During the 1980s Michie defined Machine Learning in terms of two orthogonal axes of performance: predictive accuracy and comprehensibility of generated hypotheses. Since predictive accuracy was readily measurable and comprehensibility not so, later definitions in the 1990s, such as Mitchell's, tended to use a one-dimensional approach to Machine Learning based solely on predictive accuracy, ultimately favouring statistical over symbolic Machine Learning approaches. In this paper we provide a definition of comprehensibility of hypotheses which can be estimated using human participant trials. We present two sets of experiments testing human comprehensibility of logic programs. In the first experiment we test human comprehensibility with and without predicate invention. Results indicate comprehensibility is affected not only by the complexity of the presented program but also by the existence of anonymous predicate symbols. In the second experiment we directly test whether any state-of-the-art ILP systems are ultra-strong learners in Michie's sense, and select the Metagol system for use in humans trials. Results show participants were not able to learn Editors: James Cussens and Alessandra Russo. Mach Learn (2018Learn ( ) 107:1119Learn ( -1140 the relational concept on their own from a set of examples but they were able to apply the relational definition provided by the ILP system correctly. This implies the existence of a class of relational concepts which are hard to acquire for humans, though easy to understand given an abstract explanation. We believe improved understanding of this class could have potential relevance to contexts involving human learning, teaching and verbal interaction.

Explainability in Artificial Intelligence (AI) has been revived as a topic of active research by the need of conveying safety and trust to users in the “how” and “why” of automated decision‐making in different applications such as autonomous driving, medical diagnosis, or banking and finance. While explainability in AI has recently received significant attention, the origins of this line of work go back several decades to when AI systems were mainly developed as (knowledge‐based) expert systems. Since then, the definition, understanding, and implementation of explainability have been picked up in several lines of research work, namely, expert systems, machine learning, recommender systems, and in approaches to neural‐symbolic learning and reasoning, mostly happening during different periods of AI history. In this article, we present a historical perspective of Explainable Artificial Intelligence. We discuss how explainability was mainly conceived in the past, how it is understood in the present and, how it might be understood in the future. We conclude the article by proposing criteria for explanations that we believe will play a crucial role in the development of human‐understandable explainable systems. This article is categorized under: Fundamental Concepts of Data and Knowledge > Explainable AI Technologies > Artificial Intelligence

The study and understanding of human behaviour is relevant to computer science, artificial intelligence, neural computation, cognitive science, philosophy, psychology, and several other areas. Presupposing cognition as basis of behaviour, among the most prominent tools in the modelling of behaviour are computational-logic systems, connectionist models of cognition, and models of uncertainty. Recent studies in cognitive science, artificial intelligence, and psychology have produced a number of cognitive models of reasoning, learning, and language that are underpinned by computation. In addition, efforts in computer science research have led to the development of cognitive computational systems integrating machine learning and automated reasoning. Such systems have shown promise in a range of applications, including computational biology, fault diagnosis, training and assessment in simulators, and software verification. This joint survey reviews the personal ideas and views of several researchers on neural-symbolic learning and reasoning. The article is organised in three parts: Firstly, we frame the scope and goals of neural-symbolic computation and have a look at the theoretical foundations. We then proceed to describe the realisations of neural-symbolic computation, systems, and applications. Finally we present the challenges facing the area and avenues for further research.

This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract. During the 1980s Michie defined Machine Learning in terms of two orthogonal axes of performance: predictive accuracy and comprehensibility of generated hypotheses. Since predictive accuracy was readily measurable and comprehensibility not so, later definitions in the 1990s, such as that of Mitchell, tended to use a one-dimensional approach to Machine Learning based solely on predictive accuracy, ultimately favouring statistical over symbolic Machine Learning approaches. In this paper we provide a definition of comprehensibility of hypotheses which can be estimated using human participant trials. We present the results of experiments testing human comprehensibility of logic programs learned with and without predicate invention. Results indicate that comprehensibility is affected not only by the complexity of the presented program but also by the existence of anonymous predicate symbols. Permanent repository link

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