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Demonic composition

From Wikipedia, the free encyclopedia

In mathematics, demonic composition is an operation on binary relations that is similar to the ordinary composition of relations but is robust to refinement of the relations into (partial) functions or injective relations.

Unlike ordinary composition of relations, demonic composition is not associative.

Definition

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Suppose is a binary relation between and and is a relation between and Their right demonic composition is a relation between and Its graph is defined as

Conversely, their left demonic composition is defined by

References

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  • Backhouse, Roland; van der Woude, Jaap (1993), "Demonic operators and monotype factors", Mathematical Structures in Computer Science, 3 (4): 417–433, CiteSeerX 10.1.1.40.9602, doi:10.1017/S096012950000030X, MR 1249420.