Aim & In this paper, we introduce the third system which is called the category of natural deduction (CND) for language propositional logic system(LPLS), it's essential different in its form and ways form truth -table and truth-tree for (LPLS), even itspick out (or select) the same symbolic language like that used in the system of truth-table and truth- tree for (LPLS). Anyway, with regard to truth -table and truth-tree for (LPLS), there is a terminology which is called algorithm due to mathematician Muhammed ibn Musa al-khwarizmi (780-850), from the meaning of algorithm, that is there are some mechanical procedures, that we commit to it leading us to right judgment relative to arguments. In this paper we make a new presentation method for (CND) for(LPLS), the principle of the system of natural deduction is based on Garhard Gentzen, who investigated and published his work in 1934 and 1935 about it. In this article, we represent natural deduction as a category of natural deduction for language propositional logic systems, to study the characteristics of arguments in (CND) and investigate valid and invalid arguments, types of formulas, and relations between formulas and inconsistency sets.
