Formal Theory Building Using Automated Reasoning Tools

The merits of representing scientific theories in formal logic are well-known. Expressing a scientific theory in formal logic explicates the theory as a whole, and the logic provides formal criteria for evaluating the theory, such as soundness and consistency. On the one hand, these criteria correspond to natural questions to be asked about the theory: is the theory contradiction-free? (is the theory logically consistent?) is the theoretical argumentation valid? (can a theorem be soundly derived from the premises?) and other such questions. On the other hand, testing for these criteria amounts to making many specific proof attempts or model searches: respectively, does the theory have a model? can we find a proof of a particular theorem? As a result, testing for these criteria quickly defies manual processing. Fortunately, automated reasoning provides some valuable tools for this endeavor. This paper discusses the use of first-order logic and existing automated reasoning tools for formal theory building, and illustrates this with a case study of a social science theory, Hage’s axiomatic theory of organizations.