Designing heterogeneous reasoning systems with a case study on FOL and Euler/Venn reasoning

In recent years we have witnessed a growing interest in heterogeneous reasoning systems. A heterogeneous reasoning system incorporates different representation systems, for example, in the case study of this project a sentential and a diagrammatic system. The advantage of heterogeneous systems is that they allow a reasoner to bridge the gaps among various formalisms and construct threads of proof which cross the boundaries of the systems of representation. In doing this, these heterogeneous systems allow the reasoner to take advantage of each component system's ability to express information in its area of expertise while at the same time allowing the reasoner to work with all of their information content together.; The main goal of this work is to design a framework for the definition of heterogeneous rules of inference for a broad class of heterogeneous systems. These rules of inference allow the exchange of information between the system's representations and will be referred to as recast rules. For any given heterogeneous reasoning system, this framework could be used to define many plausible notions of recasting. However in this project, I will primarily discuss a special kind of recasting, called observation, that was inspired by Dretske's notion of secondary seeing. Broadly described, observation is a process of information extraction based upon the explicit information content of a representation.; Once presented, this framework will be used as the basis of a detailed case study of the heterogeneous rules of inference in a FOL and Euler/Venn reasoning system. This case study will consist of both the mathematical theory of the heterogeneous rules of inference as well as an implementation of those rules.