In this paper five levels of specification of nonmonotonic reasoning are distinguished. The notions of semantical frame, belief state frame and reasoning frame are introduced and used as a semantical basis for the first three levels. Moreover, the semantical connections between the levels are formalized. It is shown that this general semantical framework is applicable for some well-known approa...

We study a bimodal nonmonotonic logic MBNF suggested in [Lifschitz, 1994] as a generalization of a number of nonmonotonic formalisms We show first that it is equivalent to a certain nonmodal system involving rules of a special kind Next, it is shown that the latter admits a modal representation that uses only one modal opera tor the operator of belief Moreover, under this translation the models...

A survey of proof systems for nonmonotonic logics is presented. In particular , proof methods for default logics, nonmonotonic modal logics, circum-scription, and conditional logics are discussed.

Default logic is one of the best known and most studied of the approaches to nonmonotonic reasoning. Subsequently, several variants of default logic have been proposed to give systems with properties differing from the original. In this paper we show that these variants are in a sense superfluous, in that for any of these variants of default logic, we can exactly mimic the behaviour of a varian...

The advantages of Florid as a deductive object{oriented database system are the rich object{oriented modeling facilities of its language F-logic. The focus of this paper is on Florid's multiple inheritance mechanism which turns out to be a useful means to adapt various examples of nonmonotonic reasoning in the object{oriented setting.

Consistency-based approaches in nonmonotonic reasoning may be expected to yield multiple sets of default conclusions for a given default theory. Reasoning about such extensions is carried out at the meta-level. In this paper, we show how such reasoning may be carried out at the object level for a large class of default theories. Essentially we show how one can translate a (semi-monotonic) defau...

Belief Logic Programming (BLP) is a novel form of quantitative logic programming in the presence of uncertain and inconsistent information, which was designed to be able to combine and correlate evidence obtained from non-independent information sources. BLP has non-monotonic semantics based on the concepts of belief combination functions and is inspired by Dempster-Shafer theory of evidence. M...

Lehmann, Magidor and others have investigated the eeects of adding the non-Horn rule of rational monotony to the rules for preferential inference in nonmonotonic reasoning. In particular, they have shown that every inference relation satisfying those rules is generated by some ranked preferential model. We explore the eeects of adding a number of other non-Horn rules that are stronger than or i...

The purpose of this paper is to take some of the mystery out of what is known as nonmonotonic logic, by showing that it is not as unfamiliar as may at first sight appear. In fact, it is easily accessible to anybody with a background in classical propositional logic, provided that certain misunderstandings are avoided and a tenacious habit is put aside. In effect, there are logics that act as na...