1. Ontology Structuring Mechanisms and Ontological Modularity ongoing research and targeted applications John Bateman Till Mossakowski Oliver Kutz Joana Hois http://www.sfbtr8.uni-bremen.de http://www.fb10.uni-bremen.de/ontology BREMEN ONTOLOGY RESEARCH GROUP University of Bremen + DKFI, Bremen

2. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 2 Overview of our topics today ●General orientation and our position on ontologies ●The formal framework within which we are working ●Examples of ontological modularities and re-use ●Conclusions

3. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 3 Several Research Areas currently under Investigation ●Mobility support ●Spatially-embedded tasks ●Exploration, Route Planning ●Navigation ●Interaction with diverse user groups ●Disabilities ●Age

4. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 4 Problem foci ●Spatial assistance systems ●Route planning and navigation ●Real-world environments involving ‘common-sense’ entities ●Interfacing with geographic information ●Interfacing with language technology ●Interfacing with visual presentations (maps) ●Interfacing with robotic sensor data ●Embodied systems ●Human-Robot Interaction

5. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 5 Problem ●Many different kinds of knowledge are required to get people into the loop in a way that is empowering and enriching rather than restricting

6. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 6 Voronoi map From SFB/TR8 project: A1-[RoboMap] Voronoi calculation on a scanned floor plan “where are you?”

7. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 7 Sources of relevant knowledge Location-based services Geographic Information Systems Commonsense objects and activities Spatial awareness and understanding Natural language capabilities Robot perception User Knowledge User (dis)abilities

8. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 8 Problem restated ●Getting these diverse areas of expertise to talk to each other is a serious issue ●different communities ●different interests ●different representations ●The kinds of knowledge maintained by such systems are very different

9. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 9 Essential idea… ●Providing channels to ontologies provides access to detailed contextual ‘world-knowledge’ that does not then have to be worked out again… Application Ontology

10. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 10 Many perspectives on ‘reality’: many ontologies event time space-1 space-2 event Ontologically diverse

11. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 11 Example of communication problems: When is a road not a road? ●Community 1: ●transit system designers ●roads and highways as connections between destinations (cities, towns, etc.) ●Community 2: ●environment and wildlife department ●species have habitats ●habitats have divisions separating them

12. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 12 Ontologically mediated inter-operability city A city B Hwy 456 node transit system graph ontology environment species A region ontology

13. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 13 Ontologically mediated inter-operability city A city B Hwy 456 node transit system graph ontology environment region ontology species A

14. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 14 Methodological starting point ●There is no sense in which a simple ‘merging’ of the ontologies involved is a sensible strategy to follow

15. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 15 Solution we are pursuing ●High degree of interoperability between diverse knowledge-rich systems is to be achieved by ontological engineering, taking in: ●knowledge of the human world (commonsense) ●knowledge of the robot world (programmed, emergent) ●geo-knowledge (GML, other standards) ●spatial knowledge (spatial calculi) ●knowledge of language (linguistics)

16. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 16 Ontological diversity inter-ontology mappings description time landmarks choremes event types CASL route graphs CASL

17. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 17 Perspectives / Views rather than inheritance lake geographical region Alternate theories / ontologies obstacle recreational area source of pure water link in transport network

18. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 18 Inter-ontology mappings ●... can only work if there is sufficient content to get hold of! ●That is: not a relationship between ‘terms’ but a relationship between ‘theories’. ●For this, need deep ontologies, so-called ‘axiomatized ontologies’

19. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 19 Choosing between types of ontologies ●‘Light’ ontologies: semantic web? ●‘Heavy’ ontologies: ●Rich axiomatization ●Formal principles ●Well-defined design criteria

20. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 20 Our ontological starting point Leo Obrst

21. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 21 Theories... ●We all have theories... ●theories of the world ●theories of how buildings are ●theories of the best way to get from A to B ●theories of how to persuade your boss for a raise ●‘A-ontologies’ set such theories out in an explicit specification.

22. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 22 Prerequisites for success ●unless you can reason with the axioms: non-starter ●unless you can chunk your axioms: non-starter ●unless you can parameterize and re- use theories: non-starter ●unless you can state relations between the meanings of chunks: non-starter  logic  building theories  structured logic support  inter-theory mappings

23. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 23 Essential ingredients we are drawing on in Bremen ●Existing ontologies ●DOLCE (Masalo/Borgo/Guarino) (for cross-category binding and axiomatization) ●BFO (Barry Smith) (for sites, niches and places and for SNAP/SPAN) ●GUM (John Bateman) (for linguistic semantics and natural language processing) ●State of the art logical tools ●CASL + Hets Tool

24. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 24 Ontology construction ●Axioms are grouped into logically appropriate theories ●Theories may be extended via parameterization to achieve semantic re-use ●Theories may be created and related by views: theory morphisms Only with this re-use factor can the complexity of distinct axiomatized ontologies really be harnessed and used to scale-up.

25. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 25 Approaches to ‘simplifying’ the ontologist’s life... ●Making sure that each component of a library of theories only specifies the axioms which are relevant at that point (cf. John Sowa: “That is the whole point of Ockham's razor: eliminate any axioms that are not absolutely essential to the task at hand.”) ●Making sure that unnecessary detail is hidden in ‘upstream’ libraries: CASL ●Possibilities for ‘common subsets’: ●packages such as our spatial calculi ●packages such as DOLCE’s ‘constitution’, ‘participation’, ‘quality spaces’, BFO’s ‘sites’ ●language-based generic ontology (GUM)

26. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 26 This is essential: because in analysis there are a lot of pieces to put back together!!

27. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 27 Combining theories for semantic interpretation driving along the road to Bremen on the right is a church

28. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 28 Combining theories for semantic interpretation driving along the road to Bremen on the right is a church o > hphp oriented path route graph half-planes physical object occupying a region

29. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 29 OK, go towards the mountains along the main road until you reach a large wooden house. Be careful, the road gets a bit narrow where the old church sticks out. Turn right at the house and, then, at the third intersection, turn right leaving the city limits. Then turn downhill towards the river. At the river, take the ferry over to the café.

30. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 30 OK, go towards the mountains along the main road until you reach a large wooden house. Be careful, the road gets a bit narrow where the old church sticks out. Turn right at the house and, then, at the third intersection, turn right leaving the city limits. Then turn downhill towards the river. At the river, take the ferry over to the café. theory of landmarks: mountain theory of destinations: the house theory of structural landmarks / constraints on movement and decisions: (along) the main road Theories needed for interpretation theory of shapes of physical objects: narrow road, old church (sticking out) theories of orientation: towards theory of landmarks: the house theories of orientation: right theory of ordered sequences theories of orientation: right theories of regions (administrative): city theories of orientation: towards theories of topography: slopes theory of landmarks: the river theory of structural landmarks: intersections theory of structural landmarks: (over) the river theory of landmarks: river theory of destinations: the café

31. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 31 Theories... ●Each of these contributions to the meaning of what is being said is considered to draw on a range of more or less related theories of the world… ●axiomatised ontologies set such theories out in an explicit specification.

32. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 32 John Sowa (email/web discussion) IEEE Standard Upper Ontology Working Group

33. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 33 John Sowa (email/web discussion) IEEE Standard Upper Ontology Working Group

34. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 34 John Sowa (email/web discussion) IEEE Standard Upper Ontology Working Group What kinds of ‘modules’ are these? What is the nature of relationships that can hold between them? How do these relate to different communities’ theories of the world?

35. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 35 A general approach… In the next section of the talk we discuss how we are formalizing these notions of ontological modularity and inter-module relationships. ●Formal framework: CASL ●Generic framework for describing how ontologies and modules can be related: ‘alignments’ ●Some examples

36. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 36 CASL - Common Algebraic Specification Language Standardised first-order specification language; designed by CoFI “Common Framework Initiative for algebraic specification and development” since 1995 approved by IFIP WG 1.3 “Foundations of Systems Specifications” (1998), extensive documentation (LNCS 2900, 2960) various extensions and sublanguages, including higher- order dialects, modal logic, OWL-DL; supports structured specifications including imports, hiding, renaming, union, extensions, etc.

37. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 37 CASL language constructs

38. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 38 CASL example: basic Basic specification of “Services located at rooms”

39. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 39 CASL example: structured Named structured specification of a distance function

40. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 40 CASL example: view

41. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 41 GenMereology GenParthood Lüttich & Mossakowski (FOIS 2004) DOLCE in CASL GenParthood Primitives

42. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 42 spec MEREOLOGY = PRIMITIVES then %Ad7, Ad8, Ad9 and Ad10 are generated by % instantiation of GenMereology GENMEREOLOGY [sort T] then GENMEREOLOGY [sort S] then GENMEREOLOGY [sort PD] end GenMereology GenParthoodPrimitives Mereology Lüttich & Mossakowski (FOIS 2004) DOLCE in CASL

43. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 43 The Tool HeTS

44. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 44 Varieties of Modules ●logically self-sufficient/independent conservativity; ●part of a larger “integrated” ontology DDLs, E-connections, etc. ●coupling through interface alignments ●tradition, convenience, elegance, etc. general structuring techniques “Parts” of an ontology can be considered a “module” for a variety of reasons: Realised through various theory morphisms

45. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 45 Shapes of Alignments ●we represent various alignments as diagrams of certain “shapes” ●connected through “interfaces” ●we assume alignment mappings are given ●colimits are used for an overall integration ●composition of diagrams as composition of alignments ●definitional extensions do not add ‘substance’

46. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 46 Structuring mechanism Arrows in Diagrams ● black: imports; ● dashed black: automatically constructed imports ● blue: definitional or conservative extensions; dotted red: proof obligations; theorem links; interpretation into theory; green: = proven “red” obligation; Postulating links

47. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 47 V-alignment through interface ●cannot handle subclass alignments

48. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 48 W-alignment with bridge ontology ●Integration through bridge ontology Woman Person

49. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 49 M-alignment: bridges and extensions ●Integration through bridge along extensions Woman, Bank Person, Bank Person Person, Bank Woman, Person, Financial_Bank, River_Bank

50. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 50 Bibliographical Ontology in DL logic DL spec Biblio_DL = Class: Researcher SubclassOf: name some Thing ObjectProperty: hasArticle InverseOf: hasJournal Class: Article SubclassOf: author some Thing, title some Thing, hasJournal some Journal Class: Journal SubclassOf: name some Thing, hasArticle some Thing, impactFactor some Thing end

51. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 51 Bibliographical Database Biblio_RS logic RelationalScheme spec Biblio_RS = tables person(key: id,name); author_of(person,paper); paper(key: id,title,published_in); journal(key: id,name,impact_factor) links author_of.person -> person.id; author_of.paper -> paper.id; paper.published_in -> journal.id end

52. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 52 A Heterogeneous Mapping logic CASL view Biblio_RS_in_DL : Biblio_RS to { Biblio_DL with logic DL -> CASL then %def preds journal(j,n,f:Thing) Journal(j) /\ name(j,n) /\ impactFactor(j,f); paper(a,t,j:Thing) Article(a) /\ Journal(j) /\ hasArticle(j,a) /\ title(a,t); author_of(p,a:Thing) Researcher(p) /\ Article(a) /\ author(p,a); person(p,n:Thing) Researcher(p) /\ name(p,n) } = logic RelationalScheme -> CASL end

53. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 53 Structure of bibliography example Biblio_DLBiblio_RS Ext_Biblio_DL Heterogeneous mapping between ontologies

54. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 54

55. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 55 ●‘window’ in T 1 ‘window’ in T 2 map objects in T 1 to materials in T 2

56. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 56 E-connections many sorted: extended M-alignment

57. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 57 Summary ●Relations between modules can be characterized in general in terms of the shapes of these alignment diagrams ●Providing support for expressing these structured relationships adds considerably to the ontologist’s toolkit

58. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 58 One further exploratory example… ●relating linguistic spatial information and non-linguistic descriptions

59. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 Further M-Alignment Example: Linguistic and Spatial Ontology ●natural linguistic spatial interaction linguistic ontology spatial ontologies specific spatial calculi space-specific parts

60. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 M-Alignment Example Linguistic and Spatial Ontology orientations: (e.g. DCC-8) linguistic ProjectionRelations FrontProjection BackProjection RightProjection LeftProjection ● R(linguistic,spatial) : LeftProjection. placement [LeftProjection] ⇒ leftFront ∨ left ∨ leftBack front leftFrontrightFront right leftBack left leftBack back

61. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 M-Alignment Example Linguistic and Spatial Ontology orientations: (e.g. DCC-8) linguistic ProjectionRelations FrontProjection BackProjection RightProjection LeftProjection front leftFrontrightFront right leftBack left leftBack back ●R(linguistic,spatial) : LeftProjection. direction [LeftProjection] ⇒ leftFront

62. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 M-Alignment Example Linguistic and Spatial Ontology ●R(l,s): LeftProjection.placement[LeftProjection] ⇒ leftFront ∨ left ∨ leftBack ●R(l,s):LeftProjection. direction[LeftProjection] ⇒ leftFront

63. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 63 Relation between linguistic and non-linguistic characterisations… combines different alignments between the linguistic semantics and the spatial characterisation

64. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 64 Conclusions and ongoing and future directions ●Dealing with information flexibly requires ontological treatments that are contentful ●Axiomatised ontologies are a way of approaching this ●But structured ontological specifications with well-specified possibilities for relating between ontologies/modules are then essential ●Offers us a structured path towards interoperability

65. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 65 Appendix Biblio_RS

66. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 66 Modules based on Conservativity Model-theoretic implies proof-theoretic conservativity, but not conversely. model-theoretic conservativity: Every T 1 -model can be expanded to a T 2 -model. A theory morphism is proof theoretically conservative if

67. I1-[OntoSpace] Bateman/Mossakowski/Kutz/Hois 2008 67 Modules based on Conservativity