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Analogy problems involving multiple ordered relations of the same type create mapping ambiguity, requiring some mechanism for relational integration to achieve mapping accuracy. We address the question of whether the integration of ordered relations depends on their logical form alone, or on semantic representations that differ across relation types. We developed a triplet mapping task that provides a basic paradigm to investigate analogical reasoning with simple relational structures. Experimental results showed that mapping performance differed across orderings based on category, linear order, and causal relations, providing evidence that each transitive relation has its own semantic representation. Hence, human analogical mapping of ordered relations does not depend solely on their formal property of transitivity. Instead, human ability to solve mapping problems by integrating relations relies on the semantics of relation representations. We also compared human performance to the performance of several vector-based computational models of analogy. These models performed above chance but fell short of human performance for some relations, highlighting the need for further model development.