This document proposes using OMDoc, a framework for representing formal knowledge, to improve ontology authoring and documentation. It describes how OMDoc can: 1) Provide better support for modularity, documentation at different granularities, and linking documentation to formal representations compared to languages like OWL. 2) Model existing ontologies and translate between OMDoc and OWL/RDF formats to leverage existing tools. 3) Allow comprehensive, integrated documentation of ontologies through features like literate programming. The approach is evaluated by reimplementing the FOAF ontology in OMDoc.

1. Motivation OMDoc for Ontologies Evaluation Conclusion
A Mathematical Approach to
Ontology Authoring and Documentation
Deduktionstreffen 2009
Christoph Lange and Michael Kohlhase
Jacobs University, Bremen, Germany
KWARC – Knowledge Adaptation and Reasoning for Content
October 15, 2009
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2. Motivation OMDoc for Ontologies Evaluation Conclusion
Documenting Ontologies
Semantic Web Ontology: formalization of a shared conceptualization,
used by intelligent agents, for annotating documents, . . .
Just another kind of formalization, usually a decidable FOL subset (e. g.
OWL: description logic)
Ontologies power applications, they are engineered collaboratively,
they have to be maintained ⇒ Documentation is crucial (as with
software)!
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3. Motivation OMDoc for Ontologies Evaluation Conclusion
Shortcomings of OWL
Same for other languages (even worse)
can annotate entities (classes, properties, individuals) and axioms, but
only textual annotations really work in practice.
can’t annotate subsets/sections of ontologies, can’t annotate imports,
can’t interlink documentation and formal representation (literate
programming)
poor modularity ⇒ can’t document how imported concepts are reused
extensions have been proposed, but tools don’t support them
limited expressivity is nice for decidability, but not for saying what you
intend ⇒ incomplete, ambiguous models of the world
in practice, documentation is often maintained separately in HTML ⇒
hard to maintain
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4. Motivation OMDoc for Ontologies Evaluation Conclusion
OMDoc for Ontologies: Correspondences and Differences
We know how to do integrated documentation (for mathematics) ⇒ apply
it to ontologies!
Correspondences: Three layers of knowledge representation:
1 symbols = entities
2 statements = axioms/rules
(state properties of symbols)
3 theories = ontologies
Differences:
Expressivity: logical flexibility/heterogeneity vs. description
logic
Modularity: theory morphisms vs. literal imports
Documentation: literate programming, flexible granularity
vs. limited annotations
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5. Motivation OMDoc for Ontologies Evaluation Conclusion
OMDoc as a Semantic Web Ontology Language
Plan for documenting ontologies in OMDoc:
1 model OWL and its foundations as OMDoc theories
2 introduce import syntax and semantics for referencing semantic web
ontologies from OMDoc
3 translate ontologies from OMDoc to the RDF syntax of OWL (to reuse
existing reasoners), and vica versa
4 enhance the documentation in OMDoc
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6. Motivation OMDoc for Ontologies Evaluation Conclusion
1. Knowledge Representation
basic structure of a semantic web ontology: RDF triple =
predicate(subject, object) axioms
syntactic sugar for frequently used constructs (instance-of = has-type)
can distinguish between declared and inferred knowledge
(definition/axiom vs. theorem; “provenance”), can model proofs
Example
Student = Person ≥ 1 enrolledIn
declare symbols (with types), define Student symbol
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7. Motivation OMDoc for Ontologies Evaluation Conclusion
Example in the Semantic Wiki SWiM
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8. Motivation OMDoc for Ontologies Evaluation Conclusion
2. Connecting OMDoc and Semantic Web URIs
OMDoc: theory graph URI → theory name → symbol name
Semantic Web: namespace URI → local name (like XML)
Writing ontologies from scratch in OMDoc → no problem !
But how to reimplement or reference existing semantic web
ontologies?
→ write dummy theory that points to namespace URI, further
OMDocification optional
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9. Motivation OMDoc for Ontologies Evaluation Conclusion
3. Compatibility to Reasoners etc.
Efficient DL reasoners and other ontology tools (e. g. visualization) don’t
support OMDoc – be compatible with them
extended our Krextor XML→RDF extraction framework to
OMDoc→OWL; implemented OWL/RDF→OMDoc (bootstrap editing)
formally specified (in OMDoc, of course ) how our syntactic sugar
breaks down to RDF
<file:.../uni.omdoc?university>
rdf:type owl:Ontology ;
owl:imports foaf: .
<file:.../uni.omdoc?university?Student>
rdf:type owl:Class ;
owl:equivalentClass _:d24e43 .
_:d24e43
owl:intersectionOf _:collection-d24e44 .
_:collection-d24e44
rdf:first foaf:Person ;
rdf:rest _:collection-d24e44-1 .
_:collection-d24e44-1
rdf:first _:d24e47 ;
rdf:rest rdf:nil .
_:d24e47
rdf:type owl:Restriction ;
owl:onProperty <file:.../uni.omdoc?university?enrolledIn> ;
owl:minCardinality "1"^^xsd:nonNegativeInteger .
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10. Motivation OMDoc for Ontologies Evaluation Conclusion
4. Comprehensible Manuals (here: FOAF)
JOMDoc: elaborate adaptive presentation framework
http://jomdoc.omdoc.org
JOBAD: architecture for interactive documents
http://jomdoc.omdoc.org/wiki/AI-Mashup
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11. Motivation OMDoc for Ontologies Evaluation Conclusion
Evaluation: FOAF reimplemented in OMDoc
1 FOAF references other ontologies without importing them. More
support with OMDoc.
2 Could turn all source code <!-- comments --> (e. g. section
headers) into proper documentation and document structure
3 Revised redundant axioms: some declared, some inferred in OMDoc
4 non-DL semantics of one concept expressed in FOL
5 reuse of imported entities not modeled properly – solved by views
6 seamlessly integrated completely informal documentation sections
with the formal part
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12. Motivation OMDoc for Ontologies Evaluation Conclusion
Challenges and Future Work
Ontology engineering can benefit from better documentation (and more
explicit modularity/heterogeneity) – but:
High expressivity and good documentation ⇒ extremely verbose.
Need good editor support. Plan: extend OMDoc-aware semantic wiki
SWiM for ontologies, “invade” [Collaborative] Protégé and word
processors
Consider various ontology documentation workflows:
add documentation to existing ontologies
formalize informal documents into ontologies
collaborative development
Mathematically define syntactic macros
Do the same for other languages – ideas, wishes?
Evaluate with industry-scale ontologies
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