Advances in Neural-Symbolic Learning Systems: Modal and Temporal Reasoning

Three notable hallmarks of intelligent cognition are the ability to draw rational conclusions, the ability to make plausible assumptions, and the ability to generalise from experience. Although human cognition often involves the interaction of these three abilities, in Artificial Intelligence they are typically studied in isolation. In our research programme, we seek to integrate the three abilities within neural computation, offering a unified framework for learning and reasoning that exploits the parallelism and robustness of connectionism. A neural network can be the machine for computation, inductive learning, and effective reasoning, while logic provides rigour, modularity, and explanation capability to the network. We call such systems, combining a connectionist learning component with a logical reasoning component, neural-symbolic learning systems. In what follows, I review the work on neural-symbolic learning systems, starting with logic programming and then looking at how to represent modal logic and other forms of non-classical reasoning in neural networks. The model consists of a network ensemble, each network representing the knowledge of an agent (or possible world) at a particular time point. Ensembles may be seen as in different levels of abstraction so that networks may be fibred onto (combined with) other networks to form a structure combining different logical systems or, for example, object-level and meta-level knowledge. We claim that this quite powerful yet simple structure offers a basis for an expressive yet computationally tractable cognitive model of integrated reasoning and learning.