Categorical Logic as a Foundation for Reasoning Under Uncertainty

Critical decisions must often be made in real time and based on imprecise evidence from various sources. In Phase I Metron developed a rigorous mathematical framework in which to construct models of uncertainty and to translate between them. We propose in Phase II to transition this mathematical infrastructure into a data fusion software architecture. By seamlessly integrating probabilities, belief functions, fuzzy sets, rules-based systems, neural networks, and other uncertainty management formalisms, this architecture will provide the best information from uncertain data derived from diverse sources. The software will meet specific MDA needs and will deliver valuable capabilities to government, business and academic consumers. In collaboration with Carnegie Mellon University we will also research advanced mathematical techniques for reasoning under uncertainty and for verifying conformance of data fusion algorithms to specifications. Phase II deliverables include tested software for federating existing Bayesian network and Dempster-Shafer based applications, a prototype application incorporating fuzzy logic and other uncertainty management formalisms, and a neural network application developed within our mathematical framework. In Phase I we documented our work in a 498 page Final Report. We will maintain our attention to thorough documentation in Phase II.