At last , this paper discusses 3 - valued logic , points out some deficiencies of 3 - valued logic system , and establishes a propositional logic system with 4 values : true , false , divergent and meaningless . then this paper proves that this 4 - valued logic system is truth - functionally complete , and expands its connective 最后,本文对经典的三值逻辑进行了总结,在此基础上提出了一个四值逻辑系统,扩充了该系统的连接词,并讨论了该系统的一些代数性质。
Based on the above knowledge , the core components s - boxes of the rijndael algorithm and the camellia algorithm , which are the only nonlinear components , are analyzed and compared in detail . eight algebraic properties of s - boxes such as balanceness , strict avalanche criterion , differential uniformance , algebraic order , and so on are calculated and proved . the reason that the s - boxes which are constructed by the inverse operation on finite field has the specialty of 4 - difference is analyzed 在此之后，本论文分针对rijndael和camellia算法的核心部件，也是唯一的非线性部件s盒进行了详细的分析和比较，计算并证明了s盒的平衡性、严格雪崩准则、差分均匀度、代数次数等八种代数性质，特别给出了通过有限域上的取逆运算构造的s盒其差分特性为4的原因，最后计算了两个算法s盒的两种代数结构，表明rijndael和camellia算法的s盒均具有良好的代数性质和复杂的代数结构，为今后两种算法在各个领域的应用提供了理论保障。
In this paper , a new type algebra is introduced , it is the algebraic abstract of mpm system just as boolean algebra is the algebraic abstract of 2 - valued propositional calculus . the main purpose of this paper is to investigate the various properties of the new algebra . in addition , this paper constructs an axiom set based on the medium logic propositional calculus system mpm , and gives a proof of its completeness 本文通过对mpm中介逻辑命题演算系统进行代数抽象,建立了一个新的代数系统,讨论了该代数系统的性质,并利用该代数系统的代数性质构造了中介命题演算系统mpm上的一个公理完备集合,使用该公理集合可以方便的推导出mpm上的等值和互推公式,这对于处理不完全信息数据库的查询优化有着重要作用。
The conditions for preserving structural and dynamic properties of the net after these operations were discussed . some net operations are further studied in this thesis . union operation is analyzed and one exampl e is given to make the background and meaning clearly for net decomposition operations 结合近年来petri网理论的发展，本文进一步研究了网运算，分析了并运算的代数性质；针对网的分解运算，给出实例显示了网的分解运算的背景及意义；同时讨论了网的并分解及和分解，研究了这些运算保持网的结构性质和动态性质的条件。
In the aspect of the algebraic properties of concept lattice , the paper suggests a binary operation between the elements for the set of all concepts in formal context , which turns the concept lattice in general significance into those with operators . we also proved that concept lattice is a lattice in algebraic significance and studied its algebraic properties . these results provided theoretical foundation and a new method for further study of concept lattice 在概念格的代数性质方面，本文给出了形式背景下概念集合上的元素之间的二元运算，使通常意义下的概念格成为带有算子的概念格，证明了概念格为代数意义下的格，并研究了其代数性质，为概念格的进一步研究提供了理论基础和新的研究方法。
