Characteristics of Category Natural Deduction for Language Propositional Logic System (CCND) for (LPLS)

Abstract

Abstract In this paper, we introduce the third system which is called category of natural deduction (CND) for propositional logic system (LPLS), it's essential different in its form and ways form truth -table and truth-tree for (LPLS), even its pick out (or select) the same symbolic language like that used in system of truth-table and truth- tree for (LPLS). Anyway, with regarding 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 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 system of natural deduction is based on Garhard Gentzen, how investigated and published his work in 1934 and 1935 about it. In this article, we represent natural deduction as a category natural deduction for language propositional logic system and study characteristics of arguments in (CND) and investigates valid and invalid arguments, types of formulas and relations between formulas and inconsistence sets.