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Identifying common patterns among events is a key ability in human and machine perception, as it underlies intelligent decision making. We propose an approach for learning semantic relational set abstractions on videos, inspired by human learning. We combine visual features with natural language supervision to generate high-level representations of similarities across a set of videos. This allows our model to perform cognitive tasks such as set abstraction (which general concept is in common among a set of videos?), set completion (which new video goes well with the set?), and odd one out detection (which video does not belong to the set?). Experiments on two video benchmarks, Kinetics and Multi-Moments in Time, show that robust and versatile representations emerge when learning to recognize commonalities among sets. We compare our model to several baseline algorithms and show that significant improvements result from explicitly learning relational abstractions with semantic supervision.