1. GeoInfo 2005 GIScience and Relationships Werner Kuhn Muenster Semantic Interoperability Lab (MUSIL)

2. GeoInfo 2005 Relationships Who arrived here by bus?  How do you know?  What is a bus?  WordNet: a bus is a „vehicle carrying many passengers; used for public transport” type of public transport a public transport is a „conveyance for passengers or mail or freight” type of conveyance a conveyance is „something that serves as a means of transportation” type of instrumentation etc....  So, what makes a bus a bus? The hierarchy of public transport – conveyance – instrumentation?

3. GeoInfo 2005 Relationships Context  Such questions arise in information retrieval „show me all bus connections to Campos do Jordao“ ... and in information integration „show me a map of public transportation in Brasil“  They are, of course, semantic questions.

4. GeoInfo 2005 Relationships

5. GeoInfo 2005 Relationships My thesis today 1.Relationships are the core of semantics 2.GIScience (and other information sciences) lack an understanding of basic relationships 3.Semantic tools limit what we can say about relationships 4.A better understanding will produce better information science and better tools

6. GeoInfo 2005 Relationships Overview 1.A brief History of Relationships in GIScience 2.Two Case Studies: Boathouse, Ferry 3.Toward Foundational Relationships 4.Formalization and Implementation 5.Conclusions

7. GeoInfo 2005 Relationships Brief History of Relationships in GIScience A relationship (or relation) is an association between two or more individuals or universals

9. 1888PeanoSet membership 1950MoranSpatial autocorrelation 1965ZadehFuzzy set membership 1975FreemanSpatial relations 1977TverskySimilarity 1977GibsonAffordances 1983AllenTemporal intervals 1986HerskovitsSpatial prepositions 1987SimonsMereological relations 1990KuhnGeometric relations 1991EgenhoferPoint-set topological relations 1991BarreraTemporal relations 1992FrankQualitative distances and directions 1992FreksaQualitative directions 1992RandellRegion-connection relations 2004SmithFoundational relations 2005BittnerSpatial relations between classes

10. Relations between what ? individualsettype individual temporal spatial mereological affordance conceptual lexical membershipinstance-of set inclusionmodel type is-a similarity statistics others ???

11. GeoInfo 2005 Relationships Are Types just Sets of Individuals?  If true, all relations on types can be defined in terms of relations on individuals  True for is-a relation A is-a B, iff for all a:A a:B cats are animals, iff every cat is an animal  Not true for similarity! ?A is similar to B, iff every a:A is similar to every b:B ?cats are similar to dogs, iff every cat is similar to every dog similarity relations are not defined in terms of individuals

12. GeoInfo 2005 Relationships => Types are not Sets  The notion of class in ontology unfortunately blurrs this distinction  The notion of type in computing is more restricted than the one used here a value or object can (usually) only have one type  An alternative term for type is universal

13. GeoInfo 2005 Relationships Case Study 1  What is the relation between a boat and a house in a „houseboat“?  What is it in a „boathouse“?  What kind of relations are these?

14. Structure Boathouse House Artifact is a Houseboat Boat is a Conveyance is a A concept DAG (simplified from WordNet) storing Waterbody at edge of Housing supporting is a People housing on conveying

15. GeoInfo 2005 Relationships What kind of relations ? 1.between types 2.not only is-a 3.no multiple is-a 4.some part-of (omitted, implicit in „structure“) 5.spatial (defining meaning of types!) 6.also: agent, causation,... 7.note: not just binary relations

16. GeoInfo 2005 Relationships Conclusion from Case Study 1  A limitation to is-a relations strips out essential semantics cf. glosses in WordNet  Today‘s semantic web imposes this limitation subsumption reasoning only  Needed: a way to model richer relations without resorting to multiple is-a (OntoClean) retaining decidability and reasoning efficiency

17. GeoInfo 2005 Relationships Case Study 2 How do road elements and a ferry lines relate to a transportation network ? Transportation Link Road ElementFerry Line

18. Way Road Artifact is a A concept DAG (simplified and extended from WordNet) Medium on Ferry Line is a FerryCar moving-on Conveyance is a supporting WaterLand is a

19. GeoInfo 2005 Relationships Conclusion from Case Study 2  Supports all conclusions from case study 1 our ontologies are „relationship-poor“  Significant overlap of types and relations between the two case studies  But: this is getting too complex ! need to apply Ockham‘s razor can we classify the relations ?

21. GeoInfo 2005 Relationships Toward Foundational Relations for GIScience  The list from the case studies on, supporting, moving-on, conveying, housing, storing, at-edge-of  All additional relations between types in the two case studies are spatial !

22. GeoInfo 2005 Relationships Structure Boathouse House Artifact is a Houseboat Boat is a Conveyance is a A concept DAG (simplified from WordNet) storing Waterbody at edge of Housing supporting is a People housing on conveying

23. GeoInfo 2005 Relationships Way Road Artifact is a A concept DAG (simplified and extended from WordNet) Medium on Ferry Line is a FerryCar moving-on Conveyance is a supporting WaterLand is a

24. GeoInfo 2005 Relationships A proposal for foundational relations 1.Containment: housing, storing 2.Support: on 3.Path: moving-on 4.Contact: at-edge-of 5....

25. GeoInfo 2005 Relationships What are these relations ?  All are image schematic based on sensory-motor patterns of experience proposed as basic cognitive structures [Talmy, Langacker, Lakoff, Johnson,...] invariant in semantic mappings combinable!

26. GeoInfo 2005 Relationships Containment Schema relates two types: container, item isIn? operations: enter, isIn, exit

27. GeoInfo 2005 Relationships Support Schema relates two types: surface, item isOn? operations: putOn, isOn, takeOff

28. GeoInfo 2005 Relationships Path Schema relates three types: locations, path, item operation: move

29. Combining Support and Path

30. GeoInfo 2005 Relationships Formalizing Relationships  Between individuals: predicates before (Tuesday, Wednesday) contains (Brasil, Campos do Jordao)  Between sets: set theory (predicates) (all GeoInfo2005 slides)  (this slide set)  Between types: ??? a bus is a conveyance for passengers a boathouse is a house for boats

31. GeoInfo 2005 Relationships Proposed Formalization  types modeled as theories [Goguen] not as predicates with operations and (equational) axioms a boathouse theory with operations to store/retrieve boats  theories are parametrized a house theory has a parameter for what is stored  relations between types are theory morphisms unification of parameters with other types the boathouse type unifies the „stored“ parameter in the house theory with the boat type

32. GeoInfo 2005 Relationships Boathouse Example (simplified) class HOUSE house entity class BOAT boat class (HOUSE boathouse boat, BOAT boat) => BOATHOUSE boathouse boat  HOUSE gets enter/exit operations from CONTAINMENT  BOAT gets move operation from PATH, on water from SUPPORT

33. GeoInfo 2005 Relationships Implementation  in Haskell (Hugs) using type classes tested with arbitrary data types and instances as models  set of equational theories for (case of boathouse) 9 schemas: containment, support, link, path, contact, collection, cover, part-whole, location 28 types: conveyance, vehicle, boat, house, boathouse, houseboat,...

34. GeoInfo 2005 Relationships Results  A formal account of essential aspects of geospatial semantics second order (parametrized) equational theories and morphisms  Tested with boathouse and ferry use case  Kernel of a semantic reference system referencing by instantiation instance BOATHOUSE MyBoathouse where... projection by superclassing class SUPERCLASS a => SUBCLASS a transformation by theory morphisms instance BOATHOUSE YourBoathouse where...

35. GeoInfo 2005 Relationships Related to (and inspired by)  Algebraic semiotics [Goguen]  Blendings [Turner and Fauconnier]  Frame semantics [Filmore]  Attempts at extracting relations from WordNet glosses [several authors]

36. GeoInfo 2005 Relationships Future work  Develop set of foundational relations for geospatial semantics validate with other case studies  Apply to core ontological reasoning tasks data discovery service discovery service composition schema mapping  Translation to OWL ontologies in DOLCE

37. GeoInfo 2005 Relationships Conclusions 1.GIScience has a long and successful history of modeling interesting relations 2.We have left relations between types to non-spatial ontologists 3.There is something special about spatial in such relations: image schematic basis 4.Capture this by modeling types as theories in type classes of functional languages.

38. GeoInfo 2005 Relationships For more information...  MUSIL web site (Muenster Semantic Interoperability Lab): http://musil.uni-muenster.de  email to kuhn@uni-muenster.de