Topics in Horn Contraction: Supplementary Postulates, Package Contraction, and Forgetting

摘要

In recent years there has been interest in studying belief change, specifically contraction, in Horn knowledge bases. Such work is arguably interesting since Horn clauses have found widespread use in AI; as well, since Horn reasoning is weaker than classical reasoning, this work also sheds light on the foundations of belief change. In this paper, we continue our previous work along this line. Our earlier work focused on defining contraction in terms of weak remainder sets, or maximal subsets of an agent's belief set that fail to imply a given formula. In this paper, we first examine issues regarding the extended contraction postulates with respect to Horn contraction. Second, we examine package contraction, or contraction by a set of formulas. Last, we consider the closely-related notion of forgetting in Horn clauses. This paper then serves to address remaining major issues concerning Horn contraction based on remainder sets.