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
On the basis of differently defined functions- than otherwise - for conjunction, disjunction and implication （＊）, we construct a formal system, as an axiomatic theory, on its three levels： propositional, predicate...On the basis of differently defined functions- than otherwise - for conjunction, disjunction and implication （＊）, we construct a formal system, as an axiomatic theory, on its three levels： propositional, predicate and arithmetical one, intended to be a formalizaton of identically false formulas. We argue somewhat in favor of such a system from the point of view of its meta theory （it is complete and consistent one）, of properties of duality, symmetry etc., as well as of a logic of a possible world.展开更多
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.
文摘On the basis of differently defined functions- than otherwise - for conjunction, disjunction and implication （＊）, we construct a formal system, as an axiomatic theory, on its three levels： propositional, predicate and arithmetical one, intended to be a formalizaton of identically false formulas. We argue somewhat in favor of such a system from the point of view of its meta theory （it is complete and consistent one）, of properties of duality, symmetry etc., as well as of a logic of a possible world.
