Symbolic Mathematical Laboratory

A large computer program has been developed to aid applied mathematicians in the solution of problems in non-numerical analysis which involve tedious manipulations of mathematical expressions. The mathematician uses typed commands and a light pen to direct the computer in the application of mathematical transformations; the intermediate results are displayed in standard text-book format so that the system user can decide the next step in the problem solution. Three problems selected from the literature have been solved to illustrate the use of the system. A detailed analysis of the problems of input, transformation, and display of mathematical expressions is also presented.

Hypothesis Formation and Evaluation in Medical Diagnosis

This thesis describes some aspects of a computer system for doing medical diagnosis in the specialized field of kidney disease. Because such a system faces the spectre of combinatorial explosion, this discussion concentrates on heuristics which control the number of concurrent hypotheses and efficient "compiled" representations of medical knowledge. In particular, the differential diagnosis of hematuria (blood in the urine) is discussed in detail. A protocol of a simulated doctor/patient interaction is presented and analyzed to determine the crucial structures and processes involved in the diagnosis procedure. The data structure proposed for representing medical information revolves around elementary hypotheses which are activated when certain disposing of findings, activating hypotheses, evaluating hypotheses locally and combining hypotheses globally is examined for its heuristic implications. The thesis attempts to fit the problem of medical diagnosis into the framework of other Artifcial Intelligence problems and paradigms and in particular explores the notions of pure search vs. heuristic methods, linearity and interaction, local vs. global knowledge and the structure of hypotheses within the world of kidney disease.