-- /- Annals of Operations Research 12(1988)199 - 215 LOGICAL TESTING FOR RULE-BASE MANAGEMENT Fred GLOVER Center for Applied Artificial Intelligence, Graduate School of Business, University o f Colorado, Boulder, Colorado 80309-0419, USA and Harvey J, GREENBERG Mathematics Department, University of Colorado at Denver, Denver, Colorado 80202, USA Abstract We present a procedure to logically reduce simple implications that comprise the rule-base of an expeqt system. Our method uses topological sorting on a digraph representation that detects logical inconsistency and circular reasoning in linear- - time. Then, the sort order provides an efficient method to detect and eliminate forced values and redundant rules. We consider additional diagnostic aids for the rule-base manager, notably how to range the number of propositions that could be true and how to consolodate the rule-base. We than show how the simple case may be extended to logically test a general rule-base with a decomposition principle. Keywords Expert systems, rule-base management, logical testing, combinatorial optimization, precedence graphs, computational logic. 1. Introduction We study the problems of logical inconsistency and circular reasoning, as cited by Brarner [4], associated with a rule-base. We also provide detection of redundant rules - that is, whose removal from the rule-base does not alter the set of feasible truth values - and propositions whose truth values are forced. The first main result is a linear-time algorithm that detects inconsistency, if present, in a rule-base with onIy simple implications, and provides a diagnostic in the form of a minimal cycle for the expert to rectify the logical error. If the rule-base is consistent, the algorithm detects and eliminates circular reasoning during its first O J.C. Baltzer AG, Scientific Publishing Company