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 ${{{\mathcal {A}}}}$ provides training examples that consist of formulas S and their logical consequences T. Then a machine ${{{\mathcal {M}}}}$ builds an axiomatic system that makes T a consequence of S. Alternatively, in the absence of an agent $\mathcal{A}$, a machine ${{{\mathcal {M}}}}$ 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.