Implicitly Learning to Reason in First-Order Logic

Vaishak Belle, Brendan Juba

Research output: Contribution to conferencePaperpeer-review

Abstract / Description of output

We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed probability distribution. PAC semantics, introduced by Valiant, is one rigorous, general proposal for learning to reason in formal languages: although weaker than classical entailment, it allows for a powerful model theoretic framework for answering queries while requiring minimal assumptions about the form of the distribution in question. To date, however, the most significant limitation of that approach, and more generally most machine learning approaches with robustness guarantees, is that the logical language is ultimately essentially propositional, with finitely many atoms. Indeed, the theoretical findings on the learning of relational theories in such generality have been resoundingly negative. This is despite the fact that first-order logic is widely argued to be most appropriate for representing human knowledge. In this work, we present a new theoretical approach to robustly learning to reason in first-order logic, and consider universally quantified clauses over a countably infinite domain. Our results exploit symmetries exhibited by constants in the language, and generalize the notion of implicit learnability to show how queries can be computed against (implicitly) learned first-order background knowledge.


WorkshopThe Fourth International Workshop on Declarative Learning Based Programming
Abbreviated titleDeLBP 2019
Internet address


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  • Implicitly Learning to Reason in First-Order Logic

    Belle, V. & Juba, B., 14 Dec 2019, Advances in Neural Information Processing Systems 32 (NeurIPS 2019). Neural Information Processing Systems, Vol. 32. p. 3381-3391 11 p. (Advances in Neural Information Processing Systems; vol. 32).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Open Access

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