Next steps in implementing Kaput's research programme

We explore some key constructs and research themes initiated by Jim Kaput, and attempt to illuminate them further with reference to our own research. These 'design principles' focus on the evolution of digital representations since the early nineties, and we attempt to take forward our collective understanding of the cognitive and cultural affordances they offer. There are two main organising ideas for the paper. The first centres around Kaput's notion of outsourcing of processing power, and explores the implications of this for mathematical learning. We argue that a key component for design is to create visible, transparent views of outsourcing, a transparency without which there may be as many pitfalls as opportunities for mathematical learning. The second organising idea is that of communication, a key notion for Kaput, and the importance of designing for communication in ways that recognise the mutual influence of tools for communication and for mathematical expression

Approximating the rank of a homomorphism using a Prolog based system

A system of Prolog based programs for the purpose of approximating the rank of algebraic operations of finite unary algebras is presented. The rank function is a measure of finite algebras and their algebraic operations. Rank is a recursive function used in universal algebra and was first introduced as a tool for proving strong dualizability. Logic programming. particularly Prolog, is commonly used in natural language processing, an area of study devoted to the use of computers to understand human (natural) languages. One goal of this thesis is to explore a relationship between the fields of Mathematics and Computer Science through the application of logic programming techniques on structures from universal algebra. This thesis is motivated by the idea that when universal algebra is viewed as a language, the ideas of natural language processing can be used to create a computer system which approximates rank. The outcome of the research is a computational model that computes the Kth approximation of rank. A set of Prolog programs that act as useful tools on algebraic structures are created.The original print copy of this thesis may be available here: http://wizard.unbc.ca/record=b121201

The VEX-93 environment as a hybrid tool for developing knowledge systems with different problem solving techniques

The paper describes VEX-93 as a hybrid environment for developing knowledge-based and problem solver systems. It integrates methods and techniques from artificial intelligence, image and signal processing and data analysis, which can be mixed. Two hierarchical levels of reasoning contains an intelligent toolbox with one upper strategic inference engine and four lower ones containing specific reasoning models: truth-functional (rule-based), probabilistic (causal networks), fuzzy (rule-based) and case-based (frames). There are image/signal processing-analysis capabilities in the form of programming languages with more than one hundred primitive functions. User-made programs are embeddable within knowledge basis, allowing the combination of perception and reasoning. The data analyzer toolbox contains a collection of numerical classification, pattern recognition and ordination methods, with neural network tools and a data base query language at inference engines's disposal. VEX-93 is an open system able to communicate with external computer programs relevant to a particular application. Metaknowledge can be used for elaborate conclusions, and man-machine interaction includes, besides windows and graphical interfaces, acceptance of voice commands and production of speech output. The system was conceived for real-world applications in general domains, but an example of a concrete medical diagnostic support system at present under completion as a cuban-spanish project is mentioned. Present version of VEX-93 is a huge system composed by about one and half millions of lines of C code and runs in microcomputers under Windows 3.1.Postprint (published version