A TENTATIVE NEW LOGICAL APPROACH FOR DEALING WITH KBS’e

Expert systems rules express relevant relations between their antecedents and their consequents. If the rules are manipulated by a logic (usually classical logic) in such a way that they give rise to new formulas with the form of rules (generated rules), these formulas may not express relevant relations between atecedents and consequents, and then become useless. We propose in this paper, a logic that partially avoids this problem, and in addition deals with both non-monotonicity and uncertainty, A description of the verification concept of consistency in forward and backward reasonings is given in terms of this logic. 1. Motivations and purpose of the paper Expert systems rules express relevant relations between their antecedents and their consequents. Considering these rules together with the given facts as axioms of a theory, if its underlying logic is classical logic, the generation of new formulas of the form a ~ 13 or ~(a --, [3) (where a and [3 may in their turn be complex formulas containing --b -~ , ^), from the theory and the logic, may not involve a relevant relation between a and 13, due to the so-called "implication and conjunction-implication paradoxes". An example of implication paradox is the following. If the expert proposses a fact a, as the formula a ~ (13 --* a) is a theorem in classical logic, it results that 13 ~ a is a valid generated formula. But such a formula means that 13 --, a for any 13, which makes it useless to be used in the KBS. It would then be of interest to use as the logic underlying the generation of new formulas from a given KBS, an entailment logic that could keep that idea of relevant relation in the sense that they would be paradox-free. Moreover such a logic would acquire more interest if it would accept both non-monotonicity and degrees of certainty. In this paper, we will propose a system, based on parts of Cheng’s entailment logic (Cheng & Ushijima 1990, Chang 1992), Gabbay’s non-monotonic logic (Gabbay, 1982) and Rasiowa’s regular many-valued logic (Rasiowa 1974), that, partially, captures all together the notions of relevant relation, non-monotonicity, and uncertainty. The study will be mainly based on pragmatic and semantical concepts, leaving the syntactical aspects for a future work. The semantic approach consists in that our reasoning will be based on the consideration of a particular model. The pragmatic aspect will appear in the definition of the concept of "relevant relation" between an antecedent and a consequent of an entailment. The main purpose of the paper is to propose some ideas for discussion about the convenience of using and mixing non-classical systems of logic for dealing more conveniently with KBS’s problems, rather than to propose a completed system. One reason is that this is as yet a work in progress, so that there are in it quite a number of items that are at want of a rigorous study. 2. This paper’s concept of relevant relation 2.1. Definition. Relevant relation is expressed by the following recursive definition. (1) If a ~ 13 is an entailment expressing a KB-rule, then there exists a relevant relation between ct and [3 (the pragmatic justification is that the expert has judged that such is the case). (2) If entailment formula -, [~, that results from application of G-C logic (to be defined below) from a set of other entailment formulas which express relevant relations between their antecedents and consequents, is implication and conjunction-implication paradox-free, then it expresses a relevant relation between its antecedent and its consequent. Anexample of implication paradox has been given above in I; a characterization of 129 From: AAAI Technical Report WS-93-05. Compilation copyright © 1993, AAAI (www.aaai.org). All rights reserved. conjunction-implication paradox will be given in terms of the model in 5. 2.2. Remark. This concept of relevant relation is a limited one, but at least it avoids the many cases of irrelevance that are produced by the mentioned paradoxes. 3. Cheng’s approach to implication paradox-free logic