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Applications of a Global Workspace Framework to Mathematical Discovery

Systems which combine various forms of reasoning such as deductive inference and symbolic manipulation have repeatedly been shown to be more effective than stand-alone systems. In general, however, the combined systems are ad-hoc and designed for a single task. We present a generic framework for combining reasoning processes which is based on the theory of the Global Workspace Architecture. Within this blackboard-style framework, processes attached to a workspace propose information to be broadcast, along with a rating of the importance of the information, and only the most important is broadcast to all the processes, which react accordingly. To begin to demonstrate the value of the framework, we show that the tasks undertaken by previous ad-hoc systems can be performed by a configuration of the framework. To this end, we describe configurations for theorem discovery and conjecture making respectively, which produce comparable results to the previous ICARUS and HOMER systems. We further describe a novel application where we use a configuration of the framework to identify potentially interesting specialisations of finite algebras.