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Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
Motivation                 OMDoc for Ontologies                 Evaluation                 Metadata                   Conc...
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A Mathematical Approach to Ontology Authoring and Documentation

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Workshop FGWM (Knowledge and Experience Management), September 2009

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  • Christoph:

    I appreciate your bold assertion of the limitations of RDF OWL.

    I too noticed that predicates of RDF Triples are oversimplified and highly restricted in what they can express. Thus much of what can be expressed and processed is shut off. The 'association classes' of UML are more expressive. I have proposals to use upgrade predicates to full-fledged 'association classes' and model knowledge in EXECUTABLE form which then leads to MEANING.

    I invite you to please take a look at Pentagon of Meaning and Meaning is Mediated and let me know when we can discuss details.

    putchavn@yahoo.com
    04JUL14

    felt so and I am working on some remedies /solutions.
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
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Transcript of "A Mathematical Approach to Ontology Authoring and Documentation"

  1. 1. Motivation OMDoc for Ontologies Evaluation Metadata Conclusion A Mathematical Approach to Ontology 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
  2. 2. Motivation OMDoc for Ontologies Evaluation Metadata Conclusion Overview Shortcomings of OWL (Web Ontology Language) w. r. t. documentation: limited expressivity poor modularity no full integrated documentation Those problems (and solutions!) are known from other fields: MKM (Mathematical Knowledge Management) Software Engineering (program comprehension, software documentation, UML, literate programming) ⇒ improve ontology engineering that way! Concretely: engineer OWL ontologies in our mathematical markup language OMDoc Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 2/19
  3. 3. 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 Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 3/19
  4. 4. 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 Example Example 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 of integrated documentation in general. Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 4/19
  5. 5. Motivation OMDoc for Ontologies Evaluation Metadata Conclusion Correspondences . . . OMDoc/MKM OWL/Ontology What is it? Symbols Entities (classes, prop- “atoms” erties, individuals) Statements Axioms/Rules state (= define or assert) properties of symbols Theories Ontologies collections of related symbols/statements their “deductive closure” often modularized Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 5/19
  6. 6. Motivation OMDoc for Ontologies Evaluation Metadata Conclusion . . . and Differences Expressivity: OMDoc: logically uncommitted, can implement any logic as theory heterogeneity OWL: at most SROIQ (a DL), or subsets Modularity: OMDoc: theory morphisms (symbol/formula mappings), parametric theories OWL: import complete ontologies, and import them literally (rarely used) Documentation support: OMDoc: literate programming; documentation in any granularity OWL: attach strings to entities and ontologies OWL 2: also axioms more? – in theory (reification, named graphs, XML literals, RDFa), but not in practice Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 6/19
  7. 7. Motivation OMDoc for Ontologies Evaluation Metadata Conclusion OMDoc as a Semantic Web Ontology Language Prerequisites are satisfied: URIs as identifiers, any logical foundation can be formalized Plan: 1 model OWL and its foundations RDFS and RDF (we go this way for compatibility!) 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 back Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 7/19
  8. 8. Motivation OMDoc for Ontologies Evaluation Metadata Conclusion 1. Knowledge Representation implemented OMDoc theories for RDF, RDFS, and OWL, which declare all of their symbols most elementar representation: RDF triples = predicate(subject, object) axioms syntactic sugar for frequently used constructs: individuals that are instances of classes: use OMDoc’s typing syntax Michael Person compound 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 Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 8/19
  9. 9. Motivation OMDoc for Ontologies Evaluation Metadata Conclusion Example A 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 o d u c t i o n " ><CMP> F o r our o n t o l o g y , we f i r s t i m p o r t FOAF and then i n t r o d u c e t h e c o n c ep t o f a s t u d e n t . . . . < /CMP>< / omtext> <symbol name= " S t u d e n t " x m l : i d = " s t u d e n t . sym " > <metadata> <meta p r o p e r t y = " d c : d e s c r i p t i o n " >A s t u d e n t < / 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> < d e f i n i t i o n f o r = " # s t u d e n t . sym " type= " s i m p l e " > <CMP>A s t u d e n t i s a p e r s o n who i s e n 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 n O f " / > <OMS cd= " f o a f " name= " P e r s o n " / > <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 n C a r d i n a l i t y " / > <OMI>1< / OMI>< /OMA>< /OMA>< /OMA>< / OMOBJ> < / d e f i n i t i o n >< / theory> Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 9/19
  10. 10. Motivation OMDoc for Ontologies Evaluation Metadata Conclusion Example (nicer) Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 10/19
  11. 11. 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 t o namespace U R I −−> < 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 whole rest later Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 11/19
  12. 12. Motivation OMDoc for Ontologies Evaluation Metadata 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 . Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 12/19
  13. 13. 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, compare Student = Person ≥ 1 enrolledIn to Manchester syntax: C l a s s : Student E q u i v a l e n t T o : P e r s o n t h a 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 (“what does mean again?” → JOBAD, http://jomdoc.omdoc.org/wiki/AI-Mashup) Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 13/19
  14. 14. Motivation OMDoc for Ontologies Evaluation Metadata Conclusion FOAF Rewritten and Presented in OMDoc Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 14/19
  15. 15. Motivation OMDoc for Ontologies Evaluation Metadata 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 Some comments attached to individual axioms – no problem with OMDoc’s literate programming 4 Better handling of inverse properties, e. g. foaf:maker = foaf:made− Define one direction, infer the other (and more facts about the inverse) 5 non-OWL semantics of foaf:membershipClass expressed in FOL 6 some relations to imported entities not stated properly (foaf:maker vs. dc:creator) – solved by views 7 FOAF’s documentation contains completely informal sections – we could seamlessly integrate them with the formal part Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 15/19
  16. 16. Motivation OMDoc for Ontologies Evaluation Metadata Conclusion Scalable Metadata for Technical Specifications Metadata not only needed for documenting ontologies, but also for technical specifications (e. g. revision logs), digital libraries, etc. OMDoc 1.2 OMDoc 1.6 custom XML syntax using RDFa, old syntax for com- patibility from statements upwards also inside formulæ few vocabularies hard-coded (DC, can use any URI-based vocabulary CC, plus ad hoc extensions) not extensible can even define new vocabularies in OMDoc formal semantics not clear rely on metadata ontologies Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 16/19
  17. 17. 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 wiki SWiM for ontologies, “invade” [Collaborative] Protégé and word processors Ontology documentation approaches: add documentation to existing ontologies formalize informal documents into ontologies collaborative development Mathematically define syntactic macros (and β-reduce them when generating OWL) – no longer limited to OWL’s syntactic sugar Do the same for other ontology languages Evaluate with industry-scale ontologies Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 17/19
  18. 18. Motivation OMDoc for Ontologies Evaluation Metadata Conclusion FOAF made interactive using OMDoc and JOBAD Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 18/19
  19. 19. Motivation OMDoc for Ontologies Evaluation Metadata Conclusion Conclusion We apply technology from (MK)M for M(KM). Ontology engineering can benefit from better documentation (and more explicit modularity/heterogeneity) Scalable metadata approach for any semantic markup (What semantic markup do you use?) See our poster and discuss! Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation September 22, 2009 19/19
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