On Propositional calculus (Mathematical Logic) The Soundness and TheCompleteness of The Non-Formal Systems Deduction Systems ( DSi, 1≤ i ≤ 4)

Abstract

The purpose of this paper use The writer the non Axiomatic logical systems (normal logical systems, the Axiomatic logical systems and the axiomatic logic) , Language and definitions, Operators, Inductive clause I and Inductive clause II, To proof of theorems of the non- formal systems DS1, DS2, DS3, DS4 will be presented  The deduction system the DSi,1≤ i ≤ 4  The soundness and completeness of the DSi,1≤ i ≤ 4  Definition(soundness 1  Definition a model  The Completeness Theorem  Theorem (Godel Completeness Theorem)