PAVELKA in ref. [1] established a propositional logic system whose truth values domain is an enriched residuated lattice and obtained some beautiful results. In order to study more general lattice valued logic systems...PAVELKA in ref. [1] established a propositional logic system whose truth values domain is an enriched residuated lattice and obtained some beautiful results. In order to study more general lattice valued logic systems, we proposed the concept of lattice implication algebra, discussed the corresponding lattice valued propositional logic system, and established a展开更多
Some new properties of lattice filters are presented based on the order-preserving mapping and lattice homomorphism, and two necessary and sufficient conditions for lattice filters under the chain type are given. Then...Some new properties of lattice filters are presented based on the order-preserving mapping and lattice homomorphism, and two necessary and sufficient conditions for lattice filters under the chain type are given. Then, the relations between lattice filter and lattice implication algebras （LIAs）, i. e., the relations between lattice filter and LIA-filters, and the related properties are investigated. In addition, three necessary and sufficient conditions for LIA-filters are discussed. The obtained results may serve as some theoretical supports to lattice-valued logical system.展开更多
文摘PAVELKA in ref. [1] established a propositional logic system whose truth values domain is an enriched residuated lattice and obtained some beautiful results. In order to study more general lattice valued logic systems, we proposed the concept of lattice implication algebra, discussed the corresponding lattice valued propositional logic system, and established a
基金The National Natural Science Founda-tion of China (No.60474022)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20060613007)
文摘Some new properties of lattice filters are presented based on the order-preserving mapping and lattice homomorphism, and two necessary and sufficient conditions for lattice filters under the chain type are given. Then, the relations between lattice filter and lattice implication algebras （LIAs）, i. e., the relations between lattice filter and LIA-filters, and the related properties are investigated. In addition, three necessary and sufficient conditions for LIA-filters are discussed. The obtained results may serve as some theoretical supports to lattice-valued logical system.
