Schoening, James R C-E LCMC CIO/G6 wrote: (01)
> All,
>
> Are we going to discuss the technical feasibility of interrelating
> multiple upper ontologies? To issue a communique, we'll need a good
> handle on whether we believe this is technically feasible and will
> enable semantic interoperability.
> (02)
The notes for the Upper Ontology Summit contain two key ideas:
-develop methods to relate the existing upper ontologies to each other.
- create a common subset ontology that is compatible with all of the linked
upper ontologies. (03)
There are two fundamental relationships between ontologies that we need
to consider:
1. extension
2. definable interpretation (04)
First, a few definitions:
- A theory is a set of sentences in a language conformant with
Common Logic.
- An ontology is a set of theories.
- Suppose that the nonlogical lexicon of a theory T2 is a subset
of the nonlogical lexicon of the a theory T1.
T1 is an extension of T2 if the axioms in T1 entail the axioms in T2.
- T1 is definably interpretable in T2 iff for each symbol in the
nonlogical lexicon of T1 the relation/function/constant denoted by the
symbol is definable by a sentence S in the language of T2.
- Theory T1 generalizes theory T2 iff T1 is a consistent extension of
a theory T3 and T3 is definably interpretable in T2. (05)
The idea is that we can design a Common Subset Ontology (CSO)
by solving the following problem for the theories contained in
the set of existing upper, mid-level, and domain-specific ontologies: (06)
Given two theories T1 and T2, determine whether there exists a theory
that generalizes both. (07)
Theories that do not have any generalizations
are candidates for inclusion in the CSO. (08)
Additional Comments
1. This is a well-posed problem with a definite solution;
it is not a matter of philosophical differences.
2. Evaluation of the relationships between
ontologies is made using their axioms alone;
it cannot rely on intended models of concepts that are not axiomatized.
If the axioms of an ontology are insufficient to capture their
users' intended semantics, then there is little progress that
can be made towards integration; we risk descent into logomachy,
as far too many previous efforts have done.
3. Theories may be generalizations of each other.
For example, Hilbert's geometry and Tarski's geometry are
definably interpretable in each other, even though they
have different primitives and different relations.
In such cases, either or both theories could be included in the CSO. (09)
- michael gruninger
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