部分交、核与下收缩之间的联系及其在Horn逻辑中的应用
On the Link between Partial Meet, Kernel, and Infra Contraction and its Application to Horn Logic
摘要：
标准的信念改变假设一个包含完整的经典命题逻辑的底层逻辑。然而，在表达性较低的逻辑中也有充分的理由考虑信念变化。在本文中，我们建立在最近的调查Delphon收缩霍恩逻辑。我们表明，标准的基本形式的收缩，部分满足，是太强的霍恩的情况下。这一结果与Delaware的猜想相反，Delaware猜想有序的maxichoice是Horn逻辑的适当收缩形式。然后，我们定义了一个更合适的概念的基本收缩的霍恩的情况下，受凸性属性举行充分的命题逻辑，我们称之为infra收缩。这项工作的主要贡献是一个结果表明，建设方法霍恩收缩的信念集的基础上，我们的infra剩余集完全对应于汉森的经典内核收缩的信念集，当限制到霍恩逻辑。这个结果是通过信念基的收缩绕道而得到的。我们证明，核心收缩的信念基地产生完全相同的结果作为信念基地版本的infra收缩。使用的信念基地，以获得这一结果提供了证据的猜想，霍恩信念变化最好被视为一个混合版本的信念集的变化和信念基地的变化。与基地收缩的链接的后果之一是提供一个代表性的结果霍恩收缩的信念集，其中一个版本的核心保留假设的功能。
英文摘要：
Standard belief change assumes an underlying logic containing full classical propositional logic. However, there are good reasons for considering belief change in less expressive logics as well. In this paper we build on recent investigations by Delgrande on contraction for Horn logic. We show that the standard basic form of contraction, partial meet, is too strong in the Horn case. This result stands in contrast to Delgrande's conjecture that orderly maxichoice is the appropriate form of contraction for Horn logic. We then define a more appropriate notion of basic contraction for the Horn case, influenced by the convexity property holding for full propositional logic and which we refer to as infra contraction. The main contribution of this work is a result which shows that the construction method for Horn contraction for belief sets based on our infra remainder sets corresponds exactly to Hansson's classical kernel contraction for belief sets, when restricted to Horn logic. This result is obtained via a detour through contraction for belief bases. We prove that kernel contraction for belief bases produces precisely the same results as the belief base version of infra contraction. The use of belief bases to obtain this result provides evidence for the conjecture that Horn belief change is best viewed as a hybrid version of belief set change and belief base change. One of the consequences of the link with base contraction is the provision of a representation result for Horn contraction for belief sets in which a version of the Core-retainment postulate features.
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