumptions, Beliefs and Probabilities , 1989, Artif. Intell..

[10]  David Poole,et al.  Representing Knowledge for Logic-Based Diagnosis , 1988, FGCS.

[11]  Randy Goebel,et al.  Theorist: A Logical Reasoning System for Defaults and Diagnosis , 1987 .

[12]  J. Lloyd.  Foundations of Logic Programming , 1984, Symbolic Computation.

[13]  Robert A. Kowalski,et al.  Abduction Compared with Negation by Failure , 1989, ICLP.

[14]  Eric Neufeld,et al.  Towards solving the multiple extension problem: Combining defaults and probabilities , 1987, Int. J. Approx. Reason..

[15]  David Poole,et al.  Representing Diagnostic Knowledge for Probabilistic Horn Abduction , 1991, IJCAI.

[16]  Brian C. Williams,et al.  Diagnosis with Behavioral Modes , 1989, IJCAI.

[17]  David Poole,et al.  Explanation and prediction: an architecture for default and abductive reasoning , 1989, Comput. Intell..

[18]  Brian C. Williams,et al.  Diagnosing Multiple Faults , 1987, Artif. Intell..

[19]  J. W. Lloyd,et al.  Foundations of logic programming; (2nd extended ed.) , 1987 .

[20]  Drew McDermott,et al.  Nonmonotonic Logic and Temporal Projection , 1987, Artif. Intell..

[21]  Solomon Eyal Shimony,et al.  Probabilistic Semantics for Cost Based Abduction , 1990, AAAI.

[22]  David Poole,et al.  A Dynamic Approach to Probabilistic Inference using Bayesian Networks , 1990, UAI 1990.

[23]  Gregory M. Provan.  An Analysis of ATMS-Based Techniques for Computing Dempster-Shafer Belief Functions , 1989, IJCAI.