Research On Theoretical Conclusions And Co-zeroizers And Related Properties In The MTL Propositional Logic System

Propositional logic system plays an important role in non-classical mathemat-ical logic.The fuzzy logic propositional system MTL is a more extensive and im-portant system which is popularized on the basis of BL propositional logic system.This article studies MTL from different aspects.Firstly,the paper introduces the conclusion of theory into MTL,then studies the further properties of the conclusion,proper conclusion and complete conclusion.Secondly,the single-point co-annihilator operator and the multiple-point co-annihilator operator are introduced into MTL system,the co-annihilators of a formula ? and a theory ? are defined,and the properties of them are studied.Finally,the paper discusses the relationship between co-annihilator and conclusion in MTL system,and the proof of the co-annihilator of a conclusion A is a necessary and sufficient condit,ion for a complete conclusion is valid in MTL system.Chapter 1:Preliminaries.This chapter gives some related concepts and ba-sic properties of MTL propositional logic system,including residual lattice,MTL algebra,MTL logic system and its related semantic theory.Chapter 2:The conclusion of theory and its related properties in MTL propo-sitional logic system.In this chapter,the conclusion operator,conclusion of theory and strong congruence are introduced into MTL propositional logic system,the further properties of the conclusion are studied,and the connection between the conclusion and strong congruence are discussed in MTL propositional logic system.Chapter 3:The co-annihilator operators,the corresponding co-annihilators and properties of them,we give the definitions of the single-point co-annihilator op-erator and the multiple-point co-annihilator operator in MTL system,and study corresponding co-annihilators and the properties of them.Chapter 4:The relationship between the conclusion of theory and the co-annihilators in MTL propositional logic system.In this chapter,we study the rela-tionship between the co-annihilators and the conclusion,proper conclusion,complete conclusion of theory in MTL propositional logic system,and prove the co-annihilator of a conclusion A is a necessary and suffcient condition for a complete conclusion in MTL logic system.