A Framework for the Merger and Practical Exploitation of Formal Logic and Artificial Neural Networks

The assimilation of formal logic into the domain of Software Engineering offers the possibility of enormous benefits in terms of software reliability and verifiability. To date, however, the integration of such techniques has proved difficult since they involve a significantly increased burden on the programmer in meeting the demands of the formal mechanisms being employed. The current paper investigates the advantages which may be gained by the software development process with the introduction of Artificial Neural Network technology into a formal software development system. Essentially, the adaptive artificial neural network model is employed to refine an existing formal software model in order to produce increasingly better approximations to a given solution. Each approximation is itself a valid formal system whose precise behaviour may be formally determined. The paper introduces a framework by which a programmer may define a system possessing the abstract structure of a traditional neural network but whose internal structures are taken from the formal mathematical domain of Constructive Type Theory. The system will then refine itself to produce successive approximations to a desired goal based on data presented to it. An example is presented addressing a problem domain which has previously proved difficult to model. Although the example presented is necessarily limited, it does provide an insight into the potential advantages of merging formal logic with artificial neural systems.