Some Contributions to Nonmonotonic Consequence

This paper introduces a non-Horn ruleWRM which is a weak form of rational monotony. We explorethe effects of adding this non-Horn rule to the rules for the preferentialinference. In this paper, a relation is said to be P+WRM iff it is a preferential inference and satisfies the rule WRM. We establish the representation theorem for P+WRM, and compare the strength of WRM with some non-Horn rules appearing inliteratures. Moreover, we explore the relation between P+WRM andconditional logic, and demonstrate that P+WRM is equivalent to 'flat'fragment of conditional logic CS4.2. Another contribution of thispaper is to explore the relation between two special kinds of preferentialmodels, I.e., PRC model and quasi-linear model. Main result reveals thatthe latter is a special form of the former.