Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
AMathematical Approach toOntology Authoring and Documentation
FGWM 2009
Christoph Lange and Michael Kohlhase
Jacobs University, Bremen, Germany
KWARC – Knowledge Adaptation and Reasoning for Content
September 22, 2009
Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 1/19
Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
Overview
Shortcomings of OWL (Web Ontology Language) w. r. t.documentation:
limited expressivitypoor modularityno full integrated documentation
Those problems (and solutions!) are known from other fields:MKM (Mathematical Knowledge Management)Software Engineering (program comprehension, softwaredocumentation, UML, literate programming)
⇒ improve ontology engineering that way!
Concretely: engineer OWL ontologies in our mathematical markuplanguage OMDoc
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Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
Semantic Web Ontologies
Semantic Web: the web of data and intelligent agents
Ontology (there): formalization of a shared conceptualization
mostly implemented in decidable FOL subsets
Web Ontology Language (OWL): description logic
not just decidable, but also tractable sublogics of OWL
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Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
Lack of Expressivity
What if the world is more complex than your logic?1 dumb the model down to the logic used (e. g. DOLCE in OWL)2 add informal documentation of how things actually are
ExampleExample from FOAF (Friend-of-a-Friend): foaf:membershipClass“All foaf:members of this foaf:Group have to be instances of the class C”Too complex for OWL⇒ specified in lengthy, ambiguous natural language(targets: authors and developers)
Problem is not just lack of expressivity, but also lack of modularity, and ofintegrated documentation in general.
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Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
Correspondences . . .
OMDoc/MKM OWL/Ontology What is it?Symbols Entities (classes, prop-
erties, individuals)“atoms”
Statements Axioms/Rules state (= define or assert)properties of symbols
Theories Ontologies collections of relatedsymbols/statementstheir “deductive closure”often modularized
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Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
. . . and Differences
Expressivity:OMDoc: logically uncommitted, can implement any logic as theory
; heterogeneityOWL: at most SROIQ (a DL), or subsets
Modularity:OMDoc: theory morphisms (symbol/formula mappings), parametric
theoriesOWL: import complete ontologies, and import them literally (rarely
used)Documentation support:
OMDoc: literate programming; documentation in any granularityOWL: attach strings to entities and ontologies
OWL 2: also axiomsmore? – in theory (reification, named graphs, XML literals,RDFa), but not in practice /
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Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
OMDoc as a Semantic Web Ontology Language
Prerequisites are satisfied: URIs as identifiers, any logical foundation can beformalized
Plan:1 model OWL and its foundations RDFS and RDF (we go this way for
compatibility!) as OMDoc theories2 introduce import syntax and semantics for referencing semantic web
ontologies from OMDoc3 translate ontologies from OMDoc to the RDF syntax of OWL (to reuse
existing reasoners), and back
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Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
1. Knowledge Representation
implemented OMDoc theories for RDF, RDFS, and OWL, which declareall of their symbols
most elementar representation: RDF triples =̂ predicate(subject, object)axiomssyntactic sugar for frequently used constructs:
individuals that are instances of classes: use OMDoc’s typing syntaxMichael ∶ Personcompound types for properties:knows ∶ ObjectProperty(Person→ Person)more to come (subclasses, subproperties, . . . )
can distinguish between declared and inferred knowledge(definition/axiom vs. theorem; “provenance”), can model proofs
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Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
ExampleA well-known DL axiom: Student = Person⊓ ≥ 1 enrolledIn<theory name=" u n i v e r s i t y ">
< imports from=" owl . omdoc#owl " /> < imports from=" f o a f . omdoc# f o a f " /><omtext type=" i n t r odu c t i o n "><CMP>For our ontology , we f i r s t import
FOAF and then in t roduce the concept o f a s tudent . . . . < /CMP></ omtext><symbol name=" Student " xm l : i d = " s tudent . sym ">
<metadata><meta p rope r t y= " d c : d e s c r i p t i o n ">A student< /meta></metadata>
<type system=" owl "><OMOBJ xmlns= " h t t p : / /www. openmath . org /OpenMath ">
<OMS cd=" owl " name=" C l a s s " /></OMOBJ></ type></ symbol><de f i n i t i on f o r = " # s tudent . sym " type=" s imple ">
<CMP>A student i s a person who i s en r o l l e d a t l e a s t once . < /CMP><OMOBJ xmlns= " h t t p : / /www. openmath . org /OpenMath ">
<OMA><OMS cd=" owl " name=" i n t e r s e c t i o nO f " /><OMS cd=" f o a f " name=" Person " /><OMA><OMS cd=" owl " name=" R e s t r i c t i o n " />
<OMS cd=" u n i v e r s i t y " name=" e n r o l l e d I n " /><OMA><OMS cd=" owl " name=" m i nCa r d i n a l i t y " />
<OMI>1</OMI></OMA></OMA></OMA></OMOBJ></ de f i n i t i on></ theory>
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Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
Example (nicer)
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Motivation OMDoc for Ontologies Evaluation Metadata 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?<theory name=" f o a f ">
<metadata>< !−− mapping from theory to namespace URI −−>< l i n k r e l = " odo:semWebBase " h r e f = " h t t p : / / xmlns . com/ f o a f / 0 . 1 / " />
</metadata></ theory>
Simplest migration path: start with this mapping only, OMDocify the wholerest later ,
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Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
3. Compatibility to Reasoners etc.
Efficient DL reasoners and other ontology tools (e. g. visualization) don’tsupport OMDoc – be compatible with them
extended our Krextor XML→RDF extraction framework toOMDoc→OWL; implemented OWL/RDF→OMDoc (bootstrap editing)formally specified (in OMDoc, of course ,) how our syntactic sugarbreaks 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 .
_:d24e43owl:intersectionOf _:collection-d24e44 .
_:collection-d24e44rdf:first foaf:Person ;rdf:rest _:collection-d24e44-1 .
_:collection-d24e44-1rdf:first _:d24e47 ;rdf:rest rdf:nil .
_:d24e47rdf:type owl:Restriction ;owl:onProperty <file:.../uni.omdoc?university?enrolledIn> ;owl:minCardinality "1"^^xsd:nonNegativeInteger .
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Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
Presenting Documentation
OMDoc has an elaborate adaptive presentation framework (JOMDoc,http://jomdoc.omdoc.org) – use it
define notations for our logical symbols
many context-dependent alternatives possible, compareStudent = Person⊓ ≥ 1 enrolledIn to Manchester syntax:C l a s s : Student
Equ i va l en tTo : Person tha t e n r o l l e d I n min 1
Output contains interlinked presentation and semantic markup(“parallel markup”; preserves semantic structure)can use that for interactive navigation, e. g. definition lookup (“whatdoes ⊓mean again?”→ JOBAD,http://jomdoc.omdoc.org/wiki/AI-Mashup)
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Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
FOAF Rewritten and Presented in OMDoc
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Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
Evaluation: FOAF reimplemented in OMDoc
1 FOAF references other ontologies without importing them. Moresupport with OMDoc.
2 Could turn all source code <!-- comments --> (e. g. sectionheaders) into proper documentation and document structure
3 Some comments attached to individual axioms – no problem withOMDoc’s literate programming
4 Better handling of inverse properties, e. g. foaf:maker = foaf:made−
Define one direction, infer the other (andmore facts about the inverse)5 non-OWL semantics of foaf:membershipClass expressed in FOL6 some relations to imported entities not stated properly (foaf:maker vs.
dc:creator) – solved by views7 FOAF’s documentation contains completely informal sections – we
could seamlessly integrate them with the formal part
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Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
Scalable Metadata for Technical Specifications
Metadata not only needed for documenting ontologies, but also fortechnical specifications (e. g. revision logs), digital libraries, etc.OMDoc 1.2 OMDoc 1.6custom XML syntax using RDFa, old syntax for com-
patibilityfrom statements upwards also inside formulæfew vocabularies hard-coded (DC,CC, plus ad hoc extensions)
can use any URI-based vocabulary
not extensible can even define new vocabulariesin OMDoc ,
formal semantics not clear rely on metadata ontologies
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Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
Challenges and Future Work
High expressivity and good documentation⇒ extremely verbose.
Need good editor support. Plan: extend OMDoc-aware semantic wikiSWiM for ontologies, “invade” [Collaborative] Protégé and wordprocessorsOntology documentation approaches:
add documentation to existing ontologiesformalize informal documents into ontologiescollaborative development
Mathematically define syntactic macros (and β-reduce them whengenerating OWL) – no longer limited to OWL’s syntactic sugar
Do the same for other ontology languages
Evaluate with industry-scale ontologies
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Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
FOAF made interactive using OMDoc and JOBAD
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Motivation OMDoc for Ontologies Evaluation Metadata Conclusion
Conclusion
We apply technology from (MK)M for M(KM).
Ontology engineering can benefit from better documentation (andmore explicit modularity/heterogeneity)
Scalable metadata approach for any semantic markup(What semantic markup do you use?)
See our poster and discuss!
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