Properties and interrelationships of skeptical, weakly skeptical, and credulous inference induced by classes of minimal models

Abstract

There are multiple ways of defining nonmonotonic inference relations based on a conditional knowledge base. While the axiomatic system P is an important standard for such plausible nonmonotonic reasoning, inference relations obtained from system Z or from c-representations have been designed which go beyond system P by selecting preferred models for inference. For any class of models M, we propose the notion of weakly skeptical inference, first introduced in an ECAI conference paper this article revises and extends, that lies between skeptical and credulous inference with respect to M. Weakly skeptical c-inference properly extends skeptical c-inference, but avoids disadvantages of a too liberal credulous c-inference. We extend the concepts of skeptical, weakly skeptical, and credulous c-inference modes by taking models obtained from different minimality criteria into account. We illustrate the usefulness of the obtained inference relations and show that they fulfill various desirable properties put forward for nonmonotonic reasoning. Furthermore, we elaborate in detail the interrelationships among the inference relations when taking the different inference modes and various classes of minimal models into account.