Checking the coherence of a set of rules is an important step in knowledge base validation. Coherence is also needed in the field of fuzzy systems. Indeed, rules are often used regardless of their semantics, and it sometimes leads to sets of rules that make no sense. Avoiding redundancy is also of interest in real-time systems for which the inference engine is time consuming. A knowledge base is potentially inconsistent or incoherent if there exists a piece of input data that respects integrity constraints and that leads to logical inconsistency when added to the knowledge base. We more particularly consider knowledge bases composed of parallel fuzzy rules. Then, coherence means that the projection on the input variables of the conjunctive combination of the possibility distributions representing the fuzzy rules leaves these variables completely unrestricted (i.e., any value for these variables is possible) or, at least, not more restrictive than integrity constraints. Fuzzy rule representations can be implication-based or conjunction-based; we show that only implication-based models may lead to coherence problems. However, unlike conjunction-based models, they allow to design coherence checking processes. Some conditions that a set of parallel rules has to satisfy in order to avoid inconsistency problems are given for certainty or gradual rules. The problem of redundancy, which is also of interest for fuzzy knowledge bases validation, is addressed for these two kinds of rules.

Checking the coherence and redundancy of fuzzy knowledge bases

Approximate reasoning has been a very important source of motivations for the development of fuzzy sets and possibility theory. It has also been at the origin of some of the most popular applications of fuzzy set theory. This long chapter is an attempt at providing a coherent view of the abundant body of results published in the field. After restating the necessary background, the paper discusses the representation of different kinds of fuzzy statements, and presents the basic machinery for approximate reasoning based on the combination and projection of possibility distributions. Reasoning with fuzzy rules is especially considered. Then specialized forms of approximate reasoning, such as interpolative reasoning, reasoning about preferences, temporal and qualitative reasoning, are surveyed as well as different fuzzy set-based and possibility theory-based models of plausible reasoning, including similarity-based and case-based reasoning, default reasoning, abductive reasoning, and reasoning with fuzzy quantifiers. The connection between approximate reasoning and certainty factor methods for uncertainty handling is also discussed.

Fuzzy Sets and Possibility Theory in Approximate and Plausible Reasoning

Building and maintaining high quality knowledge based systems is not a trivial task. Decision tables have sometimes been recommended in this process, mainly in verification and validation. In this paper, however, it is shown how decision tables can also be used to generate, and not just to validate, knowledge bases and how the transformation process from decision tables to knowledge bases can be organized. Several options to generate rules or other knowledge representation from decision tables are described and evauluated. The proposed generation strategy enables the knowledge engineer to concentrate on the acquisition and modelling issues and allows him to isolate the knowledge body from its implementation. The generation process has been implemented for two commercial tools, AionDS and KBMS and has been applied to real world applications.

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From decision tables to expert system shells

Reliability has become a key factor in KBS development. For this reason, it has been suggested that verification and validation (V&V) should become an integrated part of activities throughout the whole KBS development cycle. In this paper, it will be illustrated how the PROLOGA workbench integrates V&V aspects into its modelling environment, such that these techniques can be of assistance in the process of knowledge acquisition and representation. To this end, verification has to be performed incrementally and can no longer be delayed until after the system has been completed. It will be shown how this objective can be realised through an approach that uses the decision table formalism as a modelling instrument.

An illustration of verification and validation in the modelling phase of KBS development

The problem of finding potential inconsistencies during the process of validating knowledge based systems is discussed. A novel methodology, called reflecting on the inputs, is introduced. This effectively requires the knowledge base to stipulate the possible values for the inputs to the system. It is shown that the existence of potential inconsistencies manifest themselves by putting restrictions on the allowable input values. >

On discovering potential inconsistencies in validating uncertain knowledge bases by reflecting on the input

We present a new computational approach to the problem of detection of potential inconsistencies in knowledge bases. For such inconsistencies, we characterize the sets of possible input facts that will allow the knowledge based system to derive the contradiction. the state-of-the-art approach to a solution of this problem is represented by the COVADIS system which checks simple rule bases. the COVADIS approach relies on forward chaining and is strongly related to the way ATMS computes labels for deducible facts. Here, we present an alternative computation method that employs backward chaining in a kind of abductive reasoning. This approach gives a more focused reasoning, thus requiring much less computation and memory than COVADIS. Further, since our method is very similar to SLD-resolution, it is suitable for handling the more powerful knowledge base form represented by Horn claause bases. Finally, our method is easily extended to uncertain knowledge bases, assuming that the uncertainty calculus is modeled by possibilistic logic. This extension allows us to model the effect of user defined belief thresholds for inference chains.

Detection of potential inconsistencies in knowledge bases

We describe and illustrate the modeling issues in the design of a system for validation of knowledge based systems (KBSs). the domain of such a validation system is “KBSs and their validation problems.” the basic idea in our solution is the following. Since different KBSs may use different knowledge representation languages, we first represent the target KBS (i.e., the KBS to be validated) in a general formal model of KBS, and then validate it in this form. the advantage of this strategy is that validation problem solving needs only to refer to the common language of the general formal model. We present a set of possible conceptual abstraction levels in such a model, and argue that each level is associated with a related view on validation problems. Since high level characterizations are difficult to abstract from current knowledge representation languages, we consider the formal aspects of modeling mainly at the “lowest” level, the so-called inference primitive level. We illustrate the approach by formalizing a solution for selected modeling issues at this level.

Heri Nonfjall

Papers

Detection of potential inconsistencies in knowledge bases

Modeling in the design of a KBS validation system

Erratum modeling in the design of a KBS validation system