Normal forms of conditional knowledge bases respecting system P-entailments and signature renamings

Abstract Conditionals are defeasible rules of the form If A then usually B , and they play a central role in many approaches to nonmonotonic reasoning. Normal forms conditional knowledge bases consisting set such conditionals useful create, process, compare represented by them. In this article, we propose several new normal for bases. Compared previously introduced antecedent form, reduced (RANF) represents with significantly fewer taking entailments licenced system P into account. The renaming (?NF) addresses equivalences among induced renamings underlying signature. Combining concept other yields ( ? ANF) RANF). For all newly forms, show their key properties regarding, existence, uniqueness, model equivalence, inferential develop algorithms transforming every base an equivalent being respective form. most succinct RANF, present algorithm K r systematically generating over given signature RANF. We that generated consistent, pairwise not antecedentwise equivalent, under renaming. Furthermore, is complete sense that, when equivalence account, consistent generated. Observing normalizing ? RANF exactly same result as ), highlights interrelationship between transformations on one hand hand.