Abductive Learning

Abstract

1.1. Introduction To develop a unified framework which accommodates and enables machine learning and logical reasoning to work together effectively is a well-known holy grail problem in artificial intelligence. It is often claimed that advanced intelligent technologies could emerge when machine learning and logical reasoning can be seamlessly integrated as human beings generally perform problem-solving based on the leverage of perception and reasoning , where perception corresponds to a data-driven process that can be realized by machine learning whereas reasoning corresponds to a knowledge-driven process that can be realized by logical reasoning. In the history of artificial intelligence research, however , machine learning and logical reasoning are almost separately developed: Before the 1990s most attention was paid to logical reasoning (and knowledge engineering) whereas after the 1990s machine learning becomes mainstream while logical reasoning receives less attention. Among the obstacles encumbering the connection of logical reasoning with machine learning lies in their very different representations. Generally, popular logical reasoning techniques are based on first-order logic representation, whereas popular machine learning techniques are based on attribute-value representation. The latter can be regarded as an equivalence of propositional logic representation, as the attribute-value pairs can be converted to truth tables; such a conversion, however, could not bridge machine learning and logical reasoning directly as there exist big gaps. For example, consider the issues that may emerge when one tries to convert a first-order logical clause into a set of attribute-value represented data: due to the existence of the universal quantifier ∀, one clause may lead to infinite instances; each predicate may actually express a kind of relation among instances, and therefore, the conversion may lead to constraints about possible value-takings of a subset of instances rather than definite attribute-values of an individual instance; etc. Nevertheless, as the holy grail problem is fundamentally important and attractive, great efforts have been made in the past few decades. Roughly speaking, there are two general paradigms for the integration of logical reasoning and machine learning. The first paradigm attempts to introduce some elements of machine learning into logical rea