Learning Inference Rules from Data

Abstract

This paper considers the possibility of designing AI that can learn logical or non-logical inference rules from data. We first provide an abstract framework for learning logics. In this framework, an agent $${{{\mathcal {A}}}}$$ A provides training examples that consist of formulas S and their logical consequences T . Then a machine $${{{\mathcal {M}}}}$$ M builds an axiomatic system that makes T a consequence of S . Alternatively, in the absence of an agent $$\mathcal{A}$$ A , a machine $${{{\mathcal {M}}}}$$ M seeks an unknown logic underlying given data. We next consider the problem of learning logical inference rules by induction. Given a set S of propositional formulas and their logical consequences T , the goal is to find deductive inference rules that produce T from S . We show that an induction algorithm LF1T , which learns logic programs from interpretation transitions, successfully produces deductive inference rules from input data. Finally, we consider the problem of learning non-logical inference rules. We address three case studies for learning abductive inference, frame axioms, and conversational implicature. Each case study uses machine learning techniques together with metalogic programming.