Truth-space mass assignments

The theory of mass assignments allows reasoning using probability families that are either imprecise, incomplete or both. The majority of previous work has been with mass assignments defined upon arbitrary domains. This Thesis concentrates on a neglected specialisation of mass assignments, the truth-space mass assignments defined upon the power set of Booleans. The semantics of truth-space mass assignments and their operators are described, both in relation to general mass assignments and also with other methods of imprecise and incomplete reasoning. New operators are defined for truth-space mass assignments that allow them to be reasoned with in new ways consistent with other logic systems. Alterations are made to existing operators to allow them to act in a more intuitive way. Using the new and altered operators this Thesis allows mass assignment theory to act as a many-valued logic handling imprecise and incomplete truths. This opens up many new topics of research and potential for applying the method to solve problems in a new way.