Numerals in Model of Human Knowledge Representation
Numerals in Model of Human Knowledge Representation

Summary/Abstract: The purpose of this study was to create a system of knowledge representation in information systems most similar to the model of human knowledge representation. The problem of plain arithmetic operations and numerals representation was chosen as a main goal. Knowledge representation in general terms was chosen for the current problem as a first goal. For this purpose psychological theories and experiments about human knowledge representation models were overviewed. As en example, the "violin" experiment was given. This experiment confirms the idea of information representation in human's mind as a net of entities connected by associative relations. As an analogue of such structure in information technologies world semantic networks were considered. This structure was chosen because semantic networks use the same idea of knowledge representation as a graph. Ontology as a pattern of semantic networks construction is also considered. Following this pattern edges and their relations are joined into classes with common properties and behaviour. Finally, technical and psychological approaches were compared to choose the most correct way to represent information as humans do. But the problem of numerals representation in human's mind also has its own psychological problems. Such concepts of numbers for adults and children differences were shown. Requirements for this concept were specified, such as: the measure and the sequence of information representation. Guided by this rules the concept of Church numerals was chosen. This concept exists in lambda calculus, which base ideas were described in the paper as well. Church numbers approach in terms of semantic networks was also given. For calculations simplification the addition table idea was used and applied with semantic networks context. But a human usually uses place-value notation when big numbers are required. And Church numbers use too much memory in this situation (an addition table grows too fast with maximum of number defined in Church notation). So the place-value notation which uses Church numbers as digits and as a position marker was given.

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