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Based on a recently proposed framework of learning from constraints using kernel-based representations, in this brief, we naturally extend its application to the case of inferences on new constraints. We give examples for polynomials and first-order logic by showing how new constraints can be checked on the basis of given premises and data samples. Interestingly, this gives rise to a perceptual logic scheme in which the inference mechanisms do not rely only on formal schemes, but also on the data probability distribution. It is claimed that when using a properly relaxed computational checking approach, the complementary role of data samples makes it possible to break the complexity barriers of related formal checking mechanisms.