Digraphs, Knowledge Hypernets, and Neurons

A current flow network of switches, with input node I and output node O, are represented by a directed graph G. In G we define a model of a neuron, and introduce another model in which neurons are theoretically linked. In this second model, we cover invariance, information flow and noise. We show how this model arises from G, how it can be taught, and how it can be declaratively interpreted. The system is made dynamic due to the closing, from O to I, through the environment of the combined models, of a feedback circuit

Neurons, knowledge hypernets, and information flow

We described a model of a neuron and a system for modelling nets of neurons. We notice that this could lead to application of Menger’s Theorem to information flow. In this paper we deal briefly with that topic in the system model. We deduce the transport network max-flow, min-cut theorem of Ford and Fulkerson for information flow and discuss the meaning of information flow

A formal representation of the method of learning

We show how the method of learning in science, education, and mathematics can be represented by a knowledge hypernet and its concept-relationship knowledge structure interpretations. We conclude that the method of learning is invariant over the three fields. The paper is particularly suited for teachers of science, particularly physics, and of mathematics, and in the philosophy of science, but is also relevant for educators at every level of instruction. Those working in the fields of cognitive science and knowledge representation can also benefit from this paper and its main references

Relation nets and hypernets

In many respects this report is a companion work of our book "Knowledge representation and relation nets. Kluwer Academic Publishers, Boston, 1999". In some senses it runs parallel to it, while in others it is a sequel to that book. Readers not familiar with the book will find themselves refering back to it several instances to follow some of the subtleties of this work, particularly in the case of concept-relationship knowledge stuctures, abbreviated CRKS in what follows. The main application of CRKS's - namely modelling study material - is not explicitly transscribed to this paper, but that whole notion is abstracted and made independent of any specific teaching/learning metalanguage through the implications of this abstraction. Two key factors emerge from this paper on hypernets. First, unlike the case for CRKS's in which little of the general theory of relation nets applies to CRKS's, the broad theory of hypernets, as far as it is covered in this report, is often applicable to the hypernet equivalent of a CRKS. Second, we will show a link between relation net isomorphism and hypernet isomorphism which makes it considerably easier to deal with CRKS isomorphism and, thus, with structural analogy as used in a modelling based approach to teaching/learning/analogical reasoning. Finally, we must mention that it appears that the domain of potential practical applications of hypernets must inevitably be wider than that for relation nets

Modelling Knowledge Systems using Relation Nets and Hypernets

In the book "Knowledge Representation and Relation Nets" we introduced a structural model called a Relation Net and a special relation net called a Concept Relationship Knowledge Structure (CRKS). In this work we broaden the notion of a relation net to produce a new but associated structural model, a Hypernet. We show that the general theory of hypernets has applications in the acquisition/learning, representation, retrieval, accommodation and assimilation, management and communication/teaching of knowledge, and also in problem representation and solution and in modelling the various modes of reasoning. This report is a revised and extended version of Relation Nets and Hypernets, Technical Report TR-01-020, Department of Mathematics and Computer Science , University of Mannheim, 2001