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
The paper presents an extension multi-laye r p erceptron model that is capable of representing and reasoning propositional know ledge base. An extended version of propositional calculus is developed, and its some prop...The paper presents an extension multi-laye r p erceptron model that is capable of representing and reasoning propositional know ledge base. An extended version of propositional calculus is developed, and its some properties is discussed. Formulas of the extended calculus can be expressed in the extension multi-layer perceptron. Naturally, semantic deduction of prop ositional knowledge base can be implement by the extension multi-layer perceptr on, and by learning, an unknown formula set can be found.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.
文摘The paper presents an extension multi-laye r p erceptron model that is capable of representing and reasoning propositional know ledge base. An extended version of propositional calculus is developed, and its some properties is discussed. Formulas of the extended calculus can be expressed in the extension multi-layer perceptron. Naturally, semantic deduction of prop ositional knowledge base can be implement by the extension multi-layer perceptr on, and by learning, an unknown formula set can be found.
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
