Specification and formal verification of fuzzy information processing for the case of edge detection

This thesis explores how an information fusion system can be verified before it is built. Towards this aim, a system is first specified mathematically in a formal language. The specification then can be analyzed by formulating various conjectures (theorems) and proving (or disproving) them using an automatic theorem prover. In our work we use Metaslang as the formal specification language and Specware, which is a tool that supports category theory based algebraic specification of software. One of the most important aspects in information fusion is the uncertainty of the fused decisions that are based on uncertain sources. Out of many possible uncertainty types we focus on fuzzy set theory. We have specified a library of fuzzy set theory that can be used to build specifications of fuzzy information processing systems. As an example, a (fuzzy) edge detection algorithm was implemented and then verified using two theorem provers - Snark and Isabelle. With the help of this approach, reasoning about the impact of the uncertainty of input information is specified formally in every step of the fusion process and can be verified before the system is coded in a programming language.