Naive Physics, Event Perception, Lexical Semantics, and Language Acquisition

This thesis proposes a computational model of how children may come to learn the meanings of words in their native language. The proposed model is divided into two separate components. One component produces semantic descriptions of visually observed events while the other correlates those descriptions with co-occurring descriptions of those events in natural language. The first part of this thesis describes three implementations of the correlation process whereby representations of the meanings of whole utterances can be decomposed into fragments assigned as representations of the meanings of individual words. The second part of this thesis describes an implemented computer program that recognizes the occurrence of simple spatial motion events in simulated video input.

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.

The Structure of Mathematical Knowledge

This report develops a conceptual framework in which to talk about mathematical knowledge. There are several broad categories of mathematical knowledge: results which contain the traditional logical aspects of mathematics; examples which contain illustrative material; and concepts which include formal and informal ideas, that is, definitions and heuristics.