Introduction to Description Logic and Ontology Languages

1. CS6999 Presentation Introduction to Description Logic and Ontology Languages Jidi (Judy) Zhao November 21, 2014

2. Talk Outline • Introduction to Ontologies • Introduction to Description Logic (DL) • Reasoning in DL • Introduction to Ontology Languages: OWL • Extensions of DL and Research Challenges

3. What is an ontology? Many definitions have been given: from Philosophy: “a systematic explanation of being” Neches gives some guidelines: “…defines the basic terms and relations including the vocabulary of a topic area as well as the rules for combining terms and relations to define extensions to the vocabulary.” Gruber, the most quoted: “…an explicit specification of a conceptualization” An ontology defines the concepts used to describe and represent an area of knowledge, as well as relations among them.

4. Types of Ontologies Top-level Ontologies The Standard Upper Ontology (SUO): http://suo.ieee.org/

5. Types of Ontologies Top-level Ontologies The Standard Upper Ontology (SUO): http://suo.ieee.org/ WordNet: http://wordnet.princeton.edu/ Sowa’s top-level ontology Cyc’s upper ontology Domain Ontologies E-commerce Medicine Engineering Enterprise Chemistry …. Thing Nonliving Living

6. Methodologies for Ontology Engineering Building domain ontologies from huge ontologies (SENSUS, Cyc, AKT,…) OTK (On-To-Knowledge) Methodology Univ. of Karlsruhe Methontology Univ. Politecnica de Madrid

7. Methontology: A Methodology for Building Ontologies Methontology Ontology Development Process Life Cycle (Fernández-López et al., 1997;1999)

8. Tools for Ontology Engineering OilEd from University of Manchester http://oiled.man.ac.uk/ Ontolingua from KSL (Stanford University) http://www-ksl.stanford.edu OntoSaurus from ISI (USA) http://www.isi.edu/isd/ontosaurus.html OntoEdit from Karlsrhue Univ. http://ontoserver.aifb.unikarlsruhe.de/ontoedit/ Protégéfrom SMI (Stanford University) http://protege.stanford.edu/ WebOnto from KMI (Open University) http://kmi.open.ac.uk/projects/webonto/ WebODE from UPM http://webode.dia.fi.upm.es/webODE/ KAON from AIFB and FZI at the University of Karlsruhe http://kaon.semanticweb.org/

9. Talk Outline • Introduction to Ontologies • Introduction to Description Logic (DL) • Reasoning in DL • Introduction to Ontology Languages: OWL • Extensions of DL and Research Challenges

10. Description Logic Brachman and Levesque [1984] “there is a tradeoff between the expressiveness of a representation language and the difficulty of reasoning over the representations built using that language”. The more expressive the language, the harder the reasoning. Description Logics overcome the ambiguities of early semantic networks and frames first realized in the system KL-One [Brachman and Schmolze, 1985] Well-studied and decidable (most DL languages) Tight coupling between theory and practice

11. Architecture of a DL System from DL Handbook

12. DL Basics Concepts (unary predicates/formulae with one free variable) E.g., Person, Female Roles (binary predicates/formulae with two free variables) E.g., hasChild Individuals (constants) E.g., Mary, John Constructors Uniont, Intersectionu Exists restriction9: 9hasChild.Doctor Value restriction8: 8hasChild.Doctor Complement /negation:: :Mother Number restriction ≥n, ≤n Inverse role (-): isChildOf ≡ hasChild– transitive role (+): hasSister Role hierarchy : hasDaughter v hasChild Axioms Subsumptionv: MothervParent Assertion: Mary: Mother, Mary hasChild John

13. What does 8 R.C and 9 R.C mean? A DogLover is someone whose pets are all dogs, in this case {C} DogLover = 8 hasPet.Dog {p | 8 a, (p, a) 2 hasPet ! a 2 Dog} Also writen more simply as {p | hasPet(p, a) ! Dog(a) } A DogLiker is someone who owns a dog , in this case {A, C} DogLiker = 9 hasPet.Dog {p | hasPet(p, a) Æ Dog(a) } This slide is from Dr. Bruce Spencer’s slides (2007).

14. The DL Family Smallest propositionally closed DL is ALC Concepts constructed using boolean operators t , u , : plus restricted quantifiers 9 , 8 Only atomic roles E.g., Personu8hasChild.(Doctor t 9hasChild.Doctor)

15. The DL Family (cont.) S often used for ALC extended with transitive roles (R+) Additional lettersindicate other extensions, e.g.: H for role hierarchy O for nominals (e.g., {Mary, John}) I for inverse roles N for number restrictions Q for qualified number restrictions (e.g., ≥2hasChild.Doctor) R for limited complex role inclusion axioms, role disjointness ALC+ transitive role (R+)+role hierarchy (H) +O + I + Q = SHOIQ

16. DL Semantics • Semantics given by standard FO model theory • The vocabulary is the set of names (consist of concepts and roles ) we use in our model of (part of) the world • {Daisy, Cow, Animal, Person, Car, drives, …} • An interpretation I is a tuple (I, •I) • Iis the domain (a set) • •Iis a mapping that maps: • Names of objects (individuals/constants) to elements ofI • Names of unary predicates (classes/concepts) to subsets ofI • Names of binary predicates (properties/roles) to subsets ofI ×I

17. DL Semantics (adapted from Horrocks 2006) Interpretation function•I Interpretation domainI Individuals iI 2I Mary John Concepts CI µ I Teacher Student Car Roles RIµI×I hasChild owns (Teacher u Student)

18. A Knowledge Base (KB) <T,A>= a Tbox + an Abox A TBox (terminology) is a set of inclusion axioms and equivalence axioms the vocabulary of an application domain e.g.: { MothervPerson, GrandMother ≡ Personu 9hasChild.Parent } An ABox (Assertion) is a set of assertions about individuals about named individuals in terms of this vocabulary e.g.: {Mary: Mother, Anita hasChild Mary} DL Knowledge Bases

19. Talk Outline • Introduction to Ontologies • Introduction to Description Logic (DL) • Reasoning in DL • Introduction to Ontology Languages: OWL • Extensions of DL and Research Challenges

20. Tableau Reasoning (1) Key reasoning tasks Satisfiability: asat(A), whether the assertions in a KB have a model Instance checking: C(a)? Concept satisfiability: C? Retrieval: retrieve a set of individuals that instantiate C Subsumption: B vA ? A subsumes B if every individual of concept B is also of concept A. Equivalence: A≡B? , B vA ? And Av B? Reasoning tasks reducible to KB (un)satisfiability: asat(A) Instance checking: instance(a, C, A) ,:asat (A [ {a: :C}) Concept satisfiability: sat(C) , asat(A [ {a:C}) Concept subsumption: CvD w.r.t. KB A,A[ {:Du C} is not satisfiable , :asat(A [{a::D u C}) Retrieval: check each individual in the Abox, reducible to instance checking DL systems typically use tableaualgorithms to decide the satisfiability (consistency) of KB

21. Tableau Reasoning (2) Tableau algorithms work by trying to construct a concrete example (model) consistent with KB. A KB A is satisfiable iff a fully expanded clash-free graph is constructed. Tableau reasoning contains a set of completion rules operating on constraint sets or tableau Clash: a clash is an obvious contradiction, e.g., A(x), :A(x) Proof procedure: start from assertions about individuals (ABox axioms) unfold the TBox so that atomic concepts only appear on the right side of axioms transform all concepts into negation normal form (i.e. negation only occurs in front of atomic concept names): : (C u D) !:C t:D : 9R.C !8 R.:C apply completion rules in arbitrary order as long as possible stops when a clash is found terminates if no completion rule is applicable A KB is satisfiable iff a clash-free tableau can be derived CS6795 Semantic Web Techniques

22. completion rules Tableau Reasoning (3)

23. Tableau Reasoning (5): Concept Subsumption • KB: • Reasoning task: mothervwoman? • Exercise: Is the concept : woman u mother satisfiable?

24. Tableau Reasoning (4): asat(A) E.g., KB: {HappyParent≡Person u∀hasChild.(Doctor t 9hasChild.Doctor), John:HappyParent, John hasChild Mary, Mary::Doctor, Wendy hasChild Mary, Wendy marriedTo John} from Harrock, 2006 Person ∀hasChild.(Doctort∃hasChild.Doctor)

25. Tableau Reasoning (6) Some completion rules are nondeterministic (e.g., 9 , ≤ ). Blocking Strategies are often needed to ensure termination. E.g., KB: {Personv9hasParent.Person, John:Person}

26. Tableau Reasoning (7) In general, (representation of) model consists of: Named individuals forming arbitrary directed graph Trees of anonymous individuals rooted in named individuals

27. Similar tableaux expansions can be designed for more expressive DL languages. A tableau algorithm has to meet three requirements: Soundness: if a complete and clash-free graph is found by the algorithm, we can construct a model. Completeness: Given a model, the algorithm can always find an complete and clash-free graph Termination: the algorithm can terminate in finite steps with specific result. Tableau Reasoning (8)

28. Software for DL Reasoning CEL Pellet KAON2

29. Efficiency of Tableau Reasoning I can’t find an efficient algorithm, but neither can all these famous people. NP-Complete Cartoons, http://max.cs.kzoo.edu/~kschultz/CS510/ClassPresentations/NPCartoons.html

30. Talk Outline • Introduction to Ontologies • Introduction to Description Logic (DL) • Reasoning in DL • Introduction to Ontology Languages: OWL • Extensions of DL and Research Challenges

31. Traditional Ontology Languages Ontolingua and KIF LOOM OKBC F-logic Ontology Markup Languages SHOE RDF and RDF Schema OIL DAML+OIL OWL Ontology Languages

32. 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 OIL, DAML+OIL and OWL based on Description Logic The Web Ontology Language OWL

33. OWL Three species of OWL OWL full is the union of OWL syntax and RDF OWL DL restricted to FOL fragment (is equivalent to SHOIN(Dn) DL) OWL Lite is an “easier to implement” subset of OWL DL OWL DL Benefits from many years of DL research Well defined semantics Formal properties well understood (complexity, decidability) Known reasoning algorithms Implemented systems (highly optimised) Adapted from ENC 2004 Tutorial by Peter F. Patel-Schneider

34. 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 u ∀hasChild.(Doctor t ∃hasChild.Doctor):

35. Class/Concept Constructors

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

37. Talk Outline • Introduction to Ontologies • Introduction to Description Logic (DL) • Reasoning in DL • Introduction to Ontology Languages: OWL • Extensions of DL and Research Challenges

38. Extensions of DL • Combinations of DL and Logic Programs (LP) • Uncertainty extension of DL • Concrete domain constraints • Modal, epistemic, and temporal operators • Open world vs. close world • …..

39. Venn Diagram of DL, LP, and FOC

40. Motivation(1) • DL cannot represent “more than one free variable at a time”. • (1) A rule involving multiple variables. E.g., Man(?X) ∧ Woman(?Y) !PotentialFriendshipBetween(?X,?Y). • (2) Chaining to derive values of Properties. E.g., Father(?X,?Y) ∧ Father(?Y,?Z)! Grandfather(?X,?Z). (not allowed in SHOIN) Work(?X, ?Y) ∧ Live(?X, ?Z) ∧ Loc(?Y,?W) ∧ Loc(?Z,?W) • !HomeWorker(?X).

41. Motivation(2) • Horn Logic cannot represent a (1) disjunction or (2) existential in the head. • (1) State a subclass of a complex class expression which is a disjunction. E.g., • (Human u Adult) v (Man t Woman) • (2) State a subclass of a complex class expression which is an existential. E.g., • Radio v9hasPart.Tuner

42. Different approaches • Approaches reducing description logics to logic programs • DLP • OWL 2 RL • Homogeneous approaches • OWL Rules • SWRL • Hybrid approaches accessing description logic through queries in logic programs • AL-Log

43. Uncertainty extension of DL • Handling uncertain knowledge is becoming a critical research direction for the (Semantic) Web. • knowledge on the Web is often uncertain and imprecise. • E.g., many concepts needed in business domain ontology modeling lack well-defined boundaries or, precisely defined criteria of relationship between concepts • Domain modeling and Ontology reasoning • Quantify degree of an individual belonging to a class • Quantify degree of subsumption between a class and its subclasses • Concept mapping between ontologies • Quantify degree of alignment between classes of two ontologies

44. URW3 Situation Report: uncertainty ontology URW3 44

45. Probability, Possibility and Fuzzy logic Probabilistic Description Logic: Statistical information e.g. John is a student with the probability 0.6 and a teacher with the probability 0.4 Fuzzy Description Logic: Express vagueness and imprecision e.g. John is tall with the degree of truth 0.9 Possibilistic Description Logic: Particular rankings and preferences e.g. John prefers an ice cream to a beer

46. Research Challenges Syntax and Semantics Decidability Reasoning algorithms for possible extensions Soundness and completeness Complexity/efficiency Effective methods for reasoning under uncertainty

47. Questions?