Mathematical Models in Schema Theory

TL;DR

This paper develops a comprehensive mathematical schema theory integrating brain, grid automata, and block-schemas, enabling modeling across diverse fields like neurophysiology, psychology, and computer science.

Contribution

It introduces a unified mathematical framework for schemas, combining multiple theoretical roots to model various schema types across disciplines.

Findings

The theory models schemas in neurophysiology and psychology.

It enables schema representation in computer science and Internet technology.

The framework unifies diverse schema concepts mathematically.

Abstract

In this paper, a mathematical schema theory is developed. This theory has three roots: brain theory schemas, grid automata, and block-shemas. In Section 2 of this paper, elements of the theory of grid automata necessary for the mathematical schema theory are presented. In Section 3, elements of brain theory necessary for the mathematical schema theory are presented. In Section 4, other types of schemas are considered. In Section 5, the mathematical schema theory is developed. The achieved level of schema representation allows one to model by mathematical tools virtually any type of schemas considered before, including schemas in neurophisiology, psychology, computer science, Internet technology, databases, logic, and mathematics.