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What is the mathematics of Unified Modeling Language (UML)? The concepts introduced in UML such as classes, associations, association classes, subclasses smell mathematical. Is there a mathematical foundation or theory behind it?

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There is semantics of programing languages which explain "meaning" of those constructs. Type theory models types and rules of type processing in syntactic manner. Take in mind that those are broad topics.

Trismegistos
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