How To Understand The Theory Of Dogmatism In Dogmatist Theory

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1 Introduction to Description Logic and Ontology Languages Jidi (Judy) Zhao Co-supervisors: Dr. Weichang Du Dr. Harold Boley October 10, 2008

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 2

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. 3

4 Types of Ontologies Top-level Ontologies The Standard Upper Ontology (SUO): 4

5 Types of Ontologies Top-level Ontologies The Standard Upper Ontology (SUO): WordNet: t t d / Sowa s top-level ontology Cyc s upper ontology Domain Ontologies Thing E-commerce Medicine Engineering Enterprise Chemistry. Living Nonliving 5

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

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

8 Tools for Ontology Engineering OilEd from University of Manchester Ontolingua from KSL (Stanford University) OntoSaurus from ISI (USA) OntoEdit dtfrom Karlsrhue Univ. Protégé 2000 from SMI (Stanford University) edu/ WebOnto from KMI (Open University) WebODE from UPM KAON from AIFB and FZI at the University of Karlsruhe ti / 8

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 9

10 DL Basics Concepts (unary predicates/formulae with one free variable) Eg E.g., Person, Female Roles (binary predicates/formulae with two free variables) E.g., haschild Individuals (constants) E.g., Mary, John Constructors Uniont: MantWoman Intersectionu: DoctoruMother Exists restriction : haschild.doctor Value restriction : haschild.doctor Complement /negation : Manv Mother Number restriction n, n Axioms Subsumptionv: MothervParent 10

11 The DL Family Smallest propositionally closed DL is ALC Concepts constructed using boolean operators t, u, plus restricted quantifiers, Only atomic roles E.g., g, Person u haschild.(doctor t haschild.doctor) 11

12 The DL Family y( (cont.) 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 (e.g., {Mary, John}) I for inverse roles (e.g., ischildof haschild ) N for number restrictions (e.g., 2hasChild, 3hasChild) 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 12

13 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 (Δ I, I ) Δ I is the domain (a set) I is a mapping that t maps: Names of objects (individuals) to elements of Δ I Names of unary predicates (classes/concepts) to subsets of Δ I Names of binary predicates (properties/roles) to subsets of Δ I Δ I 13

14 DL Semantics (adapted from Horrocks 2006) Interpretation function I Interpretation domain Δ I Individuals i I Δ I John Mary Concepts C I Δ I Teacher Student Car Roles R I Δ I Δ I haschild owns (Teacher u Student) 14

15 DL Knowledge Bases 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.: { Mother v Person, GrandMother Person u haschild.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} 15

16 Talk Outline Introduction to Ontologies Introduction to Description Logic (DL) Reasoning in DL Introduction to Ontology Languages: OWL Extensions of DL and Research Challenges 16

17 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? Subsumption: B v A? A subsumes B if every individual of concept B is also of concept A. Equivalence: A B? B v A? And A v B? Retrieval: retrieve a set of individuals that instantiate C Reasoning tasks reducible to KB (un)satisfiability: asat(a) Instance checking: instance(a, C, A) asat (A {a: C}) Concept satisfiability: s ab ty sat(c) asat(a {a:c}) {ac}) Concept subsumption: C v D w.r.t. KB A A { D u 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 tableau algorithms to decide the satisfiability (consistency) of KB 17

18 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 R.C C 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 18 CS6795 Semantic Web Techniques

19 Tableau Reasoning (3) completion rules 19

20 Tableau Reasoning (4): asat(a) E.g., KB: {HappyParent Person Person u haschild.(doctor t haschild.doctor), John:HappyParent, John haschild Mary, Mary: Doctor,, Wendy haschild Mary, Wendy marriedto John} Person haschild.(doctor t haschild.doctor) from Harrock,

21 Tableau Reasoning (5): Concept Subsumption mother v woman? Is the concept woman u mother unsatisfiable? Application of completion rules: The concept is unsatisfiable, therefore, the concept woman subsumes the concept mother. From CS6795 Semantic Web Techniques, Spencer, 2006, 21

22 Tableau Reasoning (6) Some completion rules are nondeterministic (e.g.,, ) Cycle check (blocking) often needed to ensure termination E.g., KB: {Person v hasparent.person, John:Person} 22

23 Tableau Reasoning (7) In general, (representation of) model consists of: Named individuals forming arbitrary directed graph Trees of anonymous individuals rooted in named individuals id 23

24 Sound Tableau Reasoning (8) 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 nondeterministic 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) 24

25 Software for DL Reasoning Pellet KAON2 CEL 25

26 Talk Outline Introduction to Ontologies Introduction to Description Logic (DL) Reasoning in DL Introduction to Ontology Languages: OWL Extensions of DL and Research Challenges 26

27 Ontology Languages Traditional Ontology Languages Ontolingua and KIF LOOM OKBC F-logic Ontology Markup Languages g SHOE RDF and RDF Schema OIL DAML+OIL OWL 27

28 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 OIL, DAML+OIL and OWL based on Description Logic 28

29 OWL Adapted from ENC 2004 Tutorial by Peter F. Patel-Schneider Three species of OWL OWL full is the union of OWL syntax and RDF OWL DL restricted to FOL fragment (is equivalent to SHOIN(D n ) 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) 29

30 OWL RDF/XML Exchange Syntax E.g., Person u haschild.(doctor t haschild.doctor): <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"/> octo <owl:restriction> <owl:onproperty rdf:resource="#haschild"/> <owl:somevaluesfrom o rdf:resource="#doctor"/> </owl:restriction> </owl:unionof> </owl:allvaluesfrom> </owl:restriction> </owl:intersectionof> </owl:class> 30

31 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 P.C and P.C Restricted form of DL concrete domains 31

32 Ontology Axioms OWL ontology equivalent to DL KB (Tbox + OWL ontology equivalent to DL KB (Tbox Abox) 32

33 Talk Outline Introduction to Ontologies Introduction to Description Logic (DL) Reasoning in DL Introduction to Ontology Languages: OWL Extensions of DL and Research Challenges 33

34 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.. 34

35 Venn Diagram of DL, LP, and FOC 35

36 Motivation(1) DL cannot represent more than one free variable at a time. (1) A rule involving multiple variables. E.g., 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). 36

37 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 v haspart.tuner 37

38 Different approaches 1. Approaches reducing description logics to logic programs A. DLP B. OWL 2 RL 2. Homogeneous approaches A. OWL Rules B. SWRL 3. Hybrid approaches accessing description logic through queries in logic programs A. AL-Log 38

39 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 39

40 URW3 Situation Report: uncertainty ontology URW

41 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 41

42 Research Challenges Syntax and Semantics Decidability Reasoning algorithms for possible extensions Soundness and completeness Complexity/efficiency Effective methods for reasoning under uncertainty 42

43 Questions?