Discovery Systems: From AM to CYRANO

The emergence in 1976 of Doug Lenat's mathematical discovery program AM [Len76] [Len82a] was met with suprise and controversy; AM's performance seemed to bring the dream of super-intelligent machines to our doorstep, with amazingly simple methods to boot. However, the seeming promise of AM was not borne out: no generation of automated super-mathematicians appeared. Lenat's subsequent attempts (with his work on the Eurisko program) to explain and alleviate AM's problems were something of a novelty in Artificial Intelligence research; AI projects usually 'let lie' after a brief moment in the limelight with a handful of examples. Lenat's work on Eurisko revealed certain constraints on the design of discovery programs; in particular, Lenat discovered that a close coupling of representation syntax and semantics is neccessary for a discovery program to prosper in a given domain. After Eurisko, my own work on the discovery program Cyrano has revealed more constraints on discovery processes in general in particular, work on Cyrano has revealed a requirement of 'closure' in concept formation. The concepts generated by a discovery program's concept formation component must be usable as inputs to that same concept formation component. Beginning with a theoretical analysis of AM's actual performance, this program presents a theory of discovery and goes on to present the implementation of an experiment — the CYRANO program — based on this theory. (This article is a preliminary version of an invited paper fro the First International Symposium on Artificial Intelligence and Expert Systems, to be held in Berlin on May 18-22 1987.)MIT Artificial Intelligence Laborator

Purposive discovery of operations

The Generate, Prune & Prove (GPP) methodology for discovering definitions of mathematical operators is introduced. GPP is a task within the IL exploration discovery system. We developed GPP for use in the discovery of mathematical operators with a wider class of representations than was possible with the previous methods by Lenat and by Shen. GPP utilizes the purpose for which an operator is created to prune the possible definitions. The relevant search spaces are immense and there exists insufficient information for a complete evaluation of the purpose constraint, so it is necessary to perform a partial evaluation of the purpose (i.e., pruning) constraint. The constraint is first transformed so that it is operational with respect to the partial information, and then it is applied to examples in order to test the generated candidates for an operator's definition. In the GPP process, once a candidate definition survives this empirical prune, it is passed on to a theorem prover for formal verification. We describe the application of this methodology to the (re)discovery of the definition of multiplication for Conway numbers, a discovery which is difficult for human mathematicians. We successfully model this discovery process utilizing information which was reasonably available at the time of Conway's original discovery. As part of this discovery process, we reduce the size of the search space from a computationally intractable size to 3468 elements

HR: A System for Machine Discovery in Finite Algebras

We describe the HR concept formation program which invents mathematical definitions and conjectures in finite algebras such as group theory and ring theory. We give the methods behind and the reasons for the concept formation in HR, an evaluation of its performance in its training domain, group theory, and a look at HR in domains other than group theory

The Sentient Web

In a startling revelation, a team of university scientists has reported that a network of computers has become conscious and sentient, and is beginning to assume control of online information system. In spite of the ominous tone typically chosen for dramatic effect, a sentient Web would be more helpful and much easier for people to use. An agent is an active, persistent software component that perceives, reasons, and acts, and whose actions include communication. Agents inherently take intentional actions based on sensory information and memories of past actions. All agents have necessary communication ability, but they do not necessarily possess introspective capabilities or awareness of place and time. Four things characterize being sentient Web conscious: 1) knowing 2) having intentions 3) introspecting and 4) experiencing phenomena. For the first two, it is easy to show that most Web entities possess and demonstrate the use of knowledge, and other entities, including Web services, exhibit intentions. The last two, introspection and phenomenal experience, are facets of awareness and are not as obvious in current Web systems, so we will consider them more thoroughly and conclude with future prospects

On the Notion of Interestingness in Automated Mathematical Discovery

Deciding whether something is interesting or not is of central importance in automated mathematical discovery, as it helps determine both the search space and search strategy for finding and evaluating concepts and conjectures

Using meta-level inference to constrain search and to learn strategies in equation solving

This thesis addresses two questions:- How can search be controlled in domains with a large search space?- How can this control information be learned?It is argued that both problems can be tackled with the aid of a technique called meta-level inference.In this technique, the control information is separated from the factual information. The control information is expressed declaratively, i.e. the control information is represented as explicit rules. These rules are axioms in the meta-theory of the domain. This gives rise to a two level program, the factual information forms the object-level and the control information forms the meta-level. Inference is performed at the meta-level. and this induces inference at the object-level. Search at the object-level is replaced by search at the meta-level. This has several advantages, one of the most important being that the meta-level search space is usually much smaller than the object-level space, so the search problem is greatly reduced.Two programs are presented in this thesis to support this claim. Both programs operate in the domain of symbolic equation solving. However, the techniques used can be applied to a wide variety of domains.The first program. PRESS, solves symbolic, transcendental, non-differential equations. PRESS makes extensive use of meta-level inference to control search. This overcomes problems experienced by other approaches. For example, systems that apply rewrite rules exhaustively usually only use the rules one way round, to avoid looping. However, this often makes the system incomplete, and the techniques for completing this set are not easily mechanized. PRESS is able to use rules in both directions, using inference to decide which direction is appropriate.The second program, LP is also an equation solving program, but, unlike PRESS, it is capable of learning new equation-solving techniques. It embodies a new learning method, called Precondition Analysis. Precondition Analysis combines meta-level inference with concepts from the field of planning, and allows the program to learn even from a single example. This learning technique seems particularly suitable in domains where the operators don't have precisely defined effects and preconditions. Equation solving is such a domain