Knowledge representation for mathematical discovery: Three experiments in graph theory

This paper describes the nature of mathematical discovery (including concept definition and exploration, example generation, and theorem conjecture and proof), and considers how such an intelligent process can be simulated by a machine. Although the material is drawn primarily from graph theory, the results are immediately relevant to research in mathematical discovery and learning.The thought experiment, a protocol paradigm for the empirical study of mathematical discovery, highlights behavioral objectives for machine simulation. This thought experiment provides an insightful account of the discovery process, motivates a framework for describing mathematical knowledge in terms of object classes, and is a rich source of advice on the design of a system to perform discovery in graph theory. The evaluation criteria for a discovery system, it is argued, must include both a set of behavior to display (behavioral objectives) and a target set of facts to be discovered (factual knowledge).Cues from the thought experiment are used to formulate two hierarchies of representational languages for graphy theory. The first hierarchy is based on the superficial terminology and knowledge of the thought experiment. Generated by formal grammars with set-theoretic semantics, this eminently reasonable approach ultimately fails to meet the factual knowledge criteria. The second hierarchy uses declarative expressions, each of which has a semantic interpretation as a stylized, recursive algorithm that defines a class by generating it correctly and completely. A simple version of one such representation is validated by a successful, implemented system called Graph Theorist (GT) for mathematical research in graph theory. GT generates correct examples, defines and explores new graph theory properties, and conjectures and proves theorems.Several themes run through this paper. The first is the dual goals, behavioral objectives and factural knowledge to be discovered, and the multiplicity of their demands on a discovery system. The second theme is the central role of object classes to knowledge representation. The third is the increased power and flexibility of a constructive (generator) definition over the more traditional predicate (tester) definition. The final theme is the importance of examples and recursion in mathematical knowledge. The results provide important guidance for further research in the simulation of mathematical discovery.     

A review of object orientation and knowledge processing in office models

The purpose of this paper is to provide an analysis of the alternative modelling systems for office information systems. More specifically, we are interested in identifying the current research trends of merging office modelling ideas together with concepts that owe their origin to the object-oriented paradigm and to artificial intelligence. In this respect an office model is defined as encompassing three domains: passive office objects; dynamically defined and manipulated office procedures; and goal-directed office tasks. Following this definition we exploit the potential of using the object-oriented and knowledge representation techniques for modelling each of the three domains using evidence from real-world applications.     

A comparison of the3He melting curve,T c(P) curve,and the susceptibility of lanthanum-diluted cerium magnesium nitrate below 50 mK

The ac susceptibility of lanthanum-diluted cerium magnesium nitrate has been compared to the temperature scales as derived from the (P, T) relation determined by Halperin and that was measured recently by Greywall. It is found that the susceptibility does not obey a simple Curie-Weiss law over the temperature range between 1 and 50 mK. The results of these calibrations are also used to determine the temperatures for the second-order phase transitions into the superfluid phases of³He at several pressures. TheseT _c(P) values are compared to results of earlier experiments that used thermometry based on the susceptibility of platinum as well as other thermometry techniques.     

The Role of the γ/ γeutectic and porosity on the tensile behavior of a single-crystal nickel-base superalloy

The microstructure of a single-crystal nickel-base superalloy, PWA 1480, has been varied by heat treatment and hot isostatic pressing in order to study the role of the γ/yγ′ eutectic and porosity on subsequent tensile behavior. The level of porosity was found not to affect any of the tensile properties, while the γ/γ′ eutectic strongly influenced ductility. Eliminating the γ/γ′ eutectic increased ductility which was attributed to the cleavage fracture of this constituent. It is proposed that such cleavage of the γ/γ′ eutectic is initiated by the stress created from impinging slip bands, promoting shear localization, and final fracture along {111} slip planes. The precise nature of this fracture process is discussed with emphasis on the role of the γ/′ micro-structure. The deformation structure of PWA 1480 was also studied, and while different in some respects from many other single-crystal superalloys, its fracture process appears to be similar. Formerly Graduate Student, Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University.     

A simple handling technique for mammalian oocytes and embryos during preparation for transmission electron microscopy

Due to their small size, mammalian oocytes and embryos pose unique problems during preparation for transmission electron microscopy. This paper outlines a method which combines protein embedding with centrifugation to locate the specimens on the face of a Beem capsule mould. This method facilitates both the processing of oocytes with minimal loss and rapid location of the specimens within the block for simultaneous sectioning, staining and examination.     

Analysis of the effect of car size on accident injury probability using automobile insurance data

The Highway Loss Data Institute (HLDI) compiles injury and collision claim information from major insurance companies. These data have indicated that a disproportionately large number of injury claims are made for small cars. As a result, it might be concluded that small cars increase injury risk to their occupants. Recent advertisements by a major automobile manufacturer suggest a similar conclusion should be drawn from these data. In this paper it is shown that the apparent higher injury risk attributed to small cars can reflect the behavior of persons driving small cars. The number of injury claim accidents per collision claim accident is examined as an alternative measure of injury risk. Possible problems in interpretation are discussed.