2016/04/19 by Jake Chandler, Chandler, Jake, Richard Booth +1 · 1 citation
Computer Science · #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #I.2.3 #Logic, Reasoning, and Knowledge #Semantic Web and Ontologies #cs.AI
paper · pdf · doi:10.48550/arxiv.1604.05419
Extended version of a paper accepted to IJCAI16. 23 pages
arxiv created 2016/04/19 · openalex publication_date 2016/04/19 · arxiv updated 2016/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The field of iterated belief change has focused mainly on revision, with the other main operator of AGM belief change theory, i.e. contraction, receiving relatively little attention. In this paper we extend the Harper Identity from single-step change to define iterated contraction in terms of iterated revision. Specifically, just as the Harper Identity provides a recipe for defining the belief set resulting from contracting A in terms of (i) the initial belief set and (ii) the belief set resulting from revision by not-A, we look at ways to define the plausibility ordering over worlds resulting from contracting A in terms of (iii) the initial plausibility ordering, and (iv) the plausibility ordering resulting from revision by not-A. After noting that the most straightforward such extension leads to a trivialisation of the space of permissible orderings, we provide a family of operators for combining plausibility orderings that avoid such a result. These operators are characterised in our domain of interest by a pair of intuitively compelling properties, which turn out to enable the derivation of a number of iterated contraction postulates from postulates for iterated revision. We finish by observing that a salient member of this family allows for the derivation of counterparts for contraction of some well known iterated revision operators, as well as for defining new iterated contraction operators.