On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras

A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.

Logical Properties of Lattice Filter of Lattice Implication Algebra

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.

LI-ideal Spaces of Lattice Implication Algebra

在这份报纸，一个拓扑的空格基于格子含意代数学的 LI 理想被构造，并且它的拓扑的性质紧密和 connectedness 例如可分性，被讨论。

On Certain Filters in Lattice Implication Algebras

ＯｎＣｅｒｔａｉｎＦｉｌｔｅｒｓｉｎＬａｔｔｉｃｅＩｍｐｌｉｃａｔｉｏｎＡｌｇｅｂｒａｓＬｉｕＪｕｎ；ＸｕＹａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＳｏｕｔｈｗｅｓｔＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｃｈｅｎｇｄｕ，...

Finite Simple Lattice Implication Algebras

在这份报纸，有限格子含意代数学简单的一些必要、足够的条件是 established.Specially ，如果并且仅当，有限格子含意代数学 L 简单，这被证明如果并且仅当( L ，)是链，如果并且仅当在那里存在在 L.Also 的唯一的双原子，有一个素数的顺序的有限格子含意代数学简单，这被给。

Subalgebra and LI-Ideal of Lattice Implication Algebras

First, we reviewed the definitions of lattice implication algebras, lattice implication subalgebras, and LI-ideals, and provided an equivalent definition of LI-ideal. Then we investigated some properties of lattice implication subalgebra and U-ideal, and found the least lattice implication subalgebra. Finally, the relation between lattice implication subalgebra and LI-ideal is presented. It is proved that no LI-ideals are non-trivial lattice implication subalgebras.

On the Product and Factorization of Lattice Implication Algebras

In this paper,the concepts of product and factorization of lattice implication algebra are proposed,the relation between lattice implication product algebra and its factors and some properties of lattice implication product algebras are discussed.

L-fuzzy Lattice Implication Algebra

这份报纸介绍了 L 模糊的潜水艇格子含意代数学的概念并且讨论了它的性质。证明L模糊的潜水艇格子含意代数学的一个家庭的交叉集合是L模糊的潜水艇格子含意代数学，如果并且仅当它的每个切割集合是潜水艇格子含意代数学，一个L模糊的代用品格子含意代数学设定，这是L模糊的潜水艇格子含意代数学，并且图象和原版在格子含意同形下面L模糊的潜水艇格子含意代数学想象，这两个都是L模糊的潜水艇格子含意代数学。

Lattice Implication Algebrasand MV-algebras

Lattice implication algebras is an algebraic structure which is established by combining lattice and implication algebras. In this paper,the relationship between lattice implication algebras and MV algebra was discussed,and then proved that both of the categorys of the two algebras are categorical equivalence. Finally,the infinitely distributivity in lattice implication algebras were proved.

Prime Space of Lattice Implication Algebras

In this paper,after discussing the prime implication filter of lattice implication algebra,we introduced the concept of prime space of lattice implication algebra,in which we analysised its topological property and discussed the relation between the category of topological space and the category of lattice implication algebras.

Linguistic Truth Values Lattice Implication Algebras

In order to study uncertainty reasoning and automatic reasoning with linguistic terms, in this paper, the set of basic linguistic truth values and the set of modifiers are defined, according to common sense; partially orderings are defined on them. Based on it, a lattice implication algebra model L18 of linguistic terms is built; furthermore, its some basic properties are discussed.

Researches on Six Lattice-Valued Logic

Based on the direct product of Boolean algebra and Lukasiewicz algebra, six lattice-valued logic is put forward in this paper. The algebraic structure and properties of the lattice are analyzed profoundly and the tautologies of six-valued logic system L6P(X) are discussed deeply. The researches of this paper can be used in lattice-valued logic systems and can be helpful to automated reasoning systems.

Closure Operators of Lattice-valued Propositional Logic LP(X)

在这份报纸，珍视格子的命题逻辑 LP (X) 的闭合操作员被学习。古典闭合操作员的一个家庭被定义，在他们和 LP (X) 的闭合操作员之间的关系被调查。同时，为检查 LP (X) 的紧密的一个工具被给。

Syntactic Extension of Lattice-valued Propositional Logic LP(X)

我们交上珍视格子的命题逻辑 LP (X) 的语义延期[6 ] 。在这份报纸，我们调查它 LP (X) 的相应语法延期并且给在这二延期之间的关系。

Filters and structure of lattice implication algebra

IN order to research the logical system whose propositional value is given in a lattice from

Ideal Resolution Principle for Lattice-Valued First-Order Logic Based on Lattice Implication Algebra

As a continuate work,ideal-based resolution principle for lattice-valued first-order logic system LF(X) is proposed,which is an extension of α-resolution principle in lattice-valued logic system based on lattice implication algebra.In this principle,the resolution level is an ideal of lattice implication algebra,instead of an element in truth-value field.Moreover,the soundness theorem is given.In the light of lifting lemma,the completeness theorem is established.This can provide a new tool for automated reasoning.

Lattice-Valued Modal Propositional Logic Based on M-Lattice Implication Algebras

The modal lattice implication algebra(i.e.,M-lattice implication algebra) is introduced and its properties are investigated.The modal lattice-valued propositional logical system is introduced by considering the M-lattice implication algebra as the valuation field,and the syntax and semantic of the logical system are discussed,respectively.

Implicational lattices and generalization of Stone's representation theorem

Let F(S) be the free algebra of type (,∨,→) generated by the non_empty set S, it is proved that the logical equivalent relation defined by means of R 0_semantics is a congruence relation on F(S) and the corresponding quotient algebra is said to be the R 0_semantic Lindenbaum algebra. Taking R 0_semantic Lindenbaum algebra as a prototype, the concepts of implicational lattices and regular implicational lattices which are generalizations of the concept of Boolean algebras are introduced. Besides, the concept of fuzzy implicational spaces is introduced and the representation theorem of regular implicational lattices is obtained by means of fuzzy implicational spaces. In case of Boolean algebras, the corresponding fuzzy implicational spaces are zero_dimensional compact Hausdorff spaces and herefrom it is proved that the famous Stone’s representation theorem of Boolean algebras is a corollary of the representation theorem of regular implicational lattices.

格蕴涵代数的区间值犹豫模糊子代数

把区间值犹豫模糊集和格蕴涵代数相结合,给出格蕴涵代数的区间值犹豫模糊子代数的概念,讨论了区间值犹豫模糊子代数与其犹豫模糊子代数的关系。证明了2个区间值犹豫模糊子代数的交是区间值犹豫模糊子代数,并结合具体例子,说明2个区间值犹豫模糊子代数并不满足类似结论。

Fuzzy蕴涵代数及其理想理论

模糊逻辑代数分析是模糊逻辑研究领域的热点问题之一。运用代数学和格论的方法及原理,深入研究了Fuzzy蕴涵代数及其理想问题。首先,利用伪补算子给出了Fuzzy蕴涵代数的若干新性质。其次,在Fuzzy蕴涵代数中引入理想和生成理想的概念并考察其性质特征和等价刻画。最后,讨论了由给定Fuzzy蕴涵代数全体理想构成的集合的格论特征,证明了该集合关于集合包含序构成分配的连续(代数)格,特别地构成完备Heyting代数,进而构成Frame的重要结论。