Semantics that takes predicitons as atoms of meaning and how it works in mathematics

Semantics that takes predicitons as atoms of meaning and how it works in mathematics

Valentin Turchin
Computer Science, City College of New York
Principia Cybernetica

To process data in information systems intelligently, the programming tools we create must base their work on some understanding of the meaning of the systems records. Thus some formal semantics is needed, with its own theoretical principles and methods.

The normal way to develop a formal system is: identify some minimal, atomic, units of the system and then develop operations and statements of your theory.

So, in the firat step of the construction of formal semantics we must understand what is the atomic unit of meaning. In the epistomolgy developed in the Principia Cybernetica Project we take predictions as these atoms. A prediction is defined as the statement that a certain process comes to a certain stage. For a statement to be meaningful, it must be possible to use it as a generator of predictions.

It is natural -- in fact, necessary for the validation of our formal semantics -- to see how it works when applied to the foundation of mathematics and formal logic. It turns out that it works very well, as is shown in [1].

In this presentation I will explain in more detail the concepts and principles of our semantics using examples from mathematics, and summarise the new features of mathematics and logic built on this base.

Reference

[1] Turchin, V.F. A constructive interpretation of the full set theory. The Journal of Symbolic Logic, 52, pp.172-201, 1987.