Implicitly Learning to Reason in First-Order Logic

摘要: We consider the problem of answering queries about formulas first-order logic based on background knowledge partially represented explicitly as other formulas, and 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 powerful model theoretic framework while requiring minimal assumptions form distribution question. To date, however, most significant limitation that approach, more generally machine approaches with robustness guarantees, logical language ultimately essentially propositional, finitely many atoms. Indeed, theoretical findings relational theories such generality have been resoundingly negative. This despite fact widely argued be appropriate representing human knowledge. In this work, we present new approach robustly logic, universally quantified clauses over countably infinite domain. Our results exploit symmetries exhibited constants language, generalize notion implicit learnability show how can computed against (implicitly) learned