Concept of Abduction with Gradated Contradictions is introduced here as a form of Peirce's abduction inference. The general form of abduction criterion is formalized in the proposed Logic of Gradated Contradictions and Logic of Recursive Aggregation. Common steps of an abduction procedure as minimization of such a criterion are specified as well. It is demonstrated on examples of 14 popular textbook learners (from hierarchical clustering to k-NN and SVR) that each of them performs AGC. The proposed theory explains real life learners, yet it avoids any mention of statistics, so it can be considered as a logical alternative to the statistical learning theory.
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