Parikh proposed his relevance-sensitive axiom to remedy the weakness of the classical AGM paradigm in addressing relevant change. An insufficiency of Parikh’s criterion, however, is its dependency on the contingent beliefs of a belief set to be revised, since the former only constrains the revision process of splittable theories (i.e., theories that can be divided in mutually disjoint compartments). The case of arbitrary non-splittable belief sets remains out of the scope of Parikh’s approach. On that premise, we generalize Parikh’s criterion, introducing (both axiomatically and semantically) a new notion of relevance, which we call relevance at the sentential level. We show that the proposed notion of relevance is universal (as it is applicable to arbitrary belief sets) and acts in a more refined way as compared to Parikh’s proposal; as we illustrate, this latter feature of relevance at the sentential level potentially leads to a significant drop in the computational resources required for implementing belief revision. Furthermore, we prove that Dalal’s popular revision operator respects, to a certain extent, relevance at the sentential level. Last but not least, the tight relation between local and relevance-sensitive revision is pointed out.

Parikh 提出了他的相关敏感公理来弥补经典 AGM 范式在解决相关变化方面的弱点。然而，Parikh 标准的不足之处在于它依赖于要修改的信念集的偶然信念，因为前者仅限制可拆分理论（即可以划分为相互不相交的隔间的理论）的修改过程。任意不可分割的信念集的情况仍然超出了 Parikh 方法的范围。在此前提下，我们概括了 Parikh 的标准，引入（公理化和语义化）一个新的相关概念，我们称之为句子层面的相关性. 我们表明，与 Parikh 的提议相比，所提议的相关性概念是普遍的（因为它适用于任意信念集）并且以更精细的方式起作用；正如我们所说明的，后一个句子级别的相关性特征可能导致实施信念修正所需的计算资源显着下降。此外，我们证明 Dalal 流行的修订运算符在一定程度上尊重句子级别的相关性。最后但同样重要的是，指出了本地和相关敏感修订之间的紧密关系。