Soundness Preserving Approximation for TBox Reasoning

1. Yuan Ren, Jeff Z. Pan, Yuting Zhao University of Aberdeen AAAI-2010 Soundness Preserving Approximation for TBox Reasoning

2. What is an Ontology A model of (some aspect of) the world • Introduces vocabulary relevant to domain, e.g.: • Anatomy • Koala • Introduces vocabulary Specifies meaning (semantics) of terms • Koala eat only some part of Eucalypt • Eucalypt is Plant only some eat Plant partof Eucalypt

3. Ontology Reasoning • Infer implicitknowledge from explicit knowledge

4. Ontology Landscape • Related DL-based standards (OWL, OWL2) are established • The user community is growing fast • Swoogle searches over 10,000 online ontologies • Larger and larger ontologies • SNOMED has 379,691 concepts • More and more references to ontologies • 8,580 papers with “SNOMED” in text. (Google Scholar) • Reasoning is already difficult • FMA (Foundational Model of Anatomy, OWL DL) has 41,647 concepts and 123,564 axioms, • Existing reasoners can hardly classify it

5. Challenge: Ontology Classification Classification (TBox reasoning) is a complex reasoning service Compute the class hierarchy (subsumption among all named concepts Classification can be reduce to subsumption checking between every pair of classes which can be further reduced to class unsatisfiability checking For example, if an ontology consists of 100,000 classes then a naïve implementation needs roughly 100,000 * 100,000class unsatisfiability checking

6. Challenge: Ontology Classification (II) General class axioms C v D are widely used such as the domain constraint ObjectProperty(hasF domain (Person)) 9hasF. >v Person Expansion rules for general class axioms C v D If a new node y is added, then add a general class description D t:C in L(y) for each general class axiom C v D Case study: if an ontology consists of 100general class axioms then theoretically there are 2100 possible expansions for each node

7. Can Approximations Help? • OWL2 comes with tractable profiles • OWL2 EL has nice computation complexity for TBox reasoning OWL 2 DL 2NEXPTime- complete SROIQ OWL DL NEXPTime- complete SHOIN PTime- complete OWL 2 EL OWL 2 RL EL++ AC0 OWL 2 QL DL-Lite

8. Motivation: Syntactic Approximation • Why SROIQ (OWL2 DL) to EL++ (OWL2 EL)? • Minor syntactic gap results in major complexity difference • From most expressive/complex to most efficient for TBox • Using approximation to bridge the gap

9. What to approximate Input ontology Algorithm Quality of approximation soundness preserving completeness preserving Approximation Algorithm Inputs Outputs AAAI2010 Outstanding Paper: How Incomplete Is Your Semantic Web Reasoner? By Giorgos Stoilos, Bernardo Cuenca Grau, Ian Horrocks 9

10. We provide faithful syntactic approximation for OWL2 DL TBox reasoning Soundness preserving Practically close to complete Challenge removing axioms with non-OWL2 EL descriptions could lead to low recall In this paper … soundness preserving classification result Appr. of OWL2 DL ontology OWL2 DL ontology OWL2 DL Algorithm (Extended) OWL2 EL Algorithm classification result 10

11. How Does it Work 11 11 • TBox approximation • Directly represent non-OWL2-EL concepts with fresh named concepts • E.g., r.C subClassOf D Ar.CsubClassOf D • Maintain semantic relations for these named concepts • complementary relations • cardinality relations • ABox approximation • Internalise ABox into TBox • E.g., C(a)  {a} subClassOf C • r(a,b)  {a} subClassOf r.{b}, … • Reasoning • Using additional completion rules to recover the semantics

12. Approach: Name Assignment Herbivore C5 C1 C3 VegeFood eat some some Plant partof Eucalypt Replacing the original axioms with assigned names

13. Approach: Complement Approximation C1 C5 Herbivore nC5 some nC2 nC1 some some C3 nVegeFood nC3 eat C2 and VegeFood C4 nPlant nC4 some • Complement Table (CT) • Linear complexity (Lemma 3) Plant partof Eucalypt

14. Approach: Complement Inferences C1 C5 Herbivore nC5 some nC2 nC1 some some C3 nVegeFood nC3 eat C2 and VegeFood C4 nPlant nC4 some Plant partof Eucalypt • Complement-enriched completion rules • E.g. A subClassOf B =>B subClassOf A • Making use of CT information • 3 additional rules • Logical properties • Tractable (Theorem 6) • Soundness-preserving (Theorem 7)

15. Evaluations: Performance Comparison

16. Evaluation: Scalability Comparison

17. Conclusion: Contributions Software: http://trowl.eu/ OWL 2 DL 2NEXPTime- complete SROIQ OWL DL NEXPTime- complete SHOIN PTime- complete OWL 2 EL OWL 2 RL EL++ AC0 OWL 2 QL The proposed OWL2-DL approximate TBox reasoning services is PTIME-complete Soundness-guaranteed, and high recall on real world and benchmark ontologies DL-Lite

18. Conclusion: Future Works • Source (expressive) DL: • Supporting more constructs • Target (lightweight) DL: • Supporting more expressive but still tractable languages • e.g. Horn-SHIQ • Reasoning services: • ABox reasoning • Justification • Local closed world reasoning • Applications

19. Thank you • More information on scalable OWL reasoning can be found at AAAI2010 Tutorial on Large-Scale Ontology Reasoning and Querying http://www.abdn.ac.uk/~csc280/tutorial/aaai2010/