2022/02/04 by Kai Sauerwald, Sauerwald, Kai, Gabriele Kern-Isberner +3
Computer Science · #03B42 #Advanced Algebra and Logic #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #I.2.4 #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #acm:03B42 #cs.AI #msc:03B42
paper · pdf · doi:10.48550/arxiv.2202.03196
This is a largely extended version of the following conference paper: Kai Sauerwald, Gabriele Kern-Isberner, Christoph Beierle: A Conditional Perspective for Iterated Belief Contraction. ECAI 2020: 889-896 https://doi.org/10.3233/FAIA200180 (see also arXiv:1911.08833 )
arxiv created 2022/02/04 · openalex publication_date 2022/02/04 · arxiv updated 2022/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we consider iteration principles for contraction, with the goal of identifying properties for contractions that respect conditional beliefs. Therefore, we investigate and evaluate four groups of iteration principles for contraction which consider the dynamics of conditional beliefs. For all these principles, we provide semantic characterization theorems and provide formulations by postulates which highlight how the change of beliefs and of conditional beliefs is constrained, whenever that is possible. The first group is similar to the syntactic Darwiche-Pearl postulates. As a second group, we consider semantic postulates for iteration of contraction by Chopra, Ghose, Meyer and Wong, and by Konieczny and Pino Pérez, respectively, and we provide novel syntactic counterparts. Third, we propose a contraction analogue of the independence condition by Jin and Thielscher. For the fourth group, we consider natural and moderate contraction by Nayak. Methodically, we make use of conditionals for contractions, so-called contractionals and furthermore, we propose and employ the novel notion of α-equivalence for formulating some of the new postulates.