Abstract
CAT4 is proposed as a general method for representing information, enabling a powerful
programming method for large-scale information systems. It enables generalised machine learning,
software automation and novel AI capabilities. It is based on a special type of relation called CAT4,
which is interpreted to provide a semantic representation. This is Part 2 of a five-part introduction.
The focus here is on defining key mathematical properties of CAT2, identifying the topology and
defining essential functions over a coordinate system. The analysis is from first principles. This
develops on from the axioms introduced in Part 1. The interpretation of fact networks is introduced
in Part 3, and the full application to semantic theory comes in Part 4, where we introduce general
functions, including the language interpretation or linguistic functions. In Part 5, we turn to software
design considerations, to show how files, indexes, functions and screens can be defined to
implement a CAT4 system efficiently.