Improving the Efficiency of Reasoning Through Structure-Based Reformulation

Abstract. We investigate the possibility of improving the efficiency of reasoning through structure-based partitioning of logical theories, combined with partitionbased logical reasoning strategies. To this end, we provide algorithms for reasoning with partitions of axioms in first-order and propositional logic. We analyze the computational benefit of our algorithms and detect those parameters of a partitioning that influence the efficiency of computation. These parameters are the number of symbols shared by a pair of partitions, the size of each partition, and the topology of the partitioning. Finally, we provide a greedy algorithm that automatically reformulates a given theory into partitions, exploiting the parameters that influence the efficiency of computation.

A global workspace framework for combined reasoning

Artificial Intelligence research has produced many effective techniques for solving a wide range of problems. Practitioners tend to concentrate their efforts in one particular problem solving paradigm and, in the main, AI research describes new methods for solving particular types of problems or improvements in existing approaches. By contrast, much less research has considered how to fruitfully combine different problem solving techniques. Numerous studies have demonstrated how a combination of reasoning approaches can improve the effectiveness of one of those methods. Others have demonstrated how, by using several different reasoning techniques, a system or method can be developed to accomplish a novel task, that none of the individual techniques could perform. Combined reasoning systems, i.e., systems which apply disparate reasoning techniques in concert, can be more than the sum of their parts. In addition, they gain leverage from advances in the individual methods they encompass. However, the benefits of combined reasoning systems are not easily accessible, and systems have been hand-crafted to very specific tasks in certain domains. This approach means those systems often suffer from a lack of clarity of design and are inflexible to extension. In order for the field of combined reasoning to advance, we need to determine best practice and identify effective general approaches. By developing useful frameworks, we can empower researchers to explore the potential of combined reasoning, and AI in general. We present here a framework for developing combined reasoning systems, based upon Baars’ Global Workspace Theory. The architecture describes a collection of processes, embodying individual reasoning techniques, which communicate via a global workspace. We present, also, a software toolkit which allows users to implement systems according to the framework. We describe how, despite the restrictions of the framework, we have used it to create systems to perform a number of combined reasoning tasks. As well as being as effective as previous implementations, the simplicity of the underlying framework means they are structured in a straightforward and comprehensible manner. It also makes the systems easy to extend to new capabilities, which we demonstrate in a number of case studies. Furthermore, the framework and toolkit we describe allow developers to harness the parallel nature of the underlying theory by enabling them to readily convert their implementations into distributed systems. We have experimented with the framework in a number of application domains and, through these applications, we have contributed to constraint satisfaction problem solving and automated theory formation