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
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.