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Semantic relation among different objects is one of the most important kinds of semantics which plays the primary role for people and intelligent systems in grasping the situation accurately in the context of connected systems. The semantic relations are viewed as the most important elements in most existing information models (such as ER model, RDF and SLN) during the mapping from the physical world into the cyber world, where efficient ways of representation for semantic relations are developed. However, all these models deal with the semantic relations in a simple and intuitive way. Few works go deep into the study of semantic relations from a mathematic view. This paper aims at exploring a mathematic theory of the semantic relations between objects including representing methods, normal forms of operations, semantic orthogonal basis of the semantic relations. We also discuss the reasoning mechanism based on the proposed theory. The applications of the developed theory in semantic link network are discussed finally.