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Extracting semantic relations from text is a preliminary step towards understanding the meaning of text. The more semantic relations are extracted from a sentence, the better the representation of the knowledge encoded into that sentence. This article introduces a framework for the Composition of Semantic Relations (CSR). CSR aims to reveal more text semantics than existing semantic parsers by composing new relations out of previously extracted relations. Semantic relations are defined using vectors of semantic primitives, and an algebra is suggested to manipulate these vectors according to a CSR algorithm. Inference axioms that combine two relations and yield another relation are generated automatically. CSR is a language-agnostic, inventory-independent method to extract semantic relations. The formalism has been applied to a set of 26 well-known relations and results are reported.