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…

Requirements acquisition is one of the most important and least well supported parts of the software development process. The Requirements Apprentice (RA) will assist a human analyst in the creation and modification of software requirements. Unlike current requirements analysis tools,…

The concept of free as in "free group" is generalized to any first order theory. An interesting class of homomorphisms between models is discussed. Relations between model theory and abelian categories are discussed speculatively. This paper represents an incomplete study…

This report describes a system which maintains canonical expressions for designators under a set of equalities. Substitution is used to maintain all knowledge in terms of these canonical expressions. A partial order on designators, termed the better-name relation, is used…

The actor message-passing model of concurrent computation has inspired new ideas in the areas of knowledge-based systems, programming languages and their semantics, and computer systems architecture. The model itself grew out of computer languages such as Planner, Smalltalk, and Simula,…

In this paper we look at some of the ingredients and processes involved in the understanding of mathematics. We analyze elements of mathematical knowledge, organize them in a coherent way and take note of certain classes of items that share…

This thesis confronts the nature of the process of learning an intellectual skill, the ability to solve problems efficiently in a particular domain of discourse. The investigation is synthetic; a computational performance model, HACKER, is displayed. Hacker is a computer…

Omega is a description system for knowledge embedding which incorporates some of the attractive modes of expression in common sense reasoning such as descriptions, inheritance, quantification, negation, attributions and multiple viewpoints. A formalization of Omega is developed as a framework…

The work reported here lies in the area of overlap between artificial intelligence software engineering. As research in artificial intelligence, it is a step towards a model of problem solving in the domain of programming. In particular, this work focuses…

How can we construct a program that will understand stories that children would understand? By understand we mean the ability to answer questions about the story. We are interested here with understanding natural language in a very broad area. In…