Reasoning about the past is of fundamental importance in several applications in computer science and artificial intelligence, including reactive systems and planning. In this paper we propose efficient temporal knowledge representation algorithms to reason about and implement past time logical operators in neural-symbolic systems. We do so by extending models of the Connectionist Inductive Learning and Logic Programming System with past operators. This contributes towards integrated learning and reasoning systems considering temporal aspects. We validate the effectiveness of our approach by means of case studies.
Rafael V. Borges, Luís C. Lamb, Artur S. d'