Composition of relations
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In the mathematics of binary relations, the composition of relations is the forming of a new binary relation R; S from two given binary relations R and S. In the calculus of relations, the composition of relations is called relative multiplication,[1] and its result is called a relative product.[2]: 40 Function composition is the special case of composition of relations where all relations involved are functions.
The word uncle indicates a compound relation: for a person to be an uncle, he must be the brother of a parent. In algebraic logic it is said that the relation of Uncle () is the composition of relations "is a brother of" () and "is a parent of" ().
Beginning with Augustus De Morgan,[3] the traditional form of reasoning by syllogism has been subsumed by relational logical expressions and their composition.[4]