Lukasiewicz's Many-valued Logic And Comparisons Between It And Some Logics

Traditional logic is a 2-valued logic, but there are a lot of problems that cannot be solved by it. To deal with those problems, we should develop a new kind of logic that is different from 2-valued logic. This is many-valued logic. We call it many-valued logic in that this kind of logic studies logic theory that handles relations of propositions in which propositions have three truth values or more, even infinite, and do not limit in two truth values.The introduction of the paper introduces concisely the outline of generation of many-valued logic and its development to impress us many-valued logic a rough sketch firstly.Unit 1 is the main part of the paper. Other parts of the paper, written around it, compare with it and deepen it. Lukasiewicz, as we know, was praised the father of many-valued logic, because it was he who firstly utilized means of modern logic to study many-valued logic and developed his many-valued logic theory systematically. Therefore, the paper observes and studies Lukasiewicz's many-valued logic theory firstly and mainly. In this part, the paper inspects and studies Lukasiewicz's 3-valued logic, the truth function of 3-valued logic, the study of axiomatized system of Lukasiewicz's 3-valued logic and the many-valued generalizations of Lukasiewicz's 3-valued logic, etc. In "Lukasiewicz's 3-valued Logic", the paper studies the differences and sameness of definitions of the truth table and function of the five basic copulas between 2-valued logic and 3-valued logic, and of using two of the five basic copulas as original copulas to define the others between them, and observes whether some 2-valued logic laws are still laws in Lukasiewicz's 3-valued logic. In "Truth Function", the paper, comparing with 2-vaued logic, briefs the quantity of truth function of 3-valued logic and how to calculate it. Because 3-valued logic has a truth more than 2-valued logic, the quantity of truth of function of 3-valued logic is more than it of 2-valued logic, and 3-valued logic has a more powerful ability to handle problems than 2-valued logic does. In "The Study of Axiomatized system ofLukasiewicz's 3-vaued Logic", the paper briefs the study situation of the study of axiomatized system of Lukasiewcz's 3-vaued logic. Thereafter, the paper generates Lukasiewicz's 3-valued logic to his any definite truth valued logic and infinite truth valued logic.Unit 2 analyses causes of being many different many-valued logic systems firstly. The paper introduces concisely Bochvar's 3-valued logic system B3, Kleene's 3-vaued logic system K3, Zhu-Wujia and Xiao-Xi'an's medium logic MP and Post's many-valued logic system P3 and compares them with Lukasiewicz's many-valued logic, in order to understand many-valued logic better. The comparing order of the Unit is arranged as follows:Firstly, comparisons between B3,K3 and L3: The comparisons are between standard systems, and the systems are systems developed from the view of semantic analysis. But B3 and K3 are differences, too; B3 is developed from the view of paradoxical analyses, while K3 is developed from the combined angle of epistemology and ontology.Secondly, comparisons between MP and L3: The comparisons are between standard and non-standard system. Meanwhile, MP is a system developed from the view of semantic analyses.Last, comparisons between Pn and Ln: Pn was a system developed from the point of pure form Thereafter, the comparisons between it and Ln is the comparisons between a purely formally analyzed system and a semantic analyzed system. Meanwhile, Pn is non-standard. Therefore, the comparisons between them are also between standard and non-standard systems. The paper, inspecting Pn, has another aim, i.e., putting out its own idea.Unit 3 introduces concisely the significances and functions of many-valued logic and puts out a point of view of its own.Concluding Remarks look back and conclude the paper concisely...