SUMMARYA method of computing scenario for knowledge including preferentially ordered hypotheses is proposed. Minimum conflict sets are found for competing hypothesis sets, and acceptable hypothesis sets are then found by applying preference relation to the minimum conflict sets; the disjunction of all elements of the acceptable hypothesis set thus obtained can be added to the fact set without contradiction. A fact set combined with all such disjunctions is considered a scenario, and is used for reasoning. Basically, the acceptability of hypothesis subsets for their minimal conflict sets is to be checked in order to obtain a scenario, which requires combinatorial calculations. A method is proposed to simplify such calculations; namely, acceptability is first checked for the single-element hypothesis sets, and then set operations are employed to check the acceptability of an arbitrary hypothesis set.

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SUMMARYThere are several approaches to reasoning from an inconsistent knowledge base, such as the consistency-based method and the argument-based method, from the point of view of the definition of conclusions derived from an inconsistent knowledge base. This paper proposes a treatment focusing on the condition for assuring the validity of conclusions derived from an inconsistent knowledge base. A consistency-based method performs deductive reasoning with consistent subsets selected from an inconsistent knowledge base. There exist maximal consistent sets which derive different conclusions inconsistent with each other. Thus, we propose a condition to distinguish these sets in order to assure the validity of conclusions. On the other hand, an argument-based method takes an argument that consists of a conclusion and a consistent knowledge base which derives the conclusion. This method selects an acceptable argument according to the alternative relation of possible arguments, as a conclusion has arguments from which it is derived and alternative arguments. Thus, we propose a condition which undercuts alternative arguments, in order to assure the validity of a conclusion. We show that these two methods are essentially identical with regard to the validity of a given conclusion by proving these conditions' equivalence.

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