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[ontology-summit] [ont-of-ont] Initial ideas for properties and relation

To: ontology-summit@xxxxxxxxxxxxxxxx
From: Michael Gruninger <gruninger@xxxxxxxxxxxxxxx>
Date: Mon, 17 Mar 2008 17:11:53 -0400
Message-id: <47DEDE99.3020304@xxxxxxxxxxxxxxx>
Hello everyone,
here are some intial thoughts on the metadata we would like to use
to describe ontologies within the repository.
It is not meant to be comprehensive, just something to get discussion going.    (01)

I would like to keep the discussion grounded, either in examples of 
or examples of use-case scenarios for the repository.    (02)

- michael    (03)

---------------------------------------------------    (04)

1. Purpose of the Ontology Metadata    (05)

The metadata for ontologies should support the sharing
and reuse of ontologies within the repository.    (06)

The metadata should allow users to
- retrieve ontologies for use in domain applications;
- retrieve ontologies to be integrated with other user ontologies;
- retrieve ontologies that will be extended to create new user ontologies;
- determine whether or not an ontology can be integrated with
user ontologies;
- determine whether a set of ontologies retrieved from the repository
can be used together;
- determine whether an ontology in the repository can be partially shared.    (07)

We can consider logical metadata (logical properties of the ontology
independent of any implementation or engineering artefact, as well as
logical relationships between ontologies within the repository)
and engineering metadata (properties of the ontology as considered
as an engineering artefact).    (08)

The examples used below are not intended to be exhaustive.
People are encouraged to post additional examples of ontologies.    (09)

2. Logical Metadata    (010)

2.1 Language
What language used to specify the ontology?    (011)

Classification of languages:
- A formal language has a syntax (logical symbols together with a formally
specified grammar) and a model theory (which specifies the conditions
under which expressions in the language can be given particular truth
assignments).    (012)

The report "Evaluating Reasoning Systems"
contains a classification of formal languages used to specify ontologies.    (013)

- A formalizable language has a syntax, although it does not have
a model theory.
XML and EXPRESS, as seen in the following cases:
- Topic Maps (XML)
- folksonomy (XML)
- ISO 15926 (EXPRESS)    (014)

Some ontologies are only specified in natural language:
- Wordnet
- taxonomies
- thesauri    (015)

2.2 Modularity
Is a particular ontology a monolithic set of axioms, or is it
composed of a set of smaller modules?    (016)

Is each module considered to be a separate ontology within the
repository? If not, what are the relationships between the modules?    (017)

Which modules of an ontology can be used separately?    (018)

a) Catalog of Temporal Theories
b) The Process Specification Language (PSL,
consists of a set of modules which are extensions of a common core theory
PSL-Core. Metadata for each module specifies which other modules
must also be included when using the module.    (019)

2.3 Relationships between ontologies    (020)

2.3.1 Entailment
Is one ontology stronger than another in the sense that
any sentence in the first ontology entails the sentences in the second?
This would be the case when one ontology can be considered to be a
weaker version of another ontology within the repository.    (021)

Within the Catalog of Temporal Theories, the before
is a partial ordering (i.e. it is a transitive antisymmetric reflexive
Since this ontology axiomatizes all of these properties, it entails
an ontology that only axiomatizes the transitive property, such as OWL-Time.
In other words, OWL-Time is weaker than the first-order theories in
the Catalog.    (022)

2.3.2 Extension
An ontology T1 is an extension of another ontology T2 iff
the set of sentences in T2 contain or entail the sentences in T1.    (023)

T1 is a conservative extension of T2 whenever
every sentence in the lexicon of T1 is provable from T1 iff
it is provable from T2.    (024)

T1 is a nonconservative extension of T2 whenever
there is a sentence in the lexicon of T1 which is
provable from T2 but not from T1.    (025)

a) Within the Catalog of Temporal Theories,
nonconservative extensions of LINEAR-POINT.
Both can prove new properties of the before relation that were
not provable in LINEAR-POINT.
b) Within the Catalog of Temporal Theories,
DURATION is a conservative extension of LINEAR-POINT.
Every sentence using only the before relation is provable in DURATION
iff it was provable in LINEAR-POINT.
c) PSL is a conservative extension of LINEAR-POINT
Every sentence using only the before relation is provable in PSL
iff it was provable in LINEAR-POINT.    (026)

2.3.3 Definable Interpretation
If the ontologies have different sets of primitives and relations,
is it possible to define the primitives and relations of one ontology
using the second ontology?
If so, then it is possible to integrate an existing ontologies even
though they have different sets of primitives.    (027)

1. Within the Catalog of Temporal Theories,
LINEAR-POINT and INTERVAL-MEETING are definable interpretations of each 
2. Hilbert's Geometry has points,lines, and planes as primitives.
Tarski's Geometry only has points as primitives.
Each of these ontologies are definable interpretations of each other.    (028)

2.3.4 Mutual consistency
Which ontologies are mutually inconsistent?    (029)

a) Within the Catalog of Temporal Theories,
DENSE-LINEAR-ORDERING is inconsistent with
DISCRETE-LINEAR-ORDERING, and hence they cannot be combined
within the same ontology.    (030)

3. Engineering Metadata
- provenance
- versioning
- existing applications of the ontology
(e.g. interoperability, search, decision support)
- domain-specificity (e.g. biology, supply chain management, manufacturing)    (031)

4. References    (032)

Hayes, P. (1996) A Catalog of Temporal Theories,
Technical Report UIUC-BI-AI-96-01, University of Illinois at 
Urbana-Champaign.    (033)

Bock, C., Gruninger, M., Libes, D., Lubell, J., Subrahamian, E. (2006)
Evaluating Reasoning Systems, NISTIR 7310, National Institute of
Standards and Technology.    (034)

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