1. CSE-291: Ontologies in Data & Process Integration Department of Computer Science & Engineering University of California, San Diego CSE-291: Ontologies in Data Integration Spring 2004 Bertram Ludäscher LUDAESCH@SDSC.EDU

2. CSE-291: Ontologies in Data & Process Integration Outline Introduction to Description Logics (DLs)Introduction to Description Logics (DLs) BreakBreak First-order logic (FOL) and Mapping DLs to FOLFirst-order logic (FOL) and Mapping DLs to FOL Material based on: F. Baader, W. Nutt. Basic Description Logics. In the Description Logic Handbook, edited by F. Baader, D. Calvanese, D.L. McGuinness, D. Nardi, P.F. Patel-Schneider, Cambridge University Press, 2002, pages 47-100. F. Baader, W. Nutt. Basic Description Logics. In the Description Logic Handbook, edited by F. Baader, D. Calvanese, D.L. McGuinness, D. Nardi, P.F. Patel-Schneider, Cambridge University Press, 2002, pages 47-100. Description Logics Tutorial, Ian Horrocks and Ulrike Sattler, ECAI-2002, Lyon, France, July 23rd, 2002.Description Logics Tutorial, Ian Horrocks and Ulrike Sattler, ECAI-2002, Lyon, France, July 23rd, 2002. Emerging Sparrow toolkit (Bowers, Ludaescher)Emerging Sparrow toolkit (Bowers, Ludaescher)

3. CSE-291: Ontologies in Data & Process Integration Example: Description Logic DL definition of “Happy Father” (Example from Ian Horrocks, U Manchester, UK)DL definition of “Happy Father” (Example from Ian Horrocks, U Manchester, UK)

4. CSE-291: Ontologies in Data & Process Integration Scientific Example: Domain Map for SYNAPSE and NCMIR Domain Map = labeled graph with concepts ("classes") and roles ("associations") additional semantics: expressed as logic rules Domain Map = labeled graph with concepts ("classes") and roles ("associations") additional semantics: expressed as logic rules Domain Map (DM) Purkinje cells and Pyramidal cells have dendrites that have higher-order branches that contain spines. Dendritic spines are ion (calcium) regulating components. Spines have ion binding proteins. Neurotransmission involves ionic activity (release). Ion-binding proteins control ion activity (propagation) in a cell. Ion-regulating components of cells affect ionic activity (release). Domain Expert Knowledge DM in Description Logic

5. CSE-291: Ontologies in Data & Process Integration Source Contextualization & DM Refinement Source Contextualization & DM Refinement In addition to registering (“hanging off”) data relative to existing concepts, a source may also refine the mediator’s domain map...  sources can register new concepts at the mediator...

6. CSE-291: Ontologies in Data & Process Integration Introduction to Description Logics (aka terminological logics, member of concept languages)

7. CSE-291: Ontologies in Data & Process Integration Roots “Structured Inheritance Networks” [Brachman 1977]“Structured Inheritance Networks” [Brachman 1977] KL-ONE [Brachman, Schmolze 1985]KL-ONE [Brachman, Schmolze 1985] Core ideas:Core ideas: –Building blocks: atomic concepts (unary predicates), atomic roles (binary predicates), individuals (constants) –Constructors for building complex concepts and roles from simpler ones –Automated inference for concept subsumption and instance classification (is-a/is-instance-of are not explicitly given by the user, but inferred from concept definitions/instance properties)

8. CSE-291: Ontologies in Data & Process Integration Source: Description Logics Tutorial, Ian Horrocks and Ulrike Sattler, ECAI-2002, Lyon, France, July 23rd, 2002

9. CSE-291: Ontologies in Data & Process Integration Knowledge Base (DL-Style) Terminological Knowledge (TBox)Terminological Knowledge (TBox) –Concept Definition (naming of concepts): –Axiom (constraining of concepts): => a mediators “glue knowledge source” Assertional Knowledge (ABox) about IndividualsAssertional Knowledge (ABox) about Individuals –n27_img118 : Neuron => the concrete instances/individuals of the concepts/classes that your sources export

10. CSE-291: Ontologies in Data & Process Integration Example TBox Atomic concepts = {P,F,W, M1,…} Base concepts = {P,F} Defined concepts = {W, M1, M2, …} Roles = {h1,h2} Concept Definition Axiom where A atomic concept, C, D complex concept expressions C, D complex concept expressions

11. CSE-291: Ontologies in Data & Process Integration Example TBox Base concepts = {Person, Female} Base concepts = {Person, Female} … occur on the RHS only Defined concepts = {P, F, W, …} Defined concepts = {P, F, W, …} … occur on the LHS (& maybe RHS) Base interpretation J: interpret base concepts only Base interpretation J: interpret base concepts only Extension I of J: on same domain as J and agrees (on base) with J Extension I of J: on same domain as J and agrees (on base) with J TBox T is definitorial if every base interpretation has exactly one extension that is a model of T TBox T is definitorial if every base interpretation has exactly one extension that is a model of T

12. CSE-291: Ontologies in Data & Process Integration Exercise: Starting with the base interpretation of I(Person) := “the class of persons” I(Person) := “the class of persons” I(Female) := “the class of females” I(Female) := “the class of females” … what is the meaning of the defined concepts? … what role play the roles in this process?

13. CSE-291: Ontologies in Data & Process Integration Example TBox atomic conceptatomic concept concept def. w/ intersectionconcept def. w/ intersection … plus negation… plus negation … existential restriction… existential restriction … value restriction… value restriction

14. CSE-291: Ontologies in Data & Process Integration Digression: “Sparrow” (Prolog) Syntax for DL Sparrow “Grammar” and “Parser” Example in Sparrow Syntax

15. CSE-291: Ontologies in Data & Process Integration Back to Reasoning with the Family... concept definition: MyConcept  DL-formulaconcept definition: MyConcept  DL-formula concept inclusion: MyConcept  DL-formulaconcept inclusion: MyConcept  DL-formula finite set of definitions is a terminology or TBox if for every atomic concept A there is at most one axiom whose lhs is Afinite set of definitions is a terminology or TBox if for every atomic concept A there is at most one axiom whose lhs is A

16. CSE-291: Ontologies in Data & Process Integration Definitorial Terminologies In a Tbox T we distinguish: primitive concepts (occurring only on rhs) and defined concepts (occurring on lhs)In a Tbox T we distinguish: primitive concepts (occurring only on rhs) and defined concepts (occurring on lhs) T is definitorial if every interpretation of primitive concepts yields exactly one model of T (and thus for the defined concepts)T is definitorial if every interpretation of primitive concepts yields exactly one model of T (and thus for the defined concepts)  meaning of defined concepts is fixed once the primitive concepts are interpreted ! A directly uses B in T if B appears in the rhs of the definition of AA directly uses B in T if B appears in the rhs of the definition of A A uses B is the transitive closure of ‘directly uses’A uses B is the transitive closure of ‘directly uses’ T is cyclic if A uses A for some A; else acyclicT is cyclic if A uses A for some A; else acyclic One can show: If T is acyclic then T is definitorial What about this one? What about this one?

17. CSE-291: Ontologies in Data & Process Integration Expansion of Terminologies For acyclic T we can “unfold” concept definitions until every defined concepts is specified in terms of primitive concepts onlyFor acyclic T we can “unfold” concept definitions until every defined concepts is specified in terms of primitive concepts only  the expansion of a TBox T Example:Example:

18. CSE-291: Ontologies in Data & Process Integration Acyclic Terminologies Source: F. Baader, W. Nutt. Basic Description Logics. In Description Logic Handbook, edited by F. Baader, et al, 2002

19. CSE-291: Ontologies in Data & Process Integration Reasoning in the Tableaux calculus TBox Expansion From this We want to show this In First-order (LeanTap) syntax

20. CSE-291: Ontologies in Data & Process Integration LeanTap Demo

21. CSE-291: Ontologies in Data & Process Integration Source: Description Logics Tutorial, Ian Horrocks and Ulrike Sattler, ECAI-2002, Lyon, France, July 23rd, 2002

22. CSE-291: Ontologies in Data & Process Integration Source: Description Logics Tutorial, Ian Horrocks and Ulrike Sattler, ECAI-2002, Lyon, France, July 23rd, 2002

23. CSE-291: Ontologies in Data & Process Integration Source: Description Logics Tutorial, Ian Horrocks and Ulrike Sattler, ECAI-2002, Lyon, France, July 23rd, 2002

24. CSE-291: Ontologies in Data & Process Integration Source: Description Logics Tutorial, Ian Horrocks and Ulrike Sattler, ECAI-2002, Lyon, France, July 23rd, 2002

25. CSE-291: Ontologies in Data & Process Integration Source: Description Logics Tutorial, Ian Horrocks and Ulrike Sattler, ECAI-2002, Lyon, France, July 23rd, 2002

26. CSE-291: Ontologies in Data & Process Integration Source: Description Logics Tutorial, Ian Horrocks and Ulrike Sattler, ECAI-2002, Lyon, France, July 23rd, 2002

27. CSE-291: Ontologies in Data & Process Integration Source: Description Logics Tutorial, Ian Horrocks and Ulrike Sattler, ECAI-2002, Lyon, France, July 23rd, 2002