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Using Directed Hypergraphs to Verify Rule-Based Expert Systems
March-April 1997 (vol. 9 no. 2)
pp. 221-237

Abstract—Rule-based representation techniques have become popular for storage and manipulation of domain knowledge in expert systems. It is important that systems using such a representation are verified for accuracy before implementation. In recent years, graphical techniques have been found to provide a good framework for the detection of errors that may appear in a rule base [1], [16], [17], [19], [23]. In this work we present a graphical representation scheme that: 1) captures complex dependencies across clauses in a rule base in a compact yet intuitively clear manner and 2) is easily automated to detect structural errors in a rigorous fashion. Our technique uses a directed hypergraph to accurately detect the different types of structural errors that appear in a rule base. The technique allows rules to be represented in a manner that clearly identifies complex dependencies across compound clauses. Subsequently, the verification procedure can detect errors in an accurate fashion by using simple operations on the adjacency matrix of the directed hypergraph. The technique is shown to have a computational complexity that is comparable to that of other graphical techniques. The graphical representation coupled with the associated matrix operations illustrate how directed hypergraphs are a very appropriate representation technique for the verification task.

[1] R. Agarwal and M. Tanniru, "A Petri-Net Based Approach for Verifying the Integrity of Production Systems," Int'l J. Man-Machine Studies, Vol. 36, No. 3, Mar. 1992, pp. 447-468.
[2] R. Balachandra and A.J. Raelin, "How to Decide When to Abandon a Project," Research Management, vol. 23, no. 7, pp 81-93, 1980.
[3] C. Berge, Hypergraph,Amsterdam: North-Holland, 1989.
[4] N. Botten, A. Kusiak, and T. Raz, "Knowledge Bases: Integration, Verification, and Partitioning," European J. Operational Research, vol. 42, pp. 111-128, 1989.
[5] B.J. Cragun and H.J. Steudel, "A Decision-Table-Based Processor for Checking Completeness and Consistency in Rule-Based Expert Systems," Int'l J. Man-Machine Studies, vol. 26, pp. 633-648, 1987.
[6] R. Davis, "Knowledge-Based Systems: The View in 1986," AI in the 1980s and Beyond: An MIT Survey, pp. 13-41, W. Grimson and R.S. Patil, eds., Cambridge, Mass.: MIT Press, 1987.
[7] J.R. Geissman and R.D. Schultz, "Verification and Validation of Expert Systems," AI Expert, vol. 3, no. 2, pp. 26-33, 1988.
[8] A. Ginsberg, "A New Approach to Checking Knowledge Bases for Inconsistency and Redundancy," Proc. Third Ann. Expert Systems in Government Conf.,Washington, D.C., pp. 102-111, 1987.
[9] A. Ginsberg, "Knowledge-Base Reduction: A New Approach to Checking Knowledge Bases for Inconsistency and Redundancy," Proc. Nat'l Conf. Artificial Intelligence, pp. 589-595, 1988.
[10] F. Hayes-Roth, "Rule Based Systems," Comm. ACM, vol. 8, no. 9, pp. 921-932, 1985.
[11] J.P. Ignizio, Introduction to Expert Systems: The Development and Implementation of Rule-Based Expert Systems. McGraw-Hill, 1991.
[12] Y. Kang and T. Bahill, "A Tool for Detecting Expert Systems Errors," AI Expert, vol. 5, no. 2, pp. 42-51, 1990.
[13] W. Marek, "Completeness and Consistency in Knowledge Based Systems," Proc. First Int'l Conf. Expert Database Systems, pp. 119-126, 1987.
[14] P. Morizet-Mahoudeaux, "Maintaining Consistency of Database During Monitoring of an Evolving Process by a Knowledge-Based System," IEEE Trans. Systems, Man, and Cybernetics, vol. 21, no. 1, pp. 47-60, 1991.
[15] D.L. Nazareth, “Issues in the Verification of Knowledge in Rule-Based Systems” Int'l J. Man-Machine Studies, pp. 255-271, 1989.
[16] D. L. Nazareth, “Investigating the Applicability of Petri Nets for Rule-Based System Verification,” IEEE Trans. Knowledge and Data Eng., vol. 4, no. 3, pp. 402–415, June 1993.
[17] D.L. Nazareth and M.H. Kennedy, "Verification of Rule-Based Knowledge Using Directed Graphs," Knowledge Acquisition, vol. 3, pp. 339-360, 1991.
[18] T.A. Nguyen, W.A. Perkins, T.J. Laffey, and D. Pecora, “Knowledge Base Verification,” AI Magazine, pp. 69–75, Summer 1987.
[19] T.A. Nguyen, "Verifying Consistency of Production Systems," Proc. Third IEEE Conf. Artificial Intelligence Applications, pp. 4-8, 1987.
[20] K. Pederson, "Well-Structured Knowledge Bases," AI Expert, Vol. 4, No. 4, Apr. 1989, pp. 44-55.
[21] A.D. Preece, "A New Approach to Detecting Missing Knowledge in Expert System Rule Bases," Int'l J. Man-Machine Studies, vol. 38, pp. 661-688, 1993.
[22] M. Suwa, A. Scott, and E. Shortliffe, "An Approach to Verifying Completeness and Consistency in a Rule-Based Expert System," Artificial Intelligence, pp. 16-21, 1982.
[23] G. Valiente, “Verification of Knowledge Based Redundancy and Subsumption Using Graph Transformations,” Int'l J. Expert Systems, vol. 6, no. 3, pp. 341-355, 1993.
[24] F. Zahedi, Intelligent Systems for Business,Belmont, Calif.: Wadsworth, 1993.

Index Terms:
Error detection, hypergraphs, knowledge verification, knowledge acquisition, rule-based expert systems.
Mysore Ramaswamy, Sumit Sarkar, Ye-Sho Chen, "Using Directed Hypergraphs to Verify Rule-Based Expert Systems," IEEE Transactions on Knowledge and Data Engineering, vol. 9, no. 2, pp. 221-237, March-April 1997, doi:10.1109/69.591448
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