Foundations of modal symbolic learning

Abstract

Traditional symbolic learning is the sub-field of machine learning that aims to learn symbolic models from structured data, representing propositional logic theories, and its investigation initiated with the early days of artificial intelligence. Such an approach is yet outstanding in terms of academic performance (e.g., accuracy) and industrial one (e.g., interpretability, bias, ethical concerns) over modern techniques (e.g., deep neural networks) on structured data, but it suffers to natively address the problem of learning from unstructured data (e.g., time series, images, and graphs). By systematically exploiting inductive biases, we present the mathematical framework of modal symbolic learning for learning symbolically from unstructured data, which is the intersection between the fields of machine learning and modal logic(s) in terms of academic discipline. We study its properties from a learning perspective, enhancing standard decision trees, the quintessential expression of conventional symbolic learning, to learn modal logic theories. We demonstrate how modal data emerges from unstructured one to conduct modal symbolic learning. We experimentally prove how models learned with this framework are more accurate, precise, and sensible than classic propositional ones and at least comparable with those learned with non-symbolic ones. In addition, we show how our approach can be generalized from trees to more complex learning techniques (e.g., fuzzy and neural-symbolic trees), and we point to several ambitious and challenging directions in which modal symbolic learning, as a field, can expand. Modal symbolic learning is still in its infancy, and investigating its foundations allows a more organic and substantial development of the matter. Nevertheless, it has already shown enormous application potential, both theoretical (giving modal logic languages a new application field and fostering the study of new ones) and practical (symbolically addressing real-world problems and thus offering interpretable models for further research).