Our own early attempts (as devoted users of LISP) to use PROLOG convinced us that it would be worth the effort to create within LISP a faithful implementation of Kowalski's logic programming idea. We felt it would be very convenient to be able to set up a knowledge base of assertions inside a LISP workspace, and to compute the answers to queries simply by executing appropriate function calls.In Hayes, J. E., Michie, D., and Pao, Y.-H. (Eds.), Machine Intelligence 10. Ellis Horwood.

PROLOG is a simple and powerful progamming language based on first-order logic. This paper examines two possible extensions to the language which would generally be considered "higher-order".t The first extension introduces lambda expressions and predicate variables so that functions and relations can be treated as 'first class' data objects. We argue that this extension does not add anything to the real power of the language. The other extension concerns the introduction of set expressions to denote the set of all (provable) solutions to some goal. We argue that this extension does indeed fill a real gap in the language, but must be defined with care.In Hayes, J. E., Michie, D., and Pao, Y.-H. (Eds.), Machine Intelligence 10. Ellis Horwood.

This is the first presidential address of AAAI, the American Association for Artificial Intelligence. In the grand scheme of history of artificial intelligence (AI), this is surely a minor event. The field this scientific society represents has been thriving for quite some time. No doubt the society itself will make solid contributions to the health of our field. But it is too much to expect a presidential address to have a major impact. So what is the role of the presidential address and what is the significance of the first one? I believe its role is to set a tone, to provide an emphasis. I think the role of the first address is to take a stand about what that tone and emphasis should be-set expectations for future addresses and to communicate to my fellow presidents. Only two foci are really possible for a presidential address: the state of the society or the state of the science. I believe the latter to be correct focus. AAAI itself, its nature and its relationship to the larger society that surrounds it, are surely important. However, our main business is to help AI become a science -- albeit a science with a strong engineering flavor. Thus, though a president's address cannot be narrow or highly technical, it can certainly address a substantive issue. That is what I propose to do.

A framework for inductive inference in logic is presented: a Model Inference Problem is defined, and it is shown that problems of machine learning and program synthesis from examples can be formulated naturally as model inference problems. A general, incremental inductive inference algorithm for solving model inference problems is developed. This algorithm is based on Popper's methodology of conjectures and refutations [II]. The algorithm can be shown to identify in the limit [3] any model in a family of complexity classes of models, is most powerful of its kind, and is flexible enough to have been successfully implemented for several concrete domains. The Model Inference System is a Prolog implementation of this algorithm, specialized to infer theories in Horn form.

'Non-monotonic' logical systems are logics in which the introduction of new axioms can invalidate old theorems. Such logics are very important in modeling the benefits of active processes which, acting in the presence of incomplete information, must make and subsequently revise assumptions in light of new observations. We present the motivation and history of such logics. We develop model and proof theories, a proof procedure, and applications for one non-monotonic logic. In particular, we prove the completeness of the non-monotoic predicate calculus and the decidability of the non-monotonic sentential calculus. We also discuss characteristic properties of this logic and its relationship to stronger logics, logics of incomplete information, and truth maintenance systems. Artificial Intelligence 13:41-72.

Assume we have the following transformation rules that define integer multiplication: 0. v 0

"Circumscription is a rule of conjecture that can be used by a person or program for `jumping to certain conclusions'. Namely, the objects that can be shown to have a certain property P by reasoning from certain facts A are all the objects that satisfy P. More generally, circumscription can be used to conjecture that the tuples that can be shown to satisfy a relation P(x, y, z) are all the tuples satisfying this relation. Thus we circumscribe the set of relevant tuples."Artificial Intelligence 13:27-39. Also in Readings in Artificial Intelligence, B.L. Webber and N.J. Nilsson (eds.), Tioga Publishing, 1981.

A programming language needs simple and well defined semantics. 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.

Minsky introduced the terminology of'frames' to unify and denote a loose collection of related ideas on knowledge representation: a collection which, since the publication of his paper (Minsky, 1975) has become even looser. It is not at all clear now what frames are, or were ever intended to be. I will assume, below, that frames were put forward as a (set of ideas for the design of a) formal language for expressing knowledge, to be considered as an alternative to, for example, semantic networks or predicate calculus. At least one group have explicitly designed such a language, KRL (Bobrow/ Winograd, 1977a, 19776), based on the frames idea. But it is important to distinguish this from two other possible interpretations of what Minsky was urging, which one might call the metaphysical and the heuristic (following the terminology of (Mc Carthy/Hayes, 1968)). The "metaphysical" interpretation is, that to use frames is to make a certain kind of assumption about what entities shall be assumed to exist in the world being described.

Our purpose in studying natural language understanding in conjunction with problem solving is to bring together the constraints of what formal representation can actually be obtained with the question of what knowledge is required in order to solve a wide range of problems in a semantically rich domain. We believe that these issues cannot sensibly be tackled in isolation. In practical terms we have had the benefits of an increased awareness of common problems in both areas and a realisation that some of our techniques are applicable to both the control of inference and the control of parsing. Early work on solving mathematical problems stated in natural language was done by Bobrow (STUDENT - (i]) and Chamiak (CARPS - [5]). However the rudimentary parsing and simple semantic structures used by Bobrow and Charniak are inadequate for any but the easiest problems. Our intention has been to build on B/RG Chris This work was supported by SRC grant number 94493 and an SRC research studentship for Mellish.