Formal System

A formal system consists of axioms (statements that are true) and rules (how axioms can be manipulated). New axioms can be deduced from other axioms and rules. You formalize a system when you start defining these statements and rules.

A formal system is consistent when you can’t simultaneously prove and disprove an axiom. An inconsistent system would not be very useful e.g. a weather forecasting system that predicts it will rain and not rain at the same time.

A formal system is a complete system when all statements in the system can be proved or disproved thereby allowing you to know everything about the system.

See also: