Interoperability among Geospatial Ontologies

1. Interoperability amongGeospatial Ontologies Jerry R. Hobbs Information Sciences Institute University of Southern California Marina del Rey, California

2. My Interests How do we use world knowledge in understanding natural language? What world knowledge do we have and how is it represented? What geospatial knowledge do we have and how is it represented? Focus less on large compendia of geospatial facts, More on identifying those concepts that need to be explicated in a core theory of geospatial and other spatial representation and reasoning, Especially, concepts important in language.

3. Some Natural Language Queries Topology of Space: Is Albania a part of Europe? Does Belize touch Honduras? Dimensionality: How long is Chile? Measures: How large is North Korea? Orientation and Shape: What direction is Las Vegas from Los Angeles? Latitude and Longitude: How far is Los Angeles from Washington, as the crow flies? Political Divisions: What are the counties of Virginia? For complex queries, answer may be composed from several resources.

4. The QUARK System A system built at SRI in the AQUAINT question- answering program of ARDA. Work done with Richard Waldinger, Doug Appelt, Jennifer Dungan, John Fry, David Israel, Peter Jarvis, David Martin, Susanne Riehemann, Mark Stickel, Mabry Tyson Answered questions that required accessing multiple resources; focus on geospatial domain. Key ideas: 1. Logical analysis/decomposition of questions into component questions, using a reasoning engine 2. Bottoming out in variety of web resources and information extraction engine 3. Use of analysis of questions to determine, formulate, and present answers.

5. Composition of Informationfrom Multiple Sources Show me the region 100 km north of the capital of Afghanistan. Question Decomposition via Logical Rules What is the capital of Afghanistan? What is the lat/long 100 km north? Show that lat/long What is the lat/long of Kabul? Terravision CIA Fact Book Alexandrian Digital Library Gazetteer Geographical Formula Resources Attached to Reasoning Process

6. System Architecture Query parsing Proof with Answer GEMINI Logical Form SNARK decomposition and interpretation Other Resources Web Resources

7. Inter-Operability Query What is this language and ontology? parsing Proof with Answer GEMINI Logical Form SNARK decomposition and interpretation Other Resources Web Resources

8. Inter-Operability via multiple translations: OR Resource-1 via an “inter-theory”: Resource-6 Resource-2 Resource-1 Resource-5 Resource-3 Resource-6 Resource-2 Resource-4 Inter-theory Resource-5 Resource-3 Resource-4 Also a good excuse to develop a core theory.

9. Outline Time Ontology (OWL-Time) Event Ontology “DAML-Space”/“OWL-Space” Topics and Requirements A Sketch of Topology Granularity Half Orders of Magnitude

10. Aims of OWL-Time Ontology of time for the Semantic Web for describing temporal content of web pages temporal properties of web pages temporal properties of web services Developed in collaboration with James Allen, Pat Hayes, George Ferguson, James Pustejovsky, Adam Pease, and other researchers Maps easily into other temporal theories/ontologies (e.g., Cyc, SUMO, PSL, ...) Connects easily with various temporal resources Supports reasoning about time Growing number of users; W3C endorsement near

11. Example E-Commerce: Need book by next Tuesday Ships books within five business days ?

12. Coverage of Temporal Ontology Topological relations Durations Clock and Calendar Temporal Aggregates 5. Vague Temporal Concepts

13. Time: Topology instants interval start inside end x y before(x,y) intOverlaps(T1, T2): T1 t2 t1 t3 t4 T2

14. Duration, Clock and Calendar Measures of duration: second, minute, ... Concatenation of temporal intervals Time zones (includes a world time zone resource) Clock times: 10:15:32am Calendar dates: Tuesday, June 20, 2006 Temporal arithmetic

15. Temporal Aggregates “five business days” “every third Monday in 2001” “every morning for the last four years” “four consecutive Sundays” “the first nine months of 1997” “three weekdays after January 10” “the fourth of six days of voting”

16. Typical Durations of Events We have a lot of knowledge about how long events of various types last. “George W. Bush met with Vladimir Putin in Moscow.” How long did the meeting last? 10 seconds? One year? Probably between 1 hour and 2 days We annotated events in news articles with judgments like these to create corpus and used it in machine learning

17. Controversial Issuesand What to do about Them Are the end points of an interval a partof the interval? Can there be intervals of zero length? Is an interval of zero length an instant? ==> Avoid these issues; keep ontology silent. (Many problems arise when trying to identify 0-D and 1-D entities) Is time totally ordered? Are there points at infinity? ==> Optional extensions with triggers Total-order() --> (A t1,t2)[before(t1,t2) v t1=t2 v before(t2,t1)] Use similar devices for a geospatial core theory

18. Outline Time Ontology (OWL-Time) Event Ontology “DAML-Space”/“OWL-Space” Topics and Requirements A Sketch of Topology Granularity Half Orders of Magnitude

19. IKRIS Scenarios Inter-Theory Define an ontology or “inter-theory” that will allow various resources and languages to inter-translate statements about events, processes, and scenarios, their structure, and their causal relations Target resources: Process Specification Language (PSL), ResearchCyc, FLOWS/SWSO, SPARK (son of PRS) Funded by ARDA; April 2005 - September 2006

20. Coverage Event and state types and tokens (general rules and specific facts) Precondition-effect view of processes Input-output view of processes Control structure of processes Relation to knowledge about causality and enablement State of execution of processes (continuing, aborting, resuming, ...)

21. Outline Time Ontology (OWL-Time) Event Ontology “DAML-Space”/“OWL-Space” Topics and Requirements A Sketch of Topology Granularity Half Orders of Magnitude

22. Context The Semantic Web requires common ontologies with wide acceptance and use. OWL-S: an ontology of services Development began February 2001 About a dozen people in inner circle Growing community of users Institutional status at W3C OWL-Time: a temporal ontology Development began February 2002 Most work by 1-3 people 10 < | Users | < 100 Public review stage at W3C OWL-Space: a spatial ontology Organizational meeting April 2003 Effort suspended after early 2004 because of lack of funding Good signs of revival, including this workshop

23. Aims A widely available ontology of geographical and other spatial properties and relations Provide convenient markup and query capabilities for spatial information in Web resources Adequate abstract coverage for most spatial applications (not necessarily efficient) Link with special purpose reasoning engines for spatial theories and large-scale GIS databases Link with various ontological resources and annotation schemes Link with various standards for geographical information

24. Structure of Effort Galton Egenhoffer Cohn Hayes Abstract Theory of Space (FOL) etc Complete or Partial Realization in OWL / RuleML / ... SUMO ResearchCyc SDTS OpenGIS NLP Extraction Techniques Existing Standards Annotation Standards

25. Some Principles Delimiting the effort: Not a theory of physical objects, properties of materials, qualitative physics Link with numerical computation, don’t axiomatize it Link with large geographical DBs, don’t duplicate them Navigate past controversial issues, as in OWL-Time, by Keeping silent on issue Provide easily exercised options Use Common Logic (CL) for abstract theory; OWL-ize predicate and function declarations Provide simple, useful entry subontologies

26. Topics SPACETIME Topology Topology Dimension -- Orientation & Shape -- Length, area, volume Duration Lat/long, elevation Clock & calendar Geopolitical subdivisions -- Aggregates, distributions Temporal aggregates Vagueness Vagueness

27. Outline Time Ontology (OWL-Time) Event Ontology “DAML-Space”/“OWL-Space” Topics and Requirements A Sketch of Topology Granularity Half Orders of Magnitude

28. Target Applications (as of 2003) Some of the applications as drivers for what has to be represented Flight planning with no-fly zones Travel planning system involving lat/longs, political divisions, weather Smart meeting room system Alexandrian Digital Library Space (NASA) applications involving the structure and trajectory of rockets (3-D) Cell biology Image interpretation and description Robotics We collected brief descriptions of the requirements for spatial representation and reasoning for these applications

29. Topology Points, arcs, regions, volumes Closed loops and surfaces Ordering relations & “between” in arcs; directions on lines and loops Connectedness, continuity Boundaries & surfaces, interior & exterior, directed boundaries; “airspace above” Disjoint, touching, bordering, overlapping, containing regions (RCC8); location at Holes, knots NOT open and closed sets NOT pathological topologies

30. Dimension and Orientation Abstract characterization of dimension, projections on component dimensions, embedding dimension Links w topological notions of dimension Frames of reference: earth-based, person-based, vehicle-based, force-based Relative orientations: parallel, perpendicular Cartesian vs polar coordinate systems, bearing & range Transformations between coordinate systems Degrees of freedom Qualitative trigonometry: granularities on orientations 2 1/2 dimensions: elevation as 2nd class dimension, system mostly thought of as planar Elevation from sea level vs ground level Planar vs spherical geometry

31. Shape 2D vs 3D shapes Linking w shape descriptions in geographical databases Shape descriptors: round, tall, narrow, convex,... Relative shapes: rounder, sharper, ... Same shape as, negative-shape, fits-in Bounding boxes and their problems (e.g., USA with American Samoa includes Mexico) Symmetry Links w functionality of shape In artifacts, shape is almost always functional In natural objects, shape often has consequences ? Texture

32. Size Length, distance, area, and volume Precise and qualitative measures English-metric conversions Coarse granularities: order of magnitude, half order of magnitude, implied precision, qualitative measures (large, medium, small) relative to comparison set Encoding uncertainty: bounded error, egg yolk theories Uncertainty of location vs imprecise regions

33. Spatial Aggregates What are the most common ways of describing spatial aggregates? A qualitative theory of distributions (e.g., heavily populated) ? Texture

34. Geopolitical Regions Latitude and Longitude Natural geographical regions: Land masses: continent, island, ... Bodies of water: ocean, lake, river, ... Terrain features: mountain, valley, forest, desert, ... Political regions: Countries Political subdivisions: state, province, county, ... Municipalities: city, town, village, ... Residences and street addresses Other: Indian reservations, regulatory zones, ...

35. Outline Time Ontology (OWL-Time) Event Ontology “DAML-Space”/“OWL-Space” Topics and Requirements A Sketch of Topology Granularity Half Orders of Magnitude

36. Topology: Some Principles Terminology: OpenGIS > ResearchCyc > SUMO > new Distinguish between physical objects and their geometric realizations Stay neutral on the question of whether: A curve is composed of points. A boundary is part of a region. Invent new predicates, not , for cross-dimensional relations Ignore topological oddities (space-filling curves, ...) Stay as neutral as possible on issues of infinity

37. Topology: Some Concepts Dimension: dimension of geometric figure: point, curve, surface, solid embedding dimension, e.g., curve in 3-space Interior, Exteriors, and Boundaries Primitive predicates inside, outside, boundary Possible Relations among geometric objects of various dimensions RCC8; Egenhoffer’s relations and operators E.g., what are the possible relations between a curve and a solid? All defined in terms of inside, outside, boundary

38. Topology: Some Concepts Connectedness and continuity: connected objects in terms of overlap and tangents self-connected: no disconnected decomposition mean-value theorem or property: g1 and g2 self-connected and g1 overlaps with interior(g2) and with exterior(g2) --> g1 overlaps with boundary(g2) notions of continuity, given structure on domain and range (Galton) Holes, cavities, indentations, tunnels: n-connectedness: how many holes? n-tunnels: how many holes in surface? shape of tunnels: in terms of knot theory’s “crossings” composition by addition and subtraction of these objects Composite geometric objects

39. Outline Time Ontology (OWL-Time) Event Ontology “DAML-Space”/“OWL-Space” Topics and Requirements A Sketch of Topology Granularity Half Orders of Magnitude

40. Granularity A city can be viewed as a point, a region, or a volume. How should these different perspectives be accommodated? One approach: City is an entity with 3D, 2D, and 0D realizations. User can pick which one(s) to use. Build granularity considerations into spatial ontology from the beginning, not as an add-on.

41. Granularity Tolerances, epsilon-neighborhoods: But granularity is not just tolerances: Map of South America: Hiking Map: Boulder trail

42. Granularity Indistinguishability Relation (or Set Covering): ≈ Partition: ≈ transitive, e.g., countries Overlapping Sets: ≈ not transitive, e.g., within 1 cm Often functionality-determined, e.g. hiking map. Different granularities for different purposes. e.g. discrete vs continuous for conceptualizations of space and time. Much of our knowledge involves knowledge of various available granularities, articulations between them, and ways of shifting granularities for particular purposes.

43. Scales Set of elements with a partial ordering < Can define subscale, total ordering, dense, top, bottom, reverse, relations among subscales, Examples: distance, time, happiness, damage, preference, ... Various perspectives on space built out of independent scales

44. Levels of Structure on Scales not okay okay 0 -- + qualitative amounts Md Lo Hi orders of magnitude half orders of magnitude integers reals

45. Other Perspectives on Granularity Composite Entities can be viewed structurally: with their internal structure visible functionally: undecomposed, with their relations to the environment visible . . . . . . . . .

46. Other Perspectives on Granularity Complex events/actions have hierarchical structure: goal(a,q) goal(a,r) goal(a,p) .... .... .... Depth of decomposition defines the Granularity at which behavior is viewed.

47. Other Perspectives on Granularity Refining granularity thru transitivity axioms: change(e1,e2) & change(e2,e3) --> change(e1,e3) subevents of this out(v,c) --> in(v,c) virus cell Looking at components of cell wall virus cell out(v,c) --> penetrating(v,wl(c)) --> in(v,c)

48. Outline Time Ontology (OWL-Time) Event Ontology “DAML-Space”/“OWL-Space” Topics and Requirements A Sketch of Topology Granularity Half Orders of Magnitude

49. Some Multiple Choice Questions 1. About how many children are there in the average family? a) 1 c) 10 e) 100 2. About how many children are there in the average classroom? a) 1 c) 10 e) 100

50. Some Multiple Choice Questions 1. About how many children are there in the average family? a) 1 b) 3 c) 10 d) 30 e) 100 2. About how many children are there in the average classroom? a) 1 b) 3 c) 10 d) 30 e) 100 Often the best answer is in terms of half orders of magnitude (HOMs)