An Order-Theoretic Characterization of Consistent Inductive Inference

Abstract:When can a learner make only finitely many prediction errors along every infinite sequence labeled by a fixed, unknown hypothesis? We characterize this form of consistency for arbitrary binary hypothesis classes in ZFC, without requiring a uniform mistake bound. The characterization uses a single linear order on finite realizable traces. Each trace selects its least subtrace, and the order must satisfy two conditions: conflicting traces select different subtraces, and the order is well-founded on the traces of each fixed target. These conditions induce a learner whose selected evidence decreases on every mistake. Conversely, a consistent learner yields such an order through canonical mistake transcripts and the Kleene--Brouwer ordering. The result provides a representation of consistent prediction by finite evidence, answering a question of Lu (2024).

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2609.28551 [stat.ML]

(or arXiv:2609.28551v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2609.28551 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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