对象之间的语义关系是将现实物理世界映射到网络虚拟世界的重要元素之一，因此智能系统要理解外界环境离不开语义关系。现有的研究工作有语义关系和对象的表示以及语义关系的计算（包括精确推理、一致性检测、冗余性检测）。本文第一部分先介绍了前人的工作，主要涉及文献[1]提出的语义链网络中语义关系之间的代数计算理论。该理论引入了一些数学的概念（包括正交基，基本运算，集合，矩阵等等），可以精确地表示资源之间的语义关系以及关系之间的联系，并且在智能系统中可以通过自动推理和自主计算得出隐含的语义关系。本文第二部分基于前面的理论给出了一个简洁的操作性较强的算法，该算法只用了已给的语义基而放弃采用正交基，这使得相应的RRM 矩阵更加稀疏进而减少了运算量，提高了效率。本文最后设计了一个简化版证券市场网络，应用本文提出的算法进行了推算，得到了比较好的效果，表明了该算法合理有效。

Semantic relations among objects are regarded as one of the most important elements during mapping the physical world into the cyber world, so the smart systems cannot understand and control the situation without semantic relations.Existing research works involve the representation of semantic relations among objects and semantic relations computing include accurate reasoning, integrity checking and redundancy checking. The first section of this paper introduces existing research works, mainly involves algebraic computing theory of semantic relation in SLN. Some concepts include orthogonal basis, basic operations, sets, matrix are included in the theory. Those can be used to represent the semantic relations among resources and the relationship between relations. Implicit relations can be reduced in smart connected systems, especially for automatic and autonomous computing. Based on the theory before, the second section of this paper provides a compact and workable algorithm involving the given semantic basis instead of the orthogonal basis, which makes the corresponding RRM matrix sparser and decreases the computation. Finally, a case of a simplified version of securities market shows the effectiveness of the theory after getting a satisfying result by using the computing method.