A Mathematical Approach to Ontology Authoring and Documentation

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Conferences on Intelligent Computer Mathematics 2009, Mathematical Knowledge Management

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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 MKM 2009 Christoph Lange and Michael Kohlhase Jacobs University, Bremen, Germany KWARC – Knowledge Adaptation and Reasoning for Content This work was supported by JEM-Thematic-Network ECP-038208. July 10, 2009 Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation July 10, 2009 1/18
  2. 2. Motivation OMDoc for Ontologies Evaluation Metadata Conclusion Overview Shortcomings of OWL (Web Ontology Language): limited expressivity poor modularity no full integrated documentation All problems solved by MKM technologies ⇒ improve ontology engineering that way! Concretely: engineer OWL ontologies in OMDoc Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation July 10, 2009 2/18
  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 July 10, 2009 3/18
  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 July 10, 2009 4/18
  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 July 10, 2009 5/18
  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 July 10, 2009 6/18
  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 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) Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation July 10, 2009 7/18
  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, . . . complete from Trac can distinguish between declared and inferred knowledge (definition/axiom vs. theorem), can model proofs Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation July 10, 2009 8/18
  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 July 10, 2009 9/18
  10. 10. Motivation OMDoc for Ontologies Evaluation Metadata Conclusion Example (nicer) Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation July 10, 2009 10/18
  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 July 10, 2009 11/18
  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; also working on OWL→OMDoc 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 July 10, 2009 12/18
  13. 13. Motivation OMDoc for Ontologies Evaluation Metadata Conclusion Presenting Documentation OMDoc has an elaborate adaptive presentation framework (→ Kohlhase/Müller/Rabe, MKM 2008) – 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 is parallel markup (preserves semantic structure) can use that for interactive navigation, e. g. definition lookup (‘‘what does mean again?’’ → Giceva/Lange/Rabe on Monday) Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation July 10, 2009 13/18
  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 July 10, 2009 14/18
  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 July 10, 2009 15/18
  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) – and for the DML (David Ruddy yesterday) 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 July 10, 2009 16/18
  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’’ Protégé 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 July 10, 2009 17/18
  18. 18. 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 (OpenMath CDs? DML? . . . ?) Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation July 10, 2009 18/18

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