Three-Valued Logic for Reasoning from an Inconsistent Knowledge Base

摘要

Nontrivial reasoning under inconsistency, called paraconsistent reasoning, has been discussed mainly in two frameworks; one is the classical logic (consistency-based) framework and the other is the three-valued logic framework. In this paper, we propose a new entailment relation based on three-valued logic for reasoning from an inconsistent knowledge base, and discuss the relation between the previous two frameworks. A U-minimum model of the inconsistent knowledge base is defined in accordance with a principle of uncertainty minimization for three-valued models. We show that every set of atomic formulas assigned the additional third value in the U-minimum model is the minimum hitting set for the collection of sets each of which consists of atomic formulas occurring in the minimal inconsistent set of the knowledge base. Based on this result, we present an algorithm to compute the paraconsistent entailment relation by reducing the three-valued entailment relation to a two-valued classical entailment relation.