Abductive reasoning by constructing probabilistic deduction graphs for solving the diagnosis problem

Abstract An algorithm is proposed for finding optimal solutions of the diagnosis problem by using deduction graphs (DG) to accomplish abductions of multiple causes and multiple symptoms. The relationship among causes, symptoms, and possible intermediaries is represented by a causal network. The algorithm accomplishes the abduction by constructing a deduction graph DG(C,S) from the cause set C to the symptom set S representing the subnetwork such that the product of the prior probability, P(C), of C and the conditional probability, P(S/C), of DG(C,S) is maximized. An optimal solution is achieved by solving a 0/1 linear integer programming problem. Based on some assumptions, the algorithm can deal with a causal network involving various mutually independent deduction graphs.

[1]  Edward H. Shortliffe,et al.  A Method for Managing Evidential Reasoning in a Hierarchical Hypothesis Space , 1985, Artif. Intell..

[2]  Bruce G. Buchanan,et al.  The MYCIN Experiments of the Stanford Heuristic Programming Project , 1985 .

[3]  G. Nemhauser,et al.  Integer Programming , 2020 .

[4]  Chao-Chih Yang.  Deduction Graphs: An Algorithm and Applications , 1989, IEEE Trans. Software Eng..

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

[6]  Bruce A. Murtagh,et al.  Advanced linear programming: Computation and practice , 1981 .

[7]  Glenn Shafer,et al.  Implementing Dempster's Rule for Hierarchical Evidence , 1987, Artif. Intell..

[8]  Eric Horvitz,et al.  The Inconsistent Use of Measures of Certainty in Artificial Intelligence Research , 1985, UAI.

[9]  Drew McDermott,et al.  Introduction to artificial intelligence , 1986, Addison-Wesley series in computer science.

[10]  Judea Pearl,et al.  Embracing Causality in Formal Reasoning , 1987, AAAI.

[11]  L. N. Kanal,et al.  Uncertainty in Artificial Intelligence 5 , 1990 .

[12]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

[13]  Judea Pearl,et al.  Fusion, Propagation, and Structuring in Belief Networks , 1986, Artif. Intell..

[14]  H. Lewis Chau,et al.  Algorithms for Constructing Minimal Deduction Graphs , 1989, IEEE Trans. Software Eng..

[15]  John Yen,et al.  GERTIS: a Dempster-Shafer approach to diagnosing hierarchical hypotheses , 1989, CACM.

[16]  Han-Lin Li.  Solving discrete multicriteria decision problems based on logic-based decision support systems , 1987, Decis. Support Syst..

[17]  A. Blake.  Probabilistic inference by linear optimization , 1987 .

[18]  Chao-Chih Yang.  An Algorithm for Logically Deducing Horn Clauses and Processing Logic Queries , 1987, Int. J. Pattern Recognit. Artif. Intell..

[19]  Paul R. Cohen,et al.  Management of uncertainty in medicine , 1986, Int. J. Approx. Reason..