Draft: Integrated Learning and Reasoning

An Introduction Using PAC Semantics

Brendan Juba and Loizos Michael

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This is a current draft of a textbook on learning and reasoning using the PAC semantics, which will be published by Cambridge University Press. We are seeking comments on the draft, especially corrections and requests for clarification. Please send these to me via e-mail at first initial last name at wustl


  1. Introduction - June 26, 2026 ver.
  2. Probably Approximate Truth - June 26, 2026 ver.
  3. Representational Tradeoffs - June 26, 2026 ver.
  4. The Inductive Learning Task - June 26, 2026 ver.
  5. The Deductive Reasoning Task - June 26, 2026 ver.
  6. Learning to Reason with Full Examples - June 26, 2026 ver.
  7. Inductive Learning from Partial Examples - August 6, 2026 ver.
  8. Learning to Reason with Partial Examples - August 6, 2026 ver.
  9. Learning and First-Order Relational Reasoning - August 6, 2026 ver.
  10. Learning and Non-Monotonic Knowledge Representations - August 6, 2026 ver.
  11. Learning and Causal/Temporal Reasoning - August 6, 2026 ver.
  12. Appendix: VC Dimension for Numeric Parameters and Sample Complexity - June 26, 2026 ver.
  13. References - June 26, 2026 ver.


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McKelvey 2010B first initial last name at wustl