We investigate the space efficiency of a Propositional Knowledge Representation (PKR) formalism. Intuitively, the space efficiency of a formalism F in representing a certain piece of knowledge A, is the size of the shortest formula of F that represents A. In this paper we assume that knowledge is either a set of propositional interpretations (models) or a set of propositional formulae (theorems). We provide a formal way of talking about the relative ability of PKR formalisms to compactly represent a set of models or a set of theorems. We introduce two new compactness measures, the corresponding classes, and show that the relative space efficiency of a PKR formalism in representing models/theorems is directly related to such classes. In particular, we consider formalisms for nonmonotonic reasoning, such as circumscription and default logic, as well as belief revision operators and the stable model semantics for logic programs with negation. One interesting result is that formalisms with the same time complexity do not necessarily belong to the same space efficiency class.

Normal forms play an important role in computer science. Examples of areas where normal forms have proved fruitful include logic, where normal forms of formulae are used both for the proof of theoretical results and in automated theorem proving, and relational databases [7], where normal forms have been the driving force in the development of database theory and principles of good data modelling. In computer science, usually normal forms are supported by transformations, operational procedures that transform initial objects (such as programs or logical theories) to their normal form. Such transformations are important for two main reasons: 1. They support the understanding and assimilation of new concepts because they allow one to concentrate on certain forms and key features only. Thus transformations can be useful as theoretical tools.

We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries, and logic programming. We characterize the complexity and provide algorithms for reasoning in propositional MBNF. In particular, we show that entailment in propositional MBNF lies at the third level of the polynomial hierarchy, hence it is harder than reasoning in all the above mentioned propositional formalisms for nonmonotonic reasoning. We also prove the exact correspondence between negation as failure in MBNF and negative introspection in Moore's autoepistemic logic.

It is possible to argue, relatively convincingly, that any research topic only begins to become mature when it appears on a syllabus somewhere. Once the topic has become well enough understood that it can be explained easily to paying customers, and stable enough that anyone teaching it is not likely to have to update his/her teaching materials every few months as new developments are reported, it can be considered to have arrived. Another reasonable indicator of the maturity of a subject, a milestone along the road to academic respectability, is the publication of a really good book on the subject -- not another research monograph but a book that consolidates what is already known, surveys and relates existing ideas, and maybe even unifies some of them. Grigoris Antoniou's Nonmonotonic Reasoning is just such a milestone -- well written, informative, and a good source of information on an important and complex subject.

It is possible to argue, relatively convincingly, that any research topic only begins to become mature when it appears on a syllabus somewhere. Once the topic has become well enough understood that it can be explained easily to paying customers, and stable enough that anyone teaching it is not likely to have to update his/her teaching materials every few months as new developments are reported, it can be considered to have arrived. Another reasonable indicator of the maturity of a subject, a milestone along the road to academic respectability, is the publication of a really good book on the subject -- not another research monograph but a book that consolidates what is already known, surveys and relates existing ideas, and maybe even unifies some of them. Grigoris Antoniou's Nonmonotonic Reasoning is just such a milestone -- well written, informative, and a good source of information on an important and complex subject. Since the idea was first mooted

The Seventh International Workshop on Nonmonotonic Reasoning was held in Trento, Italy, on 30 May to 1 June 1998 in conjunction with the Sixth International Conference on the Principles of Knowledge Representation and Reasoning (KR-98). The workshop was sponsored by the Association for the Advancement of Artificial Intelligence, Compulog, Associazione Italiana per l'Intelligenza Artificiale, and the Prolog Development Center.

Fourth, causality is still an important issue; some formal models of causality have surprisingly close connections to standard nonmonotonic techniques. Fifth, the nonmonotonic logics being used most widely are the classical ones: default logic, circumscription, and by Isaac Levi; (3) Nonmonotonic Reasoning autoepistemic logic. Maybe the most remarkable trend he Seventh International Workshop was held in Trento, Italy, Tolerance by John McCarthy; (4) that became apparent during the on 30 May to 1 June 1998 in conjunction Learning to Make Nonmonotonic workshop was the new excitement with the Sixth International Inferences by Dan Roth; and (5) From among the participants. The depression Conference on the Principles of Features and Fluents to Thinking that plagued a number of people Knowledge Representation and Reasoning When Flying--Reasoning about in the field seems to be over. The workshop was Actions in an Intelligent UAV by Erik common feeling was that the theory sponsored by the American Association Sandewall.

An important characteristic of many logics for Artificial Intelligence is their nonmonotonicity. This means that adding a formula to the premises can invalidate some of the consequences. There may, however, exist formulae that can always be safely added to the premises without destroying any of the consequences: we say they respect monotonicity. Also, there may be formulae that, when they are a consequence, can not be invalidated when adding any formula to the premises: we call them conservative. We study these two classes of formulae for preferential logics, and show that they are closely linked to the formulae whose truth-value is preserved along the (preferential) ordering. We will consider some preferential logics for illustration, and prove syntactic characterization results for them. The results in this paper may improve the efficiency of theorem provers for preferential logics.

The Sixth International Workshop on Nonmonotonic Reasoning was held 10 to 12 June 1996 in Timberline, Oregon. The aim of the workshop was to bring together active researchers interested in nonmonotonic reasoning to discuss current research, results, and problems of both a theoretical and a practical nature.

Intelligence (AAAI), was held 10 to 12 have now become particularly June 1996 in Timberline, Oregon. Finally, we Netherlands, the United States, and would like to acknowledge the support Venezuela. The papers described new of AAAI for student travel funds. Moises Goldszmidt received his Ph.D. in His email address is moises@ Mathematical Institute in Russia.