Although models of word meanings based on distributional semantics have proved effective in predicting human judgments of similarity among individual concepts, it is less clear whether or how such models might be extended to account for judgments of similarity among relations between concepts. Here we combine an individual-differences approach with computational modeling to predict human judgments of similarity among word pairs instantiating a variety of abstract semantic relations (e.g., contrast, cause-effect, part-whole). A measure of cognitive capacity predicted individual differences in the ability to discriminate among distinct relations. The human pattern of relational similarity judgments, both at the group level and for individual participants, was best predicted by a model that takes representations of word meanings based on distributional semantics as its inputs and uses them to learn an explicit representation of relations. These findings indicate that although the meanings of abstract semantic relations are not directly coded in the meanings of individual words, important aspects of relational similarity can be derived from distributional semantics.