The methods used for solving equations are described, together with the service facilities. The principal technique, meta-level inference, appears to have applications in the broader field of symbolic and algebraic manipulation. Acknowledgements This work was supported by SERC grants GR/BI29252 and GR/B/73989 and various studentships. Keywords equation solving, rewrite rules, meta-level inference, logic programming I. Introduction The PRESS program was originally developed with two aims in mind. The first aim was to use the program as a vehicle to explore some ideas about controlling search in mathematical reasoning using meta-level descriptions and strategies.

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.

In IJCAI-81, p. 1064.

"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.

'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.

ACM Transactions on Programming Languages and Systems 2(1): 90-121.

A program called "AM" is described which carries on simple mathematics research,defining and studying new concepts under the guidance of a large body ofheuristic rules. The 250 heuristics communicate via an agenda mechanism, aglobal priority queue of small tasks for the program to perform, and reasons whyeach task is plausible (for example, "Find generalizations of 'primes', because'primes' turned out to be so useful a concept"). Each concept is represented asan active, structured knowledge module. One hundred very incomplete modulesare initially supplied, each one corresponding to an elementary set-theoreticconcept (for example, union). This provides a definite but immense space whichAM begins to explore. In one hour, AM rediscovers hundreds of common concepts(including singleton sets, natural numbers, arithmetic) and theorems (for example,unique factorization).Summary of Ph.D. dissertation.Hayes, J.E., D. Michie, and L. I. Mikulich (Eds.), Machine Intelligence 9, Ellis Horwood.

In this paper we have shown how it is possible to use certain combinators onrelations to produce an interpretation of a class of clauses (Horn Clauses) inpredicate logic. The work was inspired by a particular view of the task of writingcertain kinds of program, but has not yet given rise to a system implementedon a digital computer, although some initial studies have been made.Hayes, J.E., D. Michie, and L. I. Mikulich (Eds.), Machine Intelligence 9, Ellis Horwood.

In Metzing, D. (Ed.), Frame Conceptions and Text Understanding, pp. 46–61. de Gruyter.

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.