SUO: Review of IFF
Principles, Facts and Suggestions about IFF
o The IFF would represent the metalevel of the SUO. Although it has been
developed synergistically with one module's needs indicating the appropriate
content of another module, it is being released as it stabilizes in versions
top-down.
o The IFF is divided into two levels based upon the large/small distinction
in foundations -- the upper metalevel for large notions and the lower
metalevel for small notions.
o The IFF is based upon category theory, information flow and formal concept
analysis.
o The upper metalevel will consist of the IFF Core (sub)Ontology and the IFF
Category Theory (sub)Ontology.
o The IFF Core (sub)Ontology currently contains a namespace representing
classes, functions, finite limits, and some elements of topoi. In version
2.0 of the IFF Foundation Ontology this will expand to contain namespaces
for large (binary) relations, large orders, large classifications and large
concept lattices.
o The truth concept lattice, defined in versions 2.0 and 3.0, is one
(important) example of a large concept lattice. The axioms laid done in
version 2.0 will allow us to populate and manipulate truth concept lattices
and the truth adjoint pairs of monotonic functions that result from the
1st-order interpretations defined in version 3.0.
o The IFF Category Theory (sub)Ontology currently contains various
namespaces representing a baseline for category theory. Later versions of
the IFF Foundation Ontology will greatly expand on these as needs arise.
o The lower metalevel will contain the IFF Model Theory (sub)Ontology. This
will appear in version 3.0 of the IFF Foundation Ontology. The lower
metalevel could possibly contain other modules: categorical model theory;
tense, linear and modal logic; rough and fuzzy sets and logic, semiotics,
etc.
o The boundary between the object level and the metalevel should be made
explicitly obvious in the SUO.
Robert E. Kent
rekent@ontologos.org