The research pursued in the early 1980s by Rissland, Ashley, Branting, and Skalak explored the rich vein of case-based reasoning in the context of legal argument. Some of these seminal projects were presented in a special 1991 pair of issues of the International Journal of Man-Machine Studies (e.g., Ashley 1991; Branting, 1991; Rissland & Skalak, 1991). Ideas from these research projects lay the foundation of what is now termed interpretive CBR, that is, how to interpret new cases in light of past interpretations. This work has also influenced the community that develops formal models of argumentation and defeasible reasoning, and these models have in turn contributed more formal models to CBR (e.g., Bench-Capon & Sartor, 2003). The AI and law community continues to provide a rich tributary of ideas and techniques about CBR and for integrating it with other reasoning modalities in CBR hybrids, such as rule-based reasoning, heuristic search, and information retrieval.

As an indispensable supplement to reasoning cases, or mopcs) to outline an argument regarding deductively with legal rules, attorneys and judges reason how to decide the cfs based on its significant similarities to analogically with precedent cases; rule predicates are and differences from mopes. A claim lattice projects the case knowledge seldom exists to legal questions. Legal experts make base (CKB) onto the problem situation to create a neighborhood competing arguments instead, pitting conflicting interpretations of cases surrounding the problem situation in which of cases and facts against each other. We will present a Hypo, a computer program that performs case-based detailed example of a claim lattice actually generated by reasoning in the legal domain, helps attorneys analyze and Hypo to analyze a real legal case. To perform this task, indexing and retrieving relevant cases are not enough.

Also to appear in Proceedings NIE--LRDC Conference on Thinking and Learning Skills, Lawrence Erlbaum Associates.

In mathematics, examples can be said to be as important to understanding as the traditionally exalted definitions, theorems, and proofs (Rissland 1978). In fact, some mathematical areas developed in response to troublesome counter-examples like modern real function theory which has been called'the branch of mathematics which deals with counter-examples" (Munroe 1953). In the law, examples -- that is, legal cases -- are the basis from which the law derives (at least in common law systems like those of the United States and England): the law is made through court decisions by consideration of specific problems in specific cases. The cases lead to rule-like decisions which are then refined (or perhaps refuted, i.e., overturned) in subsequent cases. In linguistics, for instance in the study of syntax, linguistic rules are derived from study of examples of actual language and are then subjected to testing on more examples. Some examples are taken from the infinite store of run of the mill sentences available to every natural speaker; others, like certain difficult garden path sentences, are fabricated and used as counter-examples are in mathematics.

A. YONEZAWA and C. HEWITT 41 REPRESENTATIONS FOR ABSTRACT REASONING 4 A maximal method for set variables in automatic theorem-proving W. W. BLEDSOE

J. Do RAN 433 22 Chromosome classification and segmentation as exercises in knowing what to expect.

B.RANDELL 3 PROGRAM PROOF AND MANIPULATION 2 Some techniques for proving correctness of programs which alter data structures.

The two outstanding figures in the history of computer science are Alan Turing and John von Neumann, and they shared the view that logic was the key to understanding and automating computation. In particular, it was Turing who gave us in the mid-1930s the fundamental analysis, and the logical definition, of the concept of'computability by machine' and who discovered the surprising and beautiful basic fact that there exist universal machines which by suitable programming can be made to t This essay is an expanded and revised version of one entitled The Role of Logic in Computer Science and Artificial Intelligence, which was completed in January 1992 (and was later published in the Proceedings of the Fifth Generation computer Systems 1992 Conference). Since completing that essay I have had the benefit of extremely helpful discussions on many of the details with Professor Donald Michie and Professor I. J. Good, both of whom knew Turing well during the war years at Bletchley Park. Professor J. A. N. Lee, whose knowledge of the literature and archives of the history of computing is encyclopedic, also provided additional information, some of which is still unpublished. Further light has very recently been shed on the von Neumann side of the story by Norman Macrae's excellent biography John von Neumann (Macrae 1992). Accordingly, it seemed appropriate to undertake a more complete and thorough version of the FGCS'92 essay, focussing somewhat more on the interesting historical and biographical issues. I am grateful to Donald Michie and Stephen Muggleton for inviting me to contribute such a'second edition' to the present volume, and I would also like to thank the Institute for New Computer Technology (ICOT) for kind permission to make use of the FGCS'92 essay in this way. 1 LOGIC, COMPUTERS, TURING, AND VON NEUMANN

When you lose a game of chess to a computer then don't pretend that you didn't think at the game.

In this paper we will be concerned with such reasoning in its most general form, that is, in inferences that are defeasible: given more information, we may retract them. The purpose of this paper is to introduce a form of non-monotonic inference based on the notion of a partial model of the world. We take partial models to reflect our partial knowledge of the true state of affairs. We then define non-monotonic inference as the process of filling in unknown parts of the model with conjectures: statements that could turn out to be false, given more complete knowledge. To take a standard example from default reasoning: since most birds can fly, if Tweety is a bird it is reasonable to assume that she can fly, at least in the absence of any information to the contrary. We thus have some justification for filling in our partial picture of the world with this conjecture. If our knowledge includes the fact that Tweety is an ostrich, then no such justification exists, and the conjecture must be retracted.