  There are countless sources of data available to governments, companies, and
citizens, which can be combined for good or evil. We analyse the concepts of
combining data from common sources and linking data from different sources. We
model the data and its information content to be found in a single source by a
partial ordered monoid, and the transfer of information between sources by
different types of morphisms. To capture the linkage between a family of
sources, we use a form of Grothendieck construction to create a partial ordered
monoid that brings together the global data of the family in a single
structure. We apply our approach to database theory and axiomatic structures in
approximate reasoning. Thus, partial ordered monoids provide a foundation for
the algebraic study for information gathering in its most primitive form.

Logic in Computer Science