1. CSE-291: Ontologies in Data Integration Department of Computer Science & Engineering University of California, San Diego CSE-291: Ontologies in Data Integration Spring 2003 Bertram Ludäscher LUDAESCH@SDSC.EDU

2. CSE-291: Ontologies in Data Integration Outline Wrapping up last weekWrapping up last week What is a representation?What is a representation? [Thesauri, Topic Maps][Thesauri, Topic Maps] Predicate Logic PrimerPredicate Logic Primer Description logicsDescription logics [RDF & RDF Schema][RDF & RDF Schema] [F-logic][F-logic] Topic SelectionTopic Selection Special thanks: Alexander Maedche, Steffen Staab:Alexander Maedche, Steffen Staab: – ECAI’2002 Tutorial on Ontologies

3. CSE-291: Ontologies in Data Integration Ontologies … For What? Lack of a shared understanding leads to poor communicationLack of a shared understanding leads to poor communication => People, organizations and software systems must communicate between and among themselves Disparate modeling paradigms, languages and software tools limitDisparate modeling paradigms, languages and software tools limit => Interoperability => Knowledge sharing & reuse => Knowledge sharing & reuse [Uschold, Gruninger, 96]

4. CSE-291: Ontologies in Data Integration Origin and History (I) Ontology....Ontology.... a philosophical discipline, branch of philosophy that deals with the nature and the organisation of reality Science of Being (Aristotle, Metaphysics, IV, 1)Science of Being (Aristotle, Metaphysics, IV, 1) Tries to answer the questions:Tries to answer the questions: What is being? What are the features common to all beings?

5. CSE-291: Ontologies in Data Integration Origin and History (II) Humans require words (or at least symbols) to communicate efficiently. The mapping of words to things is only indirect possible. We do it by creating concepts that refer to things. The relation between symbols and things has been described in the form of the meaning triangle: “Jaguar“ Concept [Ogden, Richards, 1923 ]

6. CSE-291: Ontologies in Data Integration Origin and History (III) In recent years ontologies have become a hot topic of interest. Here, an ontology refers to an engineering artifact: It is constituted by a specific vocabulary used to describe a certain reality, plus a set of explicit assumptions regarding the intended meaning of the vocabulary. Thus, ontologies describe a formal partial specification of a specific domain: Shared understanding of a domain of interest Formal and machine executeable model of a domain of interest

7. CSE-291: Ontologies in Data Integration Human and machine communication (I)... Machine Agent 1 Things Human Agent 2 Ontology Description Machine Agent 2 exchange symbol, e.g. via nat. language ‘‘JAGUAR“ Internal models Concept Formal models exchange symbol, e.g. via protocols MA1 HA1 HA2 MA2 Symbol commit a specific domain, e.g. animals commit Ontology Formal Semantics Human Agent 1 Meaning Triangle [Maedche et al., 2002]

8. CSE-291: Ontologies in Data Integration Ontology & Natural Language It is important to emphasize that there is a m:n relationship between words and conceptsIt is important to emphasize that there is a m:n relationship between words and concepts This means practically:This means practically: –different words may refer to the same concept –a word may refer to several concepts Ontologies languages should provide means for making this difference explicit.Ontologies languages should provide means for making this difference explicit.

9. CSE-291: Ontologies in Data Integration Example Ontology: C = {c 1,c 2, c 3 }, R = {r 1 }, H C (c 2,c 1 ), r 1 (c 2,c 3 ), c3 c1... c2.. r 1 (c 2,c 3 ), H C (c 2,c 1 ) person employee organisation works at Lexicon: L C = {person, employee, organisation}, L R = {works at} F(person) = c 1, F(employee) = c 2, F(organisation) = c 3, G(works at) = r 1

10. CSE-291: Ontologies in Data Integration Ontology vs. Knowledge Bases There is no clear separation between ontology and knowledge baseThere is no clear separation between ontology and knowledge base Example:Example: Often it remains a modeling decision if something is modeled as concept or as instance. In many applications meta-modeling means are required.Often it remains a modeling decision if something is modeled as concept or as instance. In many applications meta-modeling means are required.

11. CSE-291: Ontologies in Data Integration Types of Ontologies (I) [Guarino, 98] describe very general concepts like space, time, event, which are independent of a particular problem or domain. It seems reasonable to have unified top-level ontologies for large communities of users. describe the vocabulary related to a generic domain by specializing the concepts introduced in the top-level ontology. describe the vocabulary related to a generic task or activity by specializing the top-level ontologies. These are the most specific ontologies. Concepts in application ontologies often correspond to roles played by domain entities while performing a certain activity.

12. CSE-291: Ontologies in Data Integration Ontologies and their Relatives (I) There are many relatives around:There are many relatives around: –Controlled vocabularies, thesauri and classification systems available in the WWW, see http://www.lub.lu.se/metadata/subject-help.htmlhttp://www.lub.lu.se/metadata/subject-help.html Classification Systems (e.g. UNSPSC, Library Science, etc.) Thesauri (e.g. Art & Architecture, Agrovoc, etc.) –Lexical Semantic Nets WordNet, see http://www.cogsci.princeton.edu/~wn/http://www.cogsci.princeton.edu/~wn/ EuroWordNet, see http://www.hum.uva.nl/~ewn/http://www.hum.uva.nl/~ewn/ –Topic Maps, http://www.topicmaps.org (e.g. used within knowledge management applications) In general it is difficult to find the border line!In general it is difficult to find the border line!

13. CSE-291: Ontologies in Data Integration Ontologies and their Relatives (II) Catalog / ID Terms/ Glossary Thesauri Informal Is-a Formal Is-a Formal Instance Frames Value Restric- tions General logical constraints Axioms Disjoint Inverse Relations,...

14. CSE-291: Ontologies in Data Integration Some Ontologies (and Friends) in Action (coming soon to a project near you)

15. CSE-291: Ontologies in Data Integration GEON Architecture Rocky Mountains Midatlantic Region

16. CSE-291: Ontologies in Data Integration SMART (Meta)data I: Logical Data Views Source: NADAM Team (Boyan Brodaric et al.) Adoption of a standard (meta)data model => wrap data sets into unified virtual views

17. CSE-291: Ontologies in Data Integration SMART Metadata II: Multihierarchical Rock Classification for “Thematic Queries” (GSC) –– or: Taxonomies are not only for biologists... Composition Genesis Fabric Texture “smart discovery & querying” via multiple, independent concept hierarchies (controlled vocabularies) data at different description levels can be found and processed

18. CSE-291: Ontologies in Data Integration Biomedical Informatics Research Network http://nbirn.net Biomedical Informatics Research Network http://nbirn.net SMART Metadata III: Source Contextualization & Ontology Refinement Focused GEON ontology working meeting last week... (GEON, SCEC/KR, GSC, ESRI)

19. CSE-291: Ontologies in Data Integration EcoCyc

20. Gene Ontology http://www.geneontology.org “a dynamic controlled vocabulary that can be applied to all eukaryotes” Built by the community for the community. Three organising principles: Molecular function, Biological process, Cellular component Isa and Part of taxonomy – but not good! ~10,000 concepts Lightweight ontology, Poor semantic rigour. Ok when small and used for annotation. Obstacle when large, evolving and used for mining.

21. CSE-291: Ontologies in Data Integration Controlled vocabulary AGROVOC: Agricultural VocabularyAGROVOC: Agricultural Vocabulary

22. CSE-291: Ontologies in Data Integration Thesauri AAT: Art & Architecture ThesaurusAAT: Art & Architecture Thesaurus

23. CSE-291: Ontologies in Data Integration Ontologies - Some Examples General purpose ontologies:General purpose ontologies: –WordNet / EuroWordNet, http://www.cogsci.princeton.edu/~wn –The Upper Cyc Ontology, http://www.cyc.com/cyc-2-1/index.html –IEEE Standard Upper Ontology, http://suo.ieee.org/ Domain and application-specific ontologies:Domain and application-specific ontologies: –RDF Site Summary RSS, http://groups.yahoo.com/group/rss-dev/files/schema.rdf –UMLS, http://www.nlm.nih.gov/research/umls/ –KA2 / Science Ontology, http://ontobroker.semanticweb.org/ontos/ka2.html –RETSINA Calendering Agent, http://ilrt.org/discovery/2001/06/schemas/ical- full/hybrid.rdf –AIFB Web Page Ontology, http://ontobroker.semanticweb.org/ontos/aifb.html –Web-KB Ontology, http://www-2.cs.cmu.edu/afs/cs.cmu.edu/project/theo- 11/www/wwkb/ –Dublin Core, http://dublincore.org/ Meta-OntologiesMeta-Ontologies –Semantic Translation, http://www.ecimf.org/contrib/onto/ST/index.html –RDFT, http://www.cs.vu.nl/~borys/RDFT/0.27/RDFT.rdfs –Evolution Ontology, http://kaon.semanticweb.org/examples/Evolution.rdfs Ontologies in a wider senseOntologies in a wider sense –Agrovoc, http://www.fao.org/agrovoc/ –Art and Architecture, http://www.getty.edu/research/tools/vocabulary/aat/ –UNSPSC, http://eccma.org/unspsc/ –DTD standardizations, e.g. HR-XML, http://www.hr-xml.org/

24. CSE-291: Ontologies in Data Integration Ontology Representation What is a „representation“? “Jaguar“ Concept

25. CSE-291: Ontologies in Data Integration Ontology Representation Languages Machines need communication with formal content to restrict meaningMachines need communication with formal content to restrict meaning What makes a language „formal“?What makes a language „formal“? –model theory (1st order predicate logic) –proof theory (Gentzen calculus) But also: –conventions (e.g. Java)

26. CSE-291: Ontologies in Data Integration What makes a language suitable? For machine communication  model theory   proof theory  tracktability  strong conventions of use  human readable names  For human communication  strong conventions of use   human readable names   „natural“ primitives 

27. CSE-291: Ontologies in Data Integration Representation Paradigms (incomplete) Ontologies TopicMaps extended ER-Modell Thesauri Predicate Logics / Description Logics Semantic Nets Taxonomies

28. CSE-291: Ontologies in Data Integration Thesaurus

29. Thesauri Example: Fruit OrangeApfelsine (german) Vegetable similarTo synonymWith NarrowerTerm - Well known in library science - cf. terminologies / classifications (Dewey) - Graph with labels edges (similar, nt, bt, synonym) - Fixed set of edge labels (aka relations) - no instances

30. CSE-291: Ontologies in Data Integration

31. Topic Maps are... Standardized: ISO/IEC 13250:2000Standardized: ISO/IEC 13250:2000 –ISO standard published Jan. 2000 –enabling standard to describe knowledge structures, electronic indices, classification schemes,... Web enabled:Web enabled: –XML Topic Maps (XTM) are ready to use Designed to:Designed to: –manage the info glut –build valuable information networks above any kind of resources / data objects –enable the structuring of unstructured information

32. CSE-291: Ontologies in Data Integration Back-of-the-Book Index “British Virgin Islands” Gorda Sound see North Sound Little Dix Bay.................... 89 North Sound....................... 90 Road Harbour see also Road Town... 73 Road Town...................... 69,71 Spanish Town................... 81,82 Tortola........................... 67 Virgin Gorda...................... 77

33. CSE-291: Ontologies in Data Integration Back-of-the-Book Index “British Virgin Islands” Gorda Sound see North Sound Little Dix Bay.................... 89 North Sound....................... 90 Road Harbour see also Road Town... 73 Road Town...................... 69,71 Spanish Town................... 81,82 Tortola........................... 67 Virgin Gorda...................... 77 Topics

34. CSE-291: Ontologies in Data Integration Back-of-the-Book Index “British Virgin Islands” Gorda Sound see North Sound Little Dix Bay.................... 89 North Sound....................... 90 Road Harbour see also Road Town... 73 Road Town...................... 69,71 Spanish Town................... 81,82 Tortola........................... 67 Virgin Gorda...................... 77 Occurrences

35. CSE-291: Ontologies in Data Integration Back-of-the-Book Index “British Virgin Islands” Gorda Sound see North Sound Little Dix Bay.................... 89 North Sound....................... 90 Road Harbour see also Road Town... 73 Road Town...................... 69,71 Spanish Town................... 81,82 Tortola........................... 67 Virgin Gorda...................... 77 Different topic classes

36. CSE-291: Ontologies in Data Integration Back-of-the-Book Index “British Virgin Islands” Gorda Sound see North Sound Little Dix Bay.................... 89 North Sound....................... 90 Road Harbour see also Road Town... 73 Road Town...................... 69,71 Spanish Town................... 81,82 Tortola........................... 67 Virgin Gorda...................... 77 Different occurrences classes

37. CSE-291: Ontologies in Data Integration Back-of-the-Book Index “British Virgin Islands” Gorda Sound see North Sound Little Dix Bay.................... 89 North Sound....................... 90 Road Harbour see also Road Town... 73 Road Town...................... 69,71 Spanish Town................... 81,82 Tortola........................... 67 Virgin Gorda...................... 77 Multiple topic names

38. CSE-291: Ontologies in Data Integration Back-of-the-Book Index “British Virgin Islands” Gorda Sound see North Sound Little Dix Bay.................... 89 North Sound....................... 90 Road Harbour see also Road Town... 73 Road Town...................... 69,71 Spanish Town................... 81,82 Tortola........................... 67 Virgin Gorda...................... 77 Association

39. CSE-291: Ontologies in Data Integration Topics – Computerized Subjects SurfBVIBVI WelcomeCaribNet Resources Topics Little Dix BayTortola Road Town Virgin Gorda Subject North Sound Subject Road Harbour Subject Spanish Town Subject BayIslandTown Topic classes

40. CSE-291: Ontologies in Data Integration SurfBVIBVI WelcomeCaribNet Occurrences Resources Topics Little Dix BayTortola Road Town Virgin Gorda North Sound Road Harbour Spanish Town Occurrences Occurrence classes ImageMapArticle Map Article Image

41. CSE-291: Ontologies in Data Integration Occurrences Resources Topics Little Dix BayTortola Road Town Virgin Gorda North Sound Road Harbour Spanish Town Occurrences SurfBVIBVI WelcomeCaribNet Occurrence classes ImageMapArticle

42. CSE-291: Ontologies in Data Integration Associations Topics Little Dix BayTortola Road Town Virgin Gorda North Sound Road Harbour Spanish Town Associations Association classes VicinityPart-Whole Geo Containment VicinityPart-Whole

43. CSE-291: Ontologies in Data Integration Associations Topics Little Dix BayTortola Road Town Virgin Gorda North Sound Road Harbour Spanish Town Associations Association classes Geo ContainmentVicinityPart-Whole

44. CSE-291: Ontologies in Data Integration Class Hierarchies Topics Little Dix BayTortola Road Town Virgin Gorda North Sound Road Harbour Spanish Town BayIslandTown Topic classes

45. CSE-291: Ontologies in Data Integration Class Hierarchies Topics Little Dix BayTortola Road Town Virgin Gorda North Sound Road Harbour Spanish Town BayIslandTown Super-classes Bay for swimming Anchor bay LandCapitalSuburb Sub-classes

46. CSE-291: Ontologies in Data Integration Scopes Brit. Virgin Islands Brit. Jungferninseln Caribbean Karibik Great Britain Großbritannien Image Bild Map Karte Article Artikel SurfBVIBVI WelcomeCaribNet Geo Containment Geo Umschließung Political Dependency Politische Abhängigkeit

47. CSE-291: Ontologies in Data Integration Scopes Brit. Virgin Islands Brit. Jungferninseln Caribbean Karibik Great Britain Großbritannien Image Bild Map Karte Article Artikel SurfBVIBVI WelcomeCaribNet Geo Containment Geo Umschließung Political Dependency Politische Abhängigkeit Scopes

48. CSE-291: Ontologies in Data Integration Scopes Brit. Virgin Islands Brit. Jungferninseln Caribbean Karibik Geo Containment Geo Umschließung Great Britain Großbritannien Political Dependency Politische Abhängigkeit Image Bild Map Karte Article Artikel SurfBVIBVI WelcomeCaribNet Names: English Deutsch Scopes

49. CSE-291: Ontologies in Data Integration Scopes Brit. Virgin Islands Brit. Jungferninseln Caribbean Karibik Geo Containment Geo Umschließung Great Britain Großbritannien Political Dependency Politische Abhängigkeit Image Bild Map Karte Article Artikel SurfBVIBVI WelcomeCaribNet Names: English Deutsch Scopes Occurrences: Public Confidential

50. CSE-291: Ontologies in Data Integration Scopes Brit. Virgin Islands Brit. Jungferninseln Caribbean Karibik Geo Containment Geo Umschließung Great Britain Großbritannien Political Dependency Politische Abhängigkeit Image Bild Map Karte Article Artikel SurfBVIBVI WelcomeCaribNet Names: English Deutsch Scopes Occurrences: Public Confidential Associations: Geography Politics

51. CSE-291: Ontologies in Data Integration Scope Examples: English, Public, Politics Brit. Virgin IslandsCaribbean Geo Containment Great Britain Political Dependency Image Map Article SurfBVIBVI WelcomeCaribNet Names: English Deutsch Scopes Occurrences: Public Confidential Associations: Geography Politics

52. CSE-291: Ontologies in Data Integration In-/Semi-formal approaches: Topic Maps, Thesauri Advantages Capture a lot of modeling experiencesCapture a lot of modeling experiences IntuitiveIntuitive Interesting primitives that are not available in other approaches (TM)Interesting primitives that are not available in other approaches (TM)Disadvantages No characterization independent from particular implementationNo characterization independent from particular implementation May be misinterpreted (TM) / few primitives (Thesauri)May be misinterpreted (TM) / few primitives (Thesauri)

53. CSE-291: Ontologies in Data Integration Common errors about ontology representation languages AI people‘s errors „it is good if it is formal“„it is good if it is formal“ „it is good if someone with a logic background may easily use it“„it is good if someone with a logic background may easily use it“ „it is good if the language allows everything“„it is good if the language allows everything“ Engineer‘s errors „it works in my application, thus it is good“„it works in my application, thus it is good“ „who needs formality anyway?“„who needs formality anyway?“ „it did not work when I looked at it 10 years ago“„it did not work when I looked at it 10 years ago“

54. CSE-291: Ontologies in Data Integration Review/Introduction: (Classical) First-order [Predicate] Logic: Short: FO or PL1

55. CSE-291: Ontologies in Data Integration But first: Propositional Logic: Syntax propositions (no internal structure) can be assigned a truth-value:propositions (no internal structure) can be assigned a truth-value: –either true or false (classical 2-valued logic: tertium non datur) Logical symbols:Logical symbols: –conjunction: , disjunction: , negation: , –implication: , equivalence: , parentheses:   Non-logical symbols:Non-logical symbols: –propositional variables p, q, r,... –signature: set of propositional variables  = {p, q, r,...} Formation rules for well-formed formulas (wff)Formation rules for well-formed formulas (wff) –an atomic formula (propositional variable) is a formula –if F, G are formulas, so are: F  G, F  G,  F, F  G, F  G,  F  propositional logic (or "propositional calculus") A system of symbolic logic using symbols to stand for whole propositions and logical connectives. Propositional logic only considers whether a proposition is true or false. In contrast to predicate logic, it does not consider the internal structure of propositions. http://wombat.doc.ic.ac.uk/foldoc/foldoc.cgi?propositional+logic logicsymbolic logicpropositionslogical connectivespredicate logic

56. CSE-291: Ontologies in Data Integration Propositional Logic: Semantics An interpretation I over a signature  is a mappingAn interpretation I over a signature  is a mapping –I:   {true, false}, associating a truth value to every propositional variable Truth tables describe how to extend I from to composite formulas (Boolean Algebra):Truth tables describe how to extend I from to composite formulas (Boolean Algebra): –F  G, F  G,  F, F  G, F  G

57. CSE-291: Ontologies in Data Integration Boolean Algebra, Truth Tables http://wombat.doc.ic.ac.uk/foldoc/foldoc.cgi?two-valued+logic

58. CSE-291: Ontologies in Data Integration Syntax of First-Order Logic (FO) Logical symbols:Logical symbols: – , , , , ,  ,  (“for all”),  (“exists”),... Non-logical symbols: A FO signature  consists ofNon-logical symbols: A FO signature  consists of –constant symbols: a,b,c,... –function symbols: f, g,... –predicate (relation) symbols: p,q,r,.... function and predicate symbols have an associated arity; –we can write, e.g., p/3, f/2 to denote the ternary predicate p and the function f with two arguments First-order variables: x, y,...First-order variables: x, y,... Formation rules for terms:Formation rules for terms: –constants and variables are terms –if t_1,...t_k are terms and f is a k-ary function symbols then f(t_1,...,t_k) is a term

59. CSE-291: Ontologies in Data Integration Syntax of First-Order Logic (FO) Formation rules for formulas:Formation rules for formulas: –if t_1,...t_k are terms and p/k is a predicate symbol (of arity k) then p(t_1,...,p_k) is an atomic formula (short: atom) all variable occurrences in p(t_1,..., t_k) are free – if F,G are formulas and x is a variable, then the following are formulas: – F  G, F  G,  F, F  G, F  G,  F , –  x: F (“for all x: F(x,...) is true”) –  x: F (“there exists x such that F(x,...) is true”) –the occurrences of a variable x within the scope of a quantifier are called bound occurrences.

60. CSE-291: Ontologies in Data Integration Examples  x malePerson(x)  person(x). malePerson(bill).child(marriage(bill,hillary),chelsea). Variable: x Constants (0-ary function symbols): bill/0, hillary/0, chelsea/0 Function symbols: marriage/2 Predicate symbols: malePerson/1, person/1, child/2

61. CSE-291: Ontologies in Data Integration Semantics of Predicate Logic Let D be a non-empty domain (a.k.a. domain of discourse, universe). A structure is a pair I = (D,I), with an interpretation I that maps...Let D be a non-empty domain (a.k.a. domain of discourse, universe). A structure is a pair I = (D,I), with an interpretation I that maps... –each constant c to an element I(c)  D –each predicate symbol p/k to a k-ary relation I(p)  D k, –each function symbol f/k to a k-ary function I(f): D k  D Given a structure I, and a set of variables X, a valuation is a mapping val: X  D, used to evaluate terms and formulas over a given FO signature Given a structure I, and a set of variables X, a valuation is a mapping val: X  D, used to evaluate terms and formulas over a given FO signature  –with this: term evaluation val(t) yields a domain element, and formula evaluation val(F) yields a truth value

62. CSE-291: Ontologies in Data Integration Example Formula F =  x malePerson(x)  person(x). Domain D = {b, h, c, d, e} Let’s pick an interpretation I: I(bill) = b, I(hillary) = h, I(chelsea) = c I(person) = {b, h, c} I(malePerson) = {b} Under this I, the formula F evaluates to true. If we choose I’ like I but I’(malePerson) = {b,d}, then F evaluates to falseIf we choose I’ like I but I’(malePerson) = {b,d}, then F evaluates to false Thus, I is a model of F, while I’ is not:Thus, I is a model of F, while I’ is not: –I |= F I’ |=/= F

63. CSE-291: Ontologies in Data Integration FO Semantics (cont’d) F entails G (G is a logical consequence of F) if every model of F is also a model of G: F |= GF entails G (G is a logical consequence of F) if every model of F is also a model of G: F |= G F is consistent or satisfiable if it has at least one modelF is consistent or satisfiable if it has at least one model F is valid or a tautology if every interpretation of F is a modelF is valid or a tautology if every interpretation of F is a model Proof Theory: Let F,G,... be FO sentences (no free variables). Then the following are equivalent: 1.F_1,..., F_k |= G 2.F_1 ...  F_k  G is valid 3.F_1 ...  F_k   G is unsatisfiable (inconsistent)

64. CSE-291: Ontologies in Data Integration Proof Theory A calculus is formal proof system to establishA calculus is formal proof system to establish –F_1,..., F_k |= G via formal (syntactic) derivationsvia formal (syntactic) derivations –F_1,..., F_k |–... |– G, where the “|–” denotes allowed proof steps Examples:Examples: –Hilbert Calculus, Gentzen Calculus, Tableaux Calculus, Natural Deduction, Resolution,... First-order logic is “semi-decidable”:First-order logic is “semi-decidable”: –the set of valid sentences is recursively enumerable, but not recursive (decidable) Some inference engines:Some inference engines: –http://www.semanticweb.org/inference.html

65. CSE-291: Ontologies in Data Integration Description Logics Decidable Fragments of FO (aka terminological logics, member of concept languages)

66. CSE-291: Ontologies in Data Integration Formalism for Ontologies: 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)

67. CSE-291: Ontologies in Data Integration Description Logic Statements as Rules Another syntax: first-order logic in rule form (implicit quantifiers):Another syntax: first-order logic in rule form (implicit quantifiers): happyFather(X)  man(X), child(X,C1), child(X,C2), blue(C1), green(C2), not ( child(X,C3), poorunhappyChild(C3) ). poorunhappyChild(C)  not rich(C), not happy(C). Note:Note: –the direction “  ” is implicit here (*sigh*) –see, e.g., Clark’s completion in Logic Programming

68. CSE-291: Ontologies in Data Integration Description Logics Terminological Knowledge (TBox)Terminological Knowledge (TBox) –Concept Definition (naming of concepts): –Axiom (constraining of concepts): => a mediators “glue knowledge source” Assertional Knowledge (ABox)Assertional Knowledge (ABox) –the marked neuron in image 27 => the concrete instances/individuals of the concepts/classes that your sources export

69. CSE-291: Ontologies in Data Integration Querying vs. Reasoning Querying:Querying: –given a DB instance I (= logic interpretation), evaluate a query expression (e.g. SQL, FO formula, Prolog program,...) –boolean query: check if I |=  (i.e., if I is a model of  ) –(ternary) query: { (X, Y, Z) | I |=  (X,Y,Z) } => check happyFathers in a given database Reasoning:Reasoning: –check if I |=  implies I |=  for all databases I, –i.e., if  =>  –undecidable for FO, F-logic, etc. –Descriptions Logics are decidable fragments  concept subsumption, concept hierarchy, classification  semantic tableaux, resolution, specialized algorithms

70. CSE-291: Ontologies in Data Integration Formalizing Glue Knowledge: 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

71. CSE-291: Ontologies in Data 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...