This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate “partial meet contraction functions”, which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are “relational” and “transitively relational”, are studied in detail, and their connections with certain “supplementary postulates” of Gardenfors investigated, with a further representation theorem established.

On the logic of theory change: Partial meet contraction and revision functions

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

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Knowledge Representation and Reasoning

The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules in a declarative manner, and a defeasible argumentation inference mechanism for warranting the entailed conclusions. In DeLP an argumentation formalism will be used for deciding between contradictory goals. Queries will be supported by arguments that could be defeated by other arguments. A query $q$ will succeed when there is an argument ${\mathcal A}$ for $q$ that is warranted, i.e. the argument ${\mathcal A}$ that supports $q$ is found undefeated by a warrant procedure that implements a dialectical analysis. The defeasible argumentation basis of DeLP allows to build applications that deal with incomplete and contradictory information in dynamic domains. Thus, the resulting approach is suitable for representing agent's knowledge and for providing an argumentation based reasoning mechanism to agents.

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Defeasible logic programming: an argumentative approach

Propositional knowledge base revision and minimal change

Knowledge Representation, which lies at the core of Artificial Intelligence, is concerned with encoding knowledge on computers to enable systems to reason automatically. The Handbook of Knowledge Representation is an up-to-date review of twenty-five key topics in knowledge representation, written by the leaders of each field.This book is an essential resource for students, researchers and practitioners in all areas of Artificial Intelligence. * Make your computer smarter* Handle qualitative and uncertain information* Improve computational tractability to solve your problems easily

Handbook of Knowledge Representation

A major problem for knowledge representation is how to revise a knowledge system in the light of new information that is inconsistent with what is already in the system. Another related problem is that of contractions, where some of the information in the knowledge system is taken away.

Here, the problems of modelling revisions and contractions are attacked in two ways. First, two sets of rationality postulates or integrity constraints are presented, one for revisions and one for contractions. On the basis of these postulates it is shown that there is a natural correspondence between revisions and contractions.

Second, a more constructive approach is adopted based on the "epistemic entrenchment" of the facts in a knowledge system which determines their priority in revisions and contractions. We introduce a set of computationally tractable constraints for an ordering of epistemic entrenchments.

The key result is a representation theorem which says that a revision method for a knowledge system satisfies the set of rationality postulates, if and only if, there exists an ordering of epistemic entrenchment satisfying the appropriate constraints such that this ordering determines the retraction priority of the facts of the knowledge system. We also prove that the amount of information needed to uniquely determine the required ordering is linear in the number of atomic facts of the knowledge system.

Revisions of knowledge systems using epistemic entrenchment

General patterns in nonmonotonic reasoning

In a range of contexts, one comes across processes resembling inference, but where input propositions are not in general included among outputs, and the operation is not in any way reversible. Examples arise in contexts of conditional obligations, goals, ideals, preferences, actions, and beliefs. Our purpose is to develop a theory of such input/output operations. Four are singled out: simple-minded, basic (making intelligent use of disjunctive inputs), simple-minded reusable (in which outputs may be recycled as inputs), and basic reusable. They are defined semantically and characterised by derivation rules, as well as in terms of relabeling procedures and modal operators. Their behaviour is studied on both semantic and syntactic levels.

David Makinson

Papers

On the logic of theory change: Partial meet contraction and revision functions

Revisions of knowledge systems using epistemic entrenchment

General patterns in nonmonotonic reasoning

Input/output logics

Nonmonotonic inference based on expectations