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Machine learning is a thriving part of computer science. There are manyefficient approaches to machine learning that do not provide strong theoreticalguarantees, and a beautiful general learning theory. Unfortunately, machinelearning approaches that give strong theoretical guarantees have not beenefficient enough to be applicable. In this paper we introduce a logicalapproach to machine learning. Models are represented by tuples of logicalformulas and inputs and outputs are logical structures. We present ourframework together with several applications where we evaluate it using SAT andSMT solvers. We argue that this approach to machine learning is particularlysuited to bridge the gap between efficiency and theoretical soundness. Weexploit results from descriptive complexity theory to prove strong theoreticalguarantees for our approach. To show its applicability, we present experimentalresults including learning complexity-theoretic reductions rules for boardgames. We also explain how neural networks fit into our framework, although thecurrent implementation does not scale to provide guarantees for real-worldneural networks.

Machine Learning with Guarantees using Descriptive Complexity and SMT Solvers