Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties. We concentrate on a number of families of nonmonotonic consequence relations, defined in the style of Gentzen. Both proof-theoretic and semantic points of view are developed in parallel. The former point of view was pioneered by D. Gabbay, while the latter has been advocated by Y. Shoham in. Five such families are defined and characterized by representation theorems, relating the two points of view. One of the families of interest, that of preferential relations, turns out to have been studied by E. Adams. The "preferential" models proposed here are a much stronger tool than Adams' probabilistic semantics. The basic language used in this paper is that of propositional logic. The extension of our results to first order predicate calculi and the study of the computational complexity of the decision problems described in this paper will be treated in another paper.

Nonmonotonic Reasoning, Preferential Models and Cumulative Logics

Dynamic Epistemic Logic is the logic of knowledge change. This is not about one logical system, but about a whole family of logics that allows us to specify static and dynamic aspects of multi-agent systems. This book provides various logics to support such formal specifications, including proof systems. Concrete examples and epistemic puzzles enliven the exposition. The book also contains exercises including answers and is eminently suitable for graduate courses in logic. A sweeping chapter-wise outline of the content of this book is the following. The chapter 'Introduction' informs the reader about the history of the subject, and its relation to other disciplines. 'Epistemic Logic' is an overview of multi-agent epistemic logic - the logic of knowledge - including modal operators for groups, such as general and common knowledge. 'Belief Revision' is an overview on how to model belief revision, both in the 'traditional' way and in a dynamic epistemic setting. 'Public Announcements' is a detailed and comprehensive introduction into the logic of knowledge to which dynamic operators for truthful public announcement are added. Many interesting applications are also presented in this chapter: a form of cryptography for ideal agents also known as 'the russian cards problem', the sum-and-product riddle, etc. 'Epistemic Actions' introduces a generalization of public announcement logic to more complex epistemic actions. A different perspective on that matter is independently presented in 'Action Models'. 'Completeness' gives details on the completeness proof for the logics introduced in 'Epistemic Logic', 'Public Announcements', and 'Action Models'. 'Expressivity' discusses various results on the expressive power of the logics presented.

Dynamic Epistemic Logic

Knowledge representation is at the very core of a radical idea for understanding intelligence. Instead of trying to understand or build brains from the bottom up, its goal is to understand and build intelligent behavior from the top down, putting the focus on what an agent needs to know in order to behave intelligently, how this knowledge can be represented symbolically, and how automated reasoning procedures can make this knowledge available as needed. 

This landmark text takes the central concepts of knowledge representation developed over the last 50 years and illustrates them in a lucid and compelling way. Each of the various styles of representation is presented in a simple and intuitive form, and the basics of reasoning with that representation are explained in detail. This approach gives readers a solid foundation for understanding the more advanced work found in the research literature. The presentation is clear enough to be accessible to a broad audience, including researchers and practitioners in database management, information retrieval, and object-oriented systems as well as artificial intelligence. This book provides the foundation in knowledge representation and reasoning that every AI practitioner needs.

*Authors are well-recognized experts in the field who have applied the techniques to real-world problems 
* Presents the core ideas of KR&R in a simple straight forward approach, independent of the quirks of research systems 
*Offers the first true synthesis of the field in over a decade

Table of Contents

1 Introduction * 2 The Language of First-Order Logic *3 Expressing Knowledge * 4 Resolution * 5 Horn Logic * 6 Procedural Control of Reasoning * 7 Rules in Production Systems * 8 Object-Oriented Representation * 9 Structured Descriptions * 10 Inheritance * 11 Numerical Uncertainty *12 Defaults *13 Abductive Reasoning *14 Actions * 15 Planning *16 A Knowledge Representation Tradeoff * Bibliography * Index

/pdf/knowledge-representation-and-reasoning-4dos5m8edp.pdf

Knowledge Representation and Reasoning

What does a conditional knowledge base entail

Propositional knowledge base revision and minimal change

Nonmonotonic reasoning, preferential models and cumulative logics

We prove, assuming the existence of a huge cardinal, the consistency of fully non-regular ultrafilters on the successor of any regular cardinal. We also construct ultrafilters with ultraproducts of small cardinality. Part II is logically independent of Part I.

Martin's Maximum, saturated ideals and non-regular ultrafilters. Part II

Since the work of Godel and Cohen, which showed that Hilbert's First Problem (the Continuum Hypothesis) was independent of the usual assumptions of mathematics (axiomatized by Zermelo–Fraenkel Set Theory with the Axiom of Choice, ZFC), there have been a myriad of independence results in many areas of mathematics. These results have led to the systematic study of several combinatorial principles that have proven effective at settling many of the important independent statements. Among the most prominent of these are the principles diamond(♢) and square(□) discovered by Jensen. Simultaneously, attempts have been made to find suitable natural strengthenings of ZFC, primarily by Large Cardinal or Reflection Axioms. These two directions have tension between them in that Jensen's principles, which tend to suggest a rather rigid mathematical universe, are at odds with reflection properties. A third development was the discovery by Shelah of "PCF Theory", a generalization of cardinal arithmetic that is largely determined inside ZFC. In this paper we consider interactions between these three theories in the context of singular cardinals, focusing on the various implications between square and scales (a fundamental notion in PCF theory), and on consistency results between relatively strong forms of square and stationary set reflection.

Menachem Magidor

Papers

Nonmonotonic reasoning, preferential models and cumulative logics

Nonmonotonic Reasoning, Preferential Models and Cumulative Logics

What does a conditional knowledge base entail

Martin's Maximum, saturated ideals and non-regular ultrafilters. Part II

Squares, scales and stationary reflection