Old and new algorithms for the Maximum Satisfiability problem are studied We first summarize the different heuristics previously proposed, ie, the approximation algorithms of Johnson and of Lieberherr for the general Maximum Satisfiability problem, and the heuristics of Lieberherr and Specker, Poljak and Turzik for the Maximum 2-Satisfiability problem We then consider two recent local search algorithmic schemes, the Simulated Annealing method of Kirkpatrick, Gelatt and Vecchi and the Steepest Ascent Mildest Descent method, and adapt them to the Maximum Satisfiability problem The resulting algorithms, which avoid being blocked as soon as a local optimum has been found, are shown empirically to be more efficient than the heuristics previously proposed in the literature

Algorithms for the maximum satisfiability problem

Publisher Summary This chapter describes several tools and techniques for validating a knowledge base, with emphasis on the rule checker. The other tools, such as the syntax checker and test case manager, also help the knowledge engineer to maintain the correctness of one's knowledge base and of the tool one is using. From the experiences with constructing different knowledge bases, one fined that many changes and additions are made during the development and maintenance of a knowledge base. The most frequent problems that CHECK has detected are unreachable and dead-end clauses. These types of errors are difficult to detect with conventional knowledge base debugging aids. It is found that redundant and conflicting rules appeared the least often. Nevertheless, CHECK'S automated facilities have saved engineers from many hours of tedious debugging. As the field of knowledge-based systems matures, large expert systems will be fielded in critical situations. As it will be impossible to test all paths beforehand, one must have assurance that deadly traps, such as circular rules and dead-end clauses do not exist in the knowledge base. Thus, verification facilities similar to the ones described in this paper becomes essential.

Knowledge base verification

The author presents an implemented computational model, based on studies of human group problem solving, for supporting conflict resolution in cooperative design. This model is based on the insights that general conflict resolution expertise exists separately from domain-level design expertise, and that this expertise can be instantiated in the context of particular conflicts into specific advice for resolving these conflicts. Conflict resolution expertise consists of a taxonomy of design conflict classes and associated general advice suitable for resolving conflicts in these classes. The abstract nature of conflict resolution expertise makes it applicable to a wide variety of design domains. The author describes this conflict resolution model and provides examples of its operation from an implemented cooperative design system for local area network design that uses machine-based design agents. How this model is being extended to support and learn from collaboration of human design agents is discussed. >

Supporting conflict resolution in cooperative design systems

This paper addresses the issues of completeness and consistency in rule-based expert systems. The approach presented uses decision tables, which have a close relationship to rule-based knowledge bases. A decision-table-supported processor is described which checks knowledge bases for completeness and consistency using this approach. It creates a large decision table from the rules of the knowledge base, splits the decision table into subtables with similar logic, checks each subtable for completeness and consistency, and reports any missing rules. This method is faster than enumeration only methods of checking completeness, and provides implicit context determination of production rules.

A decision-table-used processor for checking completeness and consistency in rule-based expert systems

This paper presents a new approach, called knowledge-base reduction, to the problem of checking knowledge bases for inconsistency and redundancy. The algorithm presented here makes use of concepts and techniques that have recently been advocated by de Kleer [deKleer, 1986] in conjunction with an assumption-based truth maintenance system. Knowledge-base reduction is more comprehensive than previous approaches to this problem in that it can in principle detect all potential contradictions and redundancies that exist in knowledge bases (having expressive power equivalent to propositional logic). While any approach that makes such a guarantee must be computationally intractable in the worst case, experience with KB-Reducer - a system that implements a specialized version of knowledge-base reduction and is described in this paper - has demonstrated that this technique is feasible and effective for fairly complex "real world" knowledge bases. Although KB-Reducer is currently intended for use by expert system developers, it is also a first step in the direction of providing safe "local end-user modifiability" for distant "sites" in a nationwide network of expert systems.

Knowledge-base reduction: a new approach to checking knowledge bases for inconsistency & redundancy

In this paper we describe a program that verifies the consistency and completeness of expert system knowledge bases which utilize the Lookheed Expert System (LES) framework. The algorithms described here are not specific to LES and can be applied to most rule-based systems. The program, called CHECK, combines logical principles as well as specific information about the knowledge representation formalism of LES. The program checks for redundant rules, conflicting rules, subsumed rules, missing rules, circular rules, unreachable clauses, and deadend clauses. It also generates a dependency chart which shows the dependencies among the rules and between the rules and the goals. CHECK can help the knowledge engineer to detect many programming errors even before the knowledge base testing phase. It also helps detect gaps in the knowledge base which the knowledge engineer and the expert might have overlooked. A wide variety of knowledge bases have been analyzed using CHECK.

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T. J. Laffey

Papers

Checking an expert systems knowledge base for consistency and completeness