Evidential Reasoning in Semantic Networks: A Formal Theory

This paper presents an evidential approach to knowledge representation and inference wherein the principle of maximum entropy is applied to deal with uncertainty and incompleteness. It focuses on a restricted representation language - similar in expressive power to semantic network formalisms, and develops a formal theory of evidential inheritance within this language. The theory applies to a limited, but we think interesting, class of inheritance problems including those that involve exceptions and multiple inheritance hierarchies. The language and the accompanying evidential inference structure provide a natural treatment of defaults and conflicting information. The evidence combination rule proposed in this paper is incremental, commutative and associative and hence, shares most of the attractive features of the Dempster-Shafer evidence combination rule. Furthermore, it is demonstrably better than the Dempster-Shafer rule in the context of the problems addressed in this paper. The resulting theory can be implemented as a highly parallel (connectionist) network made up of active elements that can solve inheritance problems in time proportional to the depth of the conceptual hierarchy.

[1]  H. Levesque.  A formal treatment of incomplete knowledge bases , 1981 .

[2]  Joseph Y. Halpern,et al.  Likelihood, probability, and knowledge , 1984, AAAI 1984.

[3]  E. T. Jaynes,et al.  Where do we Stand on Maximum Entropy , 1979 .

[4]  Nils J. Nilsson,et al.  Probabilistic Logic * , 2022 .

[5]  J. Doyle.  Some theories of reasoned assumptions : an essay in rational psychology , 1983 .

[6]  Scott E. Fahlman,et al.  NETL: A System for Representing and Using Real-World Knowledge , 1979, CL.

[7]  Mark S. Fox,et al.  Reasoning With Incomplete Knowledge in a Resource-Limited Environment: Integrating Reasoning and Knowledge Acquisition , 1981, IJCAI.

[8]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[9]  Peter C. Cheeseman,et al.  A Method of Computing Generalized Bayesian Probability Values for Expert Systems , 1983, IJCAI.

[10]  Ronald J. Brachman,et al.  ON THE EPISTEMOLOGICAL STATUS OF SEMANTIC NETWORKS , 1979 .

[11]  Raymond Reiter,et al.  On Interacting Defaults , 1981, IJCAI.

[12]  Richard O. Duda,et al.  Subjective bayesian methods for rule-based inference systems , 1976, AFIPS '76.

[13]  Edward H. Shortliffe,et al.  Computer-based medical consultations, MYCIN , 1976 .

[14]  Raymond Reiter,et al.  On Inheritance Hierarchies With Exceptions , 1983, AAAI.

[15]  Harry E. Pople,et al.  The Formation of Composite Hypotheses in Diagnostic Problem Solving: An Exercise in Synthetic Reasoning , 1977, IJCAI.

[16]  Lokendra Shastri,et al.  Semantic Networks and Neural Nets , 1984 .

[17]  田中 穂積.  E.H.Shortliffe 著, "Computer-Based Medical Consultations : MYCIN", American Elsevier, A4判, 264ぺージ, \10,080, 1976 , 1978 .

[18]  John McCarthy,et al.  Applications of Circumscription to Formalizing Common Sense Knowledge , 1987, NMR.

[19]  John D. Lowrance,et al.  An Inference Technique for Integrating Knowledge from Disparate Sources , 1981, IJCAI.

[20]  Daniel G. Bobrow,et al.  On Overview of KRL, a Knowledge Representation Language , 1976, Cogn. Sci..

[21]  Aravind K. Joshi.  SOME EXTENSIONS OF A SYSTEM FOR INFERENCE ON PARTIAL INFORMATION1 , 1978 .

[22]  Elaine Rich,et al.  Default Reasoning as Likelihood Reasoning , 1983, AAAI.

[23]  Jeffrey A. Barnett,et al.  Computational Methods for a Mathematical Theory of Evidence , 1981, IJCAI.

[24]  Matthew L. Ginsberg,et al.  Non-Monotonic Reasoning Using Dempster's Rule , 1984, AAAI.

[25]  Henry E. Kyburg,,et al.  The Reference Class , 1983, Philosophy of Science.

[26]  Drew McDermott,et al.  Non-Monotonic Logic I , 1987, Artif. Intell..

[27]  Raymond Reiter,et al.  A Logic for Default Reasoning , 1987, Artif. Intell..

[28]  David S. Touretzky,et al.  The Mathematics of Inheritance Systems , 1984 .

[29]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[30]  Aravind K. Joshi,et al.  Some extensions of a system for inferencing on partial information , 1977, SGAR.