Artificial intelligence tasks which can be formulated as constraint satisfaction problems, with which this paper is for the most part concerned, are usually solved by backtracking. By examining the thrashing behavior that nearly always accompanies backtracking, identifying three of its causes and proposing remedies for them we are led to a class of algorithms which can profitably be used to eliminate local (node, arc and path) inconsistencies before any attempt is made to construct a complete solution. A more general paradigm for attacking these tasks is the alternation of constraint manipulation and case analysis producing an OR problem graph which may be searched in any of the usual ways. Many authors, particularly Montanan i and Waltz, have contributed to the development of these ideas; a secondary aim of this paper is to trace that history. The primary aim is to provide an accessible, unified framework, within which to present the algorithms including a new path consistency ...

ABSTRACT To choose their actions, reasoning programs must be able to make assumptions and subsequently revise their beliefs when discoveries contradict these assumptions. The Truth Maintenance System (TMs) is a problem solver subsystem for performing these functions by recording and maintaining the reasons for program beliefs. Such recorded reasons are useful in constructing explanations of program actions and in guiding the course of action of a problem solver. In memory of John Sheridan Mac Nerney 1. Introduction Computer reasoning programs usually construct computational models of situations. To keep these models consistent with new information and changes in the situations being modelled, the reasoning programs frequently need to remove or change portions of their models.

ABSTRACT This talk reviews those efforts in automatic theorem proving, during the past few years, which have emphasized techniques other than resolution. These include: knowledge bases, natural deduction, reduction, (rewrite rules), typing, procedures, advice, controlled forward chaining, algebraic simplification, built-in associativity and commutativity, models, analogy, and man-machine systems. Examples are given and suggestions are made for future work. Earlier work by Newell, Simon, Shaw, and Gelernter in the middle and late 1950s emphasized the heuristic approach, but the weight soon shifted to various syntactic methods culminating in a large effort on resolution type systems in the last half of the 1960s. It was about 1970 when considerable interest was revived in heuristic methods and the use of human supplied, domain dependent, knowledge.

ABSTRACT In this paper we present a new algorithm for searching trees. It does this by attempting to find both the best arc at the root and the simplest proof, in best-first fashion. This strategy determines the order of node expansion. Any node that is expanded is assigned two values: an upper (or optimistic) bound and a lower (or pessimistic) bound. During the course of a search, these bounds at a node tend to converge, producing natural termination of the search.

R. H. Richens was born in Penge, near London, in 1919. He read natural sciences at Cambridge and is now Assistant Director of the Commonwealth Bureau of Plant Breeding and Genetics at Cambridge. He has been a member of the Cambridge Language Research Group since its foundation. His principal research interests have been the taxonomy and history of the elm, the history of Soviet genetics, and machine translation. Everything symbolized by a set of symbols constitutes the domain of symbolization of the set.

The Role of Experiences and Examples in Learning Systems Edwina L. Rissland Oliver G. Selfridge Elliot M. Soloway* Department of Computer and Information Science University of Massachusetts Amherst, MA 01003 Abstract In this paper, we discuss the role of experiences and examples in learning systems. We discuss these issues in the context of three systems in particular: Rissland and Soloway's Constrained Example Generation (CEG) System, Selfridge's COUNT, and Soloway's BASEBALL. Examples provide the basis from which generalizations, concepts and conjectures are made. They also provide the criticisms needed to refute and refine. For instance, in Winston's learning program [Winston 1975], examples of the concept to be learned, e.g., an arch, and non-examples, e.g., "near misses", are the critical input from which his program builds a structural description of a concept.

Department of Computer Science University of British Columbia This is not a comprehensive survey of machine vision which, in its broadest sense, includes all computer programs that process pictures. Restricting attention to scene analysis programs that interpret line data as polyhedral scenes makes it possible to examine those programs in depth, comment on revealing mistakes, explore the interrelationships and exhibit the thematic development of the field. Starting with Roberts' seminal work which established the paradigm, there has been an evolutionary succession of programs and proposals each approaching the problem with a different emphasis. In addition to Roberts' program this paper expounds in detail work done by Guzman, Falk, Huffman, Clowes, Mackworth, and Waltz. These programs are presented, compared, contrasted and, sometimes, criticized in order to exhibit the development of a variety of themes including the representation of the picture-formation process, segmentation, support, occlusion, lighting, the scene description, picture cues and models of the world.

That is all, except that there follows a list of initial statements (axioms) that involve the words "point', "line" and "plane", and from which other statements involving those undefined words can now be deduced by logic alone. This permits geometry to be taught to a blind man and even to a computer!" Leaving aside the attitude implicit in Kac & Ulam's use of the word'even' in the phrase even to a computer', it has become clear that programs to prove theorems in first order axiomatic theories such as geometry, working in this blind' way, are unlikely to be successful. In parentheses, one might remark that mathematicians, however they express their proofs, usually do not construct them by working entirely within the formal syntactic system (i.e. Premises: To prove: MBC M is the midpoint of segment BC BD is the perpendicular from B to AM CE is the perpendicular from C to AM. segment BD segment CE. an appropriate diagram could be that of Figure 1(a).

This paper describes some recent experiments with a computer program which is capable of useful, or at least interesting, application to a number of different problems. The program, the Graph Traverser, has been described in detail in a previous paper (Doran & Michie 1966). However, we shall here need to view the basic algorithm from a rather more general standpoint, corresponding to an actual extension in the flexibility of the program, so that a restatement of what the program can do is desirable. The Graph Traverser, which is written in Elliott 4100 Algol, is potentially applicable to problem situations which can be idealised in the following way (see for comparison Newell and Ernst 1965). There is given a set of'states', which are connected by a set of'transformations', or, as I shall call them, 'operators'.