The classical propositional calculus(often called also as“zero-order logic”),is the most fundamental two-valued logical system.It is necessary to construct the classical calculus of quantifiers(often called also as...The classical propositional calculus(often called also as“zero-order logic”),is the most fundamental two-valued logical system.It is necessary to construct the classical calculus of quantifiers(often called also as“classical calculus of predicates”or“first-order logic”),which is necessary to construct the classical functional calculus.This last one is being used for formalization of the Arithmetic System.At the beginning of this paper,we introduce a notation and we repeat certain well-known notions(among others,the notions of operation of consequence,a system,consistency in the traditional sense,consistency in the absolute sense)and certain well-known theorems.Next,we establish that classical propositional calculus is an inconsistent theory.展开更多
In this paper, the method of well-combined semantics and syntax proposed by Pavelka is applied to the research of the prepositional calculus formal system (?)*. The partial constant values are taken as formulas, formu...In this paper, the method of well-combined semantics and syntax proposed by Pavelka is applied to the research of the prepositional calculus formal system (?)*. The partial constant values are taken as formulas, formulas are fuzzified in two manners of semantics and syntax, and inferring processes are fuzzified. A sequence of new extensions {(?)_n~*} of the system ? is proposed, and the completeness of (?)_n~* is proved.展开更多
The aim of this article is the partial axiomatization for 1-level universal logic. A propositional calculus formal deductive system ULh∈（0,1） based on l-level universal AND operator of universal logic is algebra L...The aim of this article is the partial axiomatization for 1-level universal logic. A propositional calculus formal deductive system ULh∈（0,1） based on l-level universal AND operator of universal logic is algebra LПIG is introduced. The of system ULh∈（0,1） are proved. built up. The corresponding soundness and the completeness展开更多
文摘The classical propositional calculus(often called also as“zero-order logic”),is the most fundamental two-valued logical system.It is necessary to construct the classical calculus of quantifiers(often called also as“classical calculus of predicates”or“first-order logic”),which is necessary to construct the classical functional calculus.This last one is being used for formalization of the Arithmetic System.At the beginning of this paper,we introduce a notation and we repeat certain well-known notions(among others,the notions of operation of consequence,a system,consistency in the traditional sense,consistency in the absolute sense)and certain well-known theorems.Next,we establish that classical propositional calculus is an inconsistent theory.
基金supported by the National Natural Science Foundation of China(Grant No.19831040).
文摘In this paper, the method of well-combined semantics and syntax proposed by Pavelka is applied to the research of the prepositional calculus formal system (?)*. The partial constant values are taken as formulas, formulas are fuzzified in two manners of semantics and syntax, and inferring processes are fuzzified. A sequence of new extensions {(?)_n~*} of the system ? is proposed, and the completeness of (?)_n~* is proved.
基金the Special Foundation of Education Department of Shanxi Province (07JK255)Basic Scientific Research Foundation of Northwestern Polytechnical University (W018101)
文摘The aim of this article is the partial axiomatization for 1-level universal logic. A propositional calculus formal deductive system ULh∈（0,1） based on l-level universal AND operator of universal logic is algebra LПIG is introduced. The of system ULh∈（0,1） are proved. built up. The corresponding soundness and the completeness
