a mathematical approach to ontology authoring and documentation

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

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http://www.jacobs-university.de


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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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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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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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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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. . . 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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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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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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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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Example (nicer)


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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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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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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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http://jomdoc.omdoc.org

http://jomdoc.omdoc.org/wiki/AI-Mashup


FOAF Rewritten and Presented in OMDoc


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Evaluation: FOAF reimplemented in OMDoc

1 FOAF references other ontologies without importing them. Moresupport with OMDoc.

2 Could turn all source code  (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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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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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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FOAF made interactive using OMDoc and JOBAD


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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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a mathematical approach to ontology authoring and documentation

Technology

o n t o

motivation omdoc

owl ontologies

s t u d e n t i s

s e n r o

f i r s t i

p e r s o n

omdoc theories2