The paper exhibits experience, and that of others using QA2 and QA3, solutions to these problems obtained by QA3, a one of the first difficulties encountered is the computer program based on these theorem-proving representation of problems, especially statetransformation methods.

I want to review what 1 consider to be the important results of this paper. One is the observation that, when we reason, we use representations of the objects 11.2. Concluding remarks, history and thanks we are reasoning about as well as a representation of the facts about these objects.

This talk reviews those efforts in automatic theorem proving, during the past few years, which have theory, very easy for the computer.

John McCarthy, born at Boston, Mass. in 1927, received his B.S. degree in mathematics at the California Institute of Technology in 1948, and his Ph.D. also in mathematics at Princeton University in 1951. He is at present Assistant Professor of Communication Sciences at the Massachusetts Institute of Technology. His present interests are in the artificial intelligence problem, automatic programming and mathematical logic. He is co-editor with Dr. C. E. Shannon of "Automatic Studies". SUMMARY INTERESTING work is being done in programming computers to solve problems which require a high degree of intelligence in humans. However, certain elementary verbal reasoning processes so simple that they can be carried out by any non--feeble--minded human have yet to be simulated by machine programs. This paper will discuss programs to manipulate in a suitable formal language (most likely a part of the predicate calculus) common instrumental statements. The basic program will draw immediate conclusions from a list of premises. These conclusions will be either declarative or imperative sentences. When an imperative sentence is deduced the program takes a corresponding action. These actions may include printing sentences, moving sentences on lists, and reinitiating the basic deduction process on these lists. Facilities will be provided for communication with humans In the system via manual intervention and display devices connected to the computer.

If ability to perform complex calculations were a sufficient criterion, then even a conventional digital computor could lay claim to more intelligence than any of usand perhaps we had better let it make away with the word and be done with it.

Most recent work on reasoning with cases in law has taken the style of reasoning used in the CATO system as its model, and uses the notion of factors, as found in that system. Fundamental to CATO, a successor the HYPO system, were factors, which are closely related to HYPO-style dimensions. In this paper, we will argue that the simplification involved in using factors, while it has proved pragmatically useful both for clarifying understanding of certain aspects of reasoning with cases and for implementation, causes problems with domain analysis and precludes certain kinds of argument that we would wish to model. We therefore believe that the time is now ripe to go back to the original notion of dimensions, while retaining the insights that have been gained from working with the simpler notion of factors. The paper uses two case studies to argue that this is so.

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

References are to text of chapters, not to the bodies of bibliographies.

A new predicate calculus deduction system based on production rules is proposed. The system combines several developments in Artificial Intelligence and Automatic Theorem Proving research including the use of domain-specific inference rules and separate mechanisms for forward and backward reasoning. It has a clean separation between the data base, the production rules, and the control system. Goals and subgoals are maintained in an AND/OR tree structure. We introduce here a structure that is the dual of the AND/OR tree to represent assertions. The production rules modify these structures until they "connect" in a fashion that proves the goal theorem. Unlike some previous systems that used production rules, ours is not limited to rules in Horn Clause form. Unlike previous PLANNER-like systems, ours can handle the full range of predicate calculus expressions including those with quantified variables, disjunctions, and negations.

The two favoured theoretical bases for languages have been lambda calculus as advocated by Landin and others, and predicate calculus as advocated by Kowalski (see Landin (1966) and Kowalski (1973)). In this paper I adopt an approach based on predicate calculus, but in a manner that differs from the existing PROLOG language (Warren 1975 and Battani & Meloni 1973) in that I adopt a "forward inference" approach -- inferring conclusions from premises, rather than the "backward inference" approach of PROLOG, which starts with a desired conclusion and tries to find ways of inferring it. This difference is reflected in the internal structure of the associated implementations, that of PROLOG being a "backtrack search" kind of implementation, while the most obvious implementation of the system proposed here involves a kind of mass operation on tables of data, reminiscent of APL (Iverson 1962) but in fact identical in many respects with the work of Codd (Codd 1970) on relational data bases. Indeed, from one perspective this paper can be seen as an extension of Codd's work into the realm of general purpose computing. As in the case of PROLOG it is necessary for the user of the relational programming system to make statements which are not associated with the logical structure of the problem, but reflect the need to control the computation. In PROLOG these are effected by the use of extra-logical control primitives, but in our system control is exercised by the introduction of predicates for that purpose, which have exactly the same semantics as the predicates relevant to the logical structure of the problem. In later sections I deal with the problem of introducing equality into the system, in a way that reflects the normal mathematical usage of equality.