Harmonious,Consistent and the Strong Completeness of First-Order Axiom System
HU Ze-hon · Journal of South China Normal University · 2010
In the axiom system,deduction theorem is the link connecting the harmony and consistency.For axiom systems which have deduction theorem,it can be proved that the consistent formulas set is equivalent to the harmonious one.For axiom systems without deduction theorem,the difference between harmony and consistency is embodied in strong complete proof process of the axiom system.The consistency-based proof of completeness does not rely on deduction theorem,but harmony-based one is constrained by the deduction theorem.This paper will give a harmony-based strong complete proof for the first-order axiom system of QC1.