Maps between Different Kinds of Two-Level Credibility-Limited Revision Operators

Two-level credibility-limited revision is a non-prioritized revision operation. When revising through a two-level credibility-limited revision, two levels of credibility and one level of incredibility are considered. When revising by a sentence at the highest level of credibility, the operator behaves like a standard revision, if the sentence is at the second level of credibility, the revision process results in a standard contraction by the negation of that sentence. If the sentence is not credible, then the original belief set remains unchanged. In this article, we introduce a novel constructive method for two-level credibility-limited revision operators, based on a modified version of entrenchment relations. Additionally, we propose a semantics for this type of operators, based on Grove’s systems of spheres. Furthermore, we present axiomatic characterizations for the newly proposed operators.