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The tension between deduction and induction is perhaps the most fundamentalissue in areas such as philosophy, cognition and artificial intelligence (AI).The deduction camp concerns itself with questions about the expressiveness offormal languages for capturing knowledge about the world, together with proofsystems for reasoning from such knowledge bases. The learning camp attempts togeneralize from examples about partial descriptions about the world. In AI,historically, these camps have loosely divided the development of the field,but advances in cross-over areas such as statistical relational learning,neuro-symbolic systems, and high-level control have illustrated that thedichotomy is not very constructive, and perhaps even ill-formed. In thisarticle, we survey work that provides further evidence for the connectionsbetween logic and learning. Our narrative is structured in terms of threestrands: logic versus learning, machine learning for logic, and logic formachine learning, but naturally, there is considerable overlap. We place anemphasis on the following "sore" point: there is a common misconception thatlogic is for discrete properties, whereas probability theory and machinelearning, more generally, is for continuous properties. We report on resultsthat challenge this view on the limitations of logic, and expose the role thatlogic can play for learning in infinite domains.

Symbolic Logic meets Machine Learning: A Brief Survey in Infinite Domains