This is the final report on the research effort performed by George Mason University, under the agreement W911NF-11-1-0176, proposal number 59841MA, entitled "Mathematical Fundamentals of Probabilistic Semantics for High-Level Fusion" and focused on: (a) Establishing features required of any quantitative uncertainty representation for exchanging soft and hard information in a net-centric environment; (b) Developing a set of use cases involving information exchange and fusion requiring sophisticated reasoning and