OWL: A Description Logic Based Ontology Language

1. OWL: A Description Logic Based Ontology Language Ian Horrocks <horrocks@cs.man.ac.uk> Information Management Group School of Computer Science University of Manchester

2. Talk Outline • Introduction to Description Logics • Introduction to Ontologies • Introduction to Ontology Languages • Ontology Reasoning • Why do we want it? • How do we do it? • Current Work and Research Challenges • Summary

3. Introduction to Description Logics

4. What Are Description Logics? • A family of logic based Knowledge Representation formalisms • Descendants of semantic networks and KL-ONE • Describe domain in terms of concepts (classes), roles (properties, relationships) and individuals • Distinguished by: • Formal semantics (typically model theoretic) • Decidable fragments of FOL (often contained in C2) • Closely related to Propositional Modal & Dynamic Logics • Closely related to Guarded Fragment • Provision of inference services • Decision procedures for key problems (satisfiability, subsumption, etc) • Implemented systems (highly optimised)

5. DL Basics • Concepts (unary predicates/formulae with one free variable) • E.g., Person, Doctor, HappyParent, (Doctor t Lawyer) • Roles (binary predicates/formulae with two free variables) • E.g., hasChild, loves, (hasBrother±hasDaughter) • Individuals (constants) • E.g., John, Mary, Italy • Operators (for forming concepts and roles) restricted so that: • Satisfiability/subsumption is decidable and, if possible, of low complexity • No need for explicit use of variables • Restricted form of 9 and 8 (direct correspondence with ◊ and []) • Features such as counting can be succinctly expressed

6. The DL Family (1) • Smallest propositionally closed DL is ALC (equiv modal K(m)) • Concepts constructed using booleans u, t, :, plus restricted quantifiers 9, 8 • Only atomic roles E.g., Person all of whose children are either Doctors or have a child who is a Doctor: Person u8hasChild.(Doctor t 9hasChild.Doctor)

7. The DL Family (2) • S often used for ALC extended with transitive roles (R+) • Additional letters indicate other extensions, e.g.: • H for role hierarchy (e.g., hasDaughter v hasChild) • O for nominals/singleton classes (e.g., {Italy}) • I for inverse roles (e.g., isChildOf ´ hasChild–) • N for number restrictions (e.g., >2hasChild, 63hasChild) • Q for qualified number restrictions (e.g., >2hasChild.Doctor) • F for functional number restrictions (e.g., 61hasMother) • S + role hierarchy (H) + inverse (I) + QNR (Q) = SHIQ • SHIQ is the basis for W3C’s OWL Web Ontology Language • OWL DL ¼SHIQ extended with nominals (i.e., SHOIQ) • OWL Lite ¼SHIQ with only functional restrictions (i.e., SHIF)

8. DL Semantics Semantics given by standard FO model theory: Interpretation function I Interpretation domain I IndividualsiI2I John Mary ConceptsCIµI Lawyer Doctor Vehicle RolesrIµI£I hasChild owns (Lawyer u Doctor)

9. DL Knowledge Base • A TBox is a set of “schema” axioms (sentences), e.g.: {Doctor v Person, HappyParent´Person u8hasChild.(Doctor t 9hasChild.Doctor)} • An ABox is a set of “data” axioms (ground facts), e.g.: {John:HappyParent, John hasChild Mary} • A Knowledge Base (KB) is just a TBox plus an ABox

10. Introduction to Ontologies

11. See other talk…

12. Introduction toOntology Languages

13. The Web Ontology Language OWL • Semantic Web led to requirement for a “web ontology language” • set up Web-Ontology (WebOnt) Working Group • WebOnt developed OWL language • OWL based on earlier languages OIL and DAML+OIL • OWL now a W3C recommendation(i.e., a standard) • OIL, DAML+OIL and OWL based on Description Logics • OWL effectively a “Web-friendly” syntax for SHOIN

14. OWL RDF/XML Exchange Syntax <owl:Class> <owl:intersectionOf rdf:parseType=" collection"> <owl:Class rdf:about="#Person"/> <owl:Restriction> <owl:onProperty rdf:resource="#hasChild"/> <owl:allValuesFrom> <owl:unionOf rdf:parseType=" collection"> <owl:Class rdf:about="#Doctor"/> <owl:Restriction> <owl:onProperty rdf:resource="#hasChild"/> <owl:someValuesFrom rdf:resource="#Doctor"/> </owl:Restriction> </owl:unionOf> </owl:allValuesFrom> </owl:Restriction> </owl:intersectionOf> </owl:Class> E.g., Person u8hasChild.(Doctor t 9hasChild.Doctor):

15. Class/Concept Constructors • C is a concept (class); P is a role (property); x is an individual name • XMLS datatypes as well as classes in 8P.C and 9P.C • Restricted form of DL concrete domains

16. Ontology Axioms • OWL ontology equivalent to DL KB (Tbox + Abox)

17. Why Description Logic? • OWL exploits results of 15+ years of DL research • Well defined (model theoretic) semantics

18. Why Description Logic? • OWL exploits results of 15+ years of DL research • Well defined (model theoretic) semantics • Formal properties well understood (complexity, decidability) I can’t find an efficient algorithm, but neither can all these famous people. [Garey & Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, 1979.]

19. Why Description Logic? • OWL exploits results of 15+ years of DL research • Well defined (model theoretic) semantics • Formal properties well understood (complexity, decidability) • Known reasoning algorithms

20. Why Description Logic? • OWL exploits results of 15+ years of DL research • Well defined (model theoretic) semantics • Formal properties well understood (complexity, decidability) • Known reasoning algorithms • Implemented systems (highly optimised) Pellet

21. Why Description Logic? • Foundational research was crucial to design of OWL • Informed Working Group decisions at every stage, e.g.: • “Why not extend the language with feature x, which is clearly harmless?” • “Adding x would lead to undecidability - see proof in […]”

22. Ontology Reasoning:Why do We Want It?

23. See other talk…

24. Ontology Reasoning:How do we do it?

25. Using Standard DL Techniques • Key reasoning tasks reducible to KB (un)satisfiability • E.g., C v D w.r.t. KB K iff K[ {x:(C u:D)} is not satisfiable • State of the art DL systems typically use (highly optimised) tableaux algorithms to decide satisfiability (consistency) of KB • Tableaux algorithms work by trying to construct a concrete example (model) consistent with KB axioms: • Start from ground facts (ABox axioms) • Explicate structure implied by complex concepts and TBox axioms • Syntactic decomposition using tableaux expansion rules • Infer constraints on (elements of) model

26. Tableaux Reasoning (1) • E.g., KB: {HappyParent´Person u8hasChild.(Doctor t 9hasChild.Doctor), John:HappyParent, John hasChild Mary, Mary:: Doctor Wendy hasChild Mary, Wendy marriedTo John} Person 8hasChild.(Doctor t 9hasChild.Doctor)

27. Tableaux Reasoning (2) • Tableau rules correspond to constructors in logic (u, 9 etc) • E.g., John:(Person u Doctor) --!John:Person andJohn:Doctor • Stop when no more rules applicable or clash occurs • Clash is an obvious contradiction, e.g., A(x), :A(x) • Some rules are nondeterministic (e.g., t, 6) • In practice, this means search • Cycle check (blocking) often needed to ensure termination • E.g., KB: {Personv9hasParent.Person, John:Person}

28. Tableaux Reasoning (3) • In general, (representation of) model consists of: • Named individuals forming arbitrary directed graph • Trees of anonymous individuals rooted in named individuals

29. Decision Procedures • Algorithms are decision procedures, i.e., KB is satisfiable iff rules can be applied such that fully expanded clash free graph is constructed: Sound • Given a fully expanded and clash-free graph, we can trivially construct a model Complete • Given a model, we can use it to guide application of non-deterministic rules in such a way as to construct a clash-free graph Terminating • Bounds on number of named individuals, out-degree of trees (rule applications per node), and depth of trees (blocking) • Crucially depends on (some form of) tree model property

30. Ontology Reasoning:A Tableaux Algorithm for SHOIQ

31. Motivation for OWL Design • Exploit results of DL research: • Well defined semantics • Formal properties well understood (complexity, decidability) • Known tableaux decision procedures and implemented systems But not for SHOIN(until recently)! So why is/was SHOIN so hard?

32. SHIQ is Already Tricky • Does not have finite model property, e.g.: {ITN v61edge–u9edge.ITN, R:(ITN u60edge–)} • Double blocking • Block interpreted as infinite repetition

33. SHIQ is Already Tricky • Does not have finite model property, e.g.: {ITN v61edge–u9edge.ITN, R:(ITN u60edge–)} • Double blocking • Block interpreted as infinite repetition • Termination problem due to > and 6, e.g.: {John:9hasChild.Doctor u>2 hasChild.Lawyer u62hasChild} • Add inequalities between nodes generated by > rule • Clash if 6 rule only applicable to  nodes

34. SHOIQ: Loss (almost) of TMP • Interactions between O, I, and Q lead to new termination problems • Anonymous branches can loop back to named individuals (O) • E.g., 9r.{Mary} • Number restrictions (Q) on incoming edges (I) lead to non-tree structure • E.g., Mary:61r– • Result is anonymous nodes that act like named individual nodes • Blocking sequence cannot include such nodes • Don’t know how to build a model from a graph including such a block

35. Intuition: Nominal Nodes • Nominal nodes (N-nodes) include: • Named individual nodes • Nodes affected by number restriction via outgoing edge to N-node • Blocking sequence cannot include N-nodes • Bound on number of N-nodes • Must initially have been on a path between named individual nodes • Length of such paths bounded by blocking • Number of incoming edges at an N-node is limited by number restrictions

36. Generate & Merge Problem is Back! E.g., KB: {VMP´Person u9loves.{Mary} u9hasFriend.VMP, John:9hasFriend.VMP Mary:62loves–} • Blocking prevented by N-nodes • Repeated generation and merging of nodes leads to non-termination

37. Intuition: Guess Exact Cardinality • New Ro?-rule guesses exact cardinality constraint on N-nodes {VMP´Person u9loves.{Mary} u9hasFriend.VMP, John:9hasFriend.VMP Mary:62loves–} • Inequality between resulting N-nodes fixes generate & merge problem • Introduces new source of non-determinism • But only if nominals used in a “nasty” way • Usage in ontologies typically “harmless” • Otherwise behaves as forSHIQ

38. Research Challenges:What next?

39. Increasing Expressive Power • OWL not expressive enough for some applications • Constructors mainly for classes (unary predicates) • No complex datatypes or built in predicates (e.g., arithmetic) • No variables • No higher arity predicates • Extensions (of OWL) that have/are being considered include: • (Decidable) extensions to underlying DL • “Rule” language extensions • The focus of much research/debate (e.g., W3C RIF working group) • First order logic (e.g., SWRL-FOL) • (Syntactically) higher order extensions (e.g., Common Logic)

40. Extend Underlying DL • Role box (SROIQ) [Horrocks, Kutz & Sattler, KR-06] • E.g., hasLocation ± partOf v hasLocation • Reflexive, irreflexive, and antisymmetric roles • Basis for OWL 1.1 effort • Concrete domains/datatypes [Lutz, IJCAI-99; Pan et al, ISWC-03] • E.g., value comparison (income > expenditure) • Custom datatypes (integer >25) • Database style keys[Lutz et al, JAIR 2004] • E.g., make + model + chassis-number is a key for Vehicles • … Note that role box + concrete domains is basis for OWL 1.1

41. Rule Language Extensions (to OWL) • First Order extension (e.g., SWRL) [Horrocks et al, JWS, 2005] • Horn clauses where predicates are OWL classes and properties • Resulting language is undecidable • Reasoning support currently only via FOL theorem provers (Hoolet) • Hybrid language extensions being investigated • Restricting language “interaction” maintains decidability • DL extended with Answer Set Programming [Eiter et al, KR-04] • DL extended with Datalog rules [Motik et al, ISWC-04; Rosati, JWS, 2005] • LP/F-logic rule language • Claimed “interoperability” with OWL via DLP subset [de Bruijn et al, WWW-05]

42. Improving Scalability • Optimisation techniques • Improve performance of DL reasoners, e.g., [Sirin et al, KR-06] • Reduction to disjunctive Datalog[Motik et at, KR-04] • Transform DL ontology to DatalogÇ rules • Use LP techniques to deal with large numbers of ground facts • Hybrid DL-DB systems[Horrocks et al, CADE-05] • Use DB to store “Abox” (individual) axioms • Cache inferences and use DB queries to answer/scope logical queries • Polynomial time algorithmsfor sub-ALC logics [Baader et al, IJCAI-05] • Graph based techniques for subsumption computation

43. Other Reasoning Tasks • Querying [Calvanese et al, PODS-98, Fikes et al, JWS, 2004] • Retrieval and instantiation wont be sufficient • Would like, e.g., DB style conjunctive query language • May also need “what can I say about x?” style of query • Explanation [Schlobach & Cornet, DL-03; Parsia et al, WWW-04] • To support ontology design • Justifications and proofs (e.g., of query results)

44. Entity Endurant Perdurant Quality Substantial Event Stative Achievement Accomplishment Other Reasoning Tasks • “Non-Standard Inferences” (e.g., LCS, matching, …) [Küsters, 2001] • To support ontology integration • To support “bottom up” design of ontologies • Design methodologies, e.g., [Wolter & Lutz, KR-06] • Foundational ontologies, conservative extensions, modularisation, etc.

45. Tools and Infrastructure • Editors/environments • Oiled, Protégé, Swoop, Construct, Ontotrack, …

46. Tools and Infrastructure • Editors/environments • Oiled, Protégé, Swoop, Construct, Ontotrack, … • Reasoning systems • Cerebra, FaCT++, Kaon2, Pellet, Racer, … Pellet

47. Summary • DLs are a family of logic basedKR formalisms • Describe domain in terms of concepts, roles and individuals • DLs have many applications • But best known as basis of ontologylanguages such as OWL

48. Summary • Reasoning is crucialto use of ontologies • E.g., in design, maintenance and deployment • Reasoning support via underlying logic • E.g., based on DL systems • Many challenges remain, including: • Well founded language extensions • Extending range and effectiveness of reasoning services Enough work to keep logic based KR community busy for many years to come 

49. Acknowledgements Thanks to my many friends in the DL and ontology communities, in particular: • Alan Rector • Franz Baader • Uli Sattler

50. Resources • Slides from this talk • http://www.cs.man.ac.uk/~horrocks/Slides/cisa06.ppt • FaCT++ system (open source) • http://owl.man.ac.uk/factplusplus/ • Protégé • http://protege.stanford.edu/plugins/owl/ • W3C Web-Ontology (WebOnt) working group (OWL) • http://www.w3.org/2001/sw/WebOnt/ • DL Handbook, Cambridge University Press • http://books.cambridge.org/0521781760.htm