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

Interoperability amongGeospatial Ontologies

Jerry R. HobbsInformation Sciences Institute

University of Southern CaliforniaMarina del Rey, California

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.

Some Natural Language QueriesTopology 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.

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 TysonAnswered questions that required accessing multiple resources; focus on geospatial domain.Key ideas:1. Logical analysis/decomposition of questions into component questions, using a reasoning engine2. Bottoming out in variety of web resources and information extraction engine3. Use of analysis of questions to determine, formulate, and present answers.

Composition of Informationfrom Multiple Sources

Show me the region 100 km north of the capital of Afghanistan.

What is the capitalof Afghanistan?

What is the lat/long100 km north?

What is the lat/longof Kabul?

CIAFact Book Geographical

Formula

QuestionDecomposition

via Logical Rules

AlexandrianDigital Library

Gazetteer

Show thatlat/long

Terravision

ResourcesAttached toReasoning

Process

System Architecture

GEMINI

SNARK

Query

Logical Form

Web Resources Other Resources

parsing

decomposition and interpretation

Proof withAnswer

Inter-Operability

GEMINI

SNARK

Query

Logical Form

Web Resources Other Resources

parsing

decomposition and interpretation

Proof withAnswer

What is thislanguage and

ontology?

Inter-Operability

Resource-4

Resource-3Resource-5

Resource-2Resource-6

Resource-1

Resource-4

Resource-3Resource-5

Resource-2Resource-6

Resource-1

Inter-theory

via multiple translations:

via an “inter-theory”:

OR

Also a good excuse to develop a core theory.

Outline

Time Ontology (OWL-Time)

Event Ontology

“DAML-Space”/“OWL-Space”

Topics and Requirements

A Sketch of Topology

Granularity

Half Orders of Magnitude

Ontology of time for the Semantic Web for describing temporal content of web pages temporal properties of web pages temporal properties of web servicesDeveloped in collaboration with James Allen, Pat Hayes, George Ferguson, James Pustejovsky, Adam Pease, and other researchersMaps easily into other temporal theories/ontologies (e.g., Cyc, SUMO, PSL, ...)Connects easily with various temporal resourcesSupports reasoning about time

Growing number of users; W3C endorsement near

Aims of OWL-Time

Example

Need bookby nextTuesday

Ships bookswithin five

business days?

E-Commerce:

Coverage of Temporal Ontology

1. Topological relations2. Durations3. Clock and Calendar4. Temporal Aggregates5. Vague Temporal Concepts

Time: Topology

interval instants

start endinside

x ybefore(x,y)

T1

T2

t2

t3 t4

t1

intOverlaps(T1, T2):

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

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”

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

Controversial Issuesand What to do about Them

Are the end points of an interval a part of 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

Outline

Time Ontology (OWL-Time)

Event Ontology

“DAML-Space”/“OWL-Space”

Topics and Requirements

A Sketch of Topology

Granularity

Half Orders of Magnitude

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

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, ...)

Outline

Time Ontology (OWL-Time)

Event Ontology

“DAML-Space”/“OWL-Space”

Topics and Requirements

A Sketch of Topology

Granularity

Half Orders of Magnitude

ContextThe 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

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

Structure of Effort

Abstract Theoryof Space

(FOL)

Complete or Partial Realization in

OWL / RuleML / ...

SUMO ResearchCyc

Cohn Hayes

Annotation Standards

etc

Existing Standards NLP ExtractionTechniques

EgenhofferGalton

OpenGISSDTS

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

Topics SPACE TIME

Topology Topology

Dimension --

Orientation & Shape --

Length, area, volume Duration

Lat/long, elevation Clock & calendar

Geopolitical subdivisions --

Aggregates, distributions Temporal aggregates

Vagueness Vagueness

Outline

Time Ontology (OWL-Time)

Event Ontology

“DAML-Space”/“OWL-Space”

Topics and Requirements

A Sketch of Topology

Granularity

Half Orders of Magnitude

Target Applications

Some of the applications as drivers for what has to be represented

Flight planning with no-fly zonesTravel planning system involving lat/longs, political divisions, weatherSmart meeting room systemAlexandrian Digital Library Space (NASA) applications involving the structure and trajectory of rockets (3-D)Cell biology Image interpretation and descriptionRobotics

We collected brief descriptions of the requirements for spatial representation and reasoning for these applications

(as of 2003)

Topology

Points, arcs, regions, volumesClosed loops and surfacesOrdering relations & “between” in arcs; directions on lines and loopsConnectedness, continuityBoundaries & surfaces, interior & exterior, directed boundaries; “airspace above”Disjoint, touching, bordering, overlapping, containing regions (RCC8); location atHoles, knotsNOT open and closed setsNOT pathological topologies

Dimension and Orientation

Abstract characterization of dimension, projections on component dimensions, embedding dimensionLinks w topological notions of dimensionFrames of reference: earth-based, person-based, vehicle-based, force-basedRelative orientations: parallel, perpendicularCartesian vs polar coordinate systems, bearing & rangeTransformations between coordinate systemsDegrees of freedomQualitative trigonometry: granularities on orientations2 1/2 dimensions: elevation as 2nd class dimension, system mostly thought of as planarElevation from sea level vs ground levelPlanar vs spherical geometry

Shape

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

Size

Length, distance, area, and volumePrecise and qualitative measuresEnglish-metric conversionsCoarse granularities: order of magnitude, half order of magnitude, implied precision, qualitative measures (large, medium, small) relative to comparison setEncoding uncertainty: bounded error, egg yolk theoriesUncertainty of location vs imprecise regions

Spatial Aggregates

What are the most common ways of describing spatial aggregates?

A qualitative theory of distributions (e.g., heavily populated)

? Texture

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, ...

Outline

Time Ontology (OWL-Time)

Event Ontology

“DAML-Space”/“OWL-Space”

Topics and Requirements

A Sketch of Topology

Granularity

Half Orders of Magnitude

Topology: Some PrinciplesTerminology: 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

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

Topology: Some ConceptsConnectedness 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

Outline

Time Ontology (OWL-Time)

Event Ontology

“DAML-Space”/“OWL-Space”

Topics and Requirements

A Sketch of Topology

Granularity

Half Orders of Magnitude

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.

Granularity

Tolerances, epsilon-neighborhoods:

But granularity is not just tolerances:Map of South America:

Hiking Map:

Bouldertrail

GranularityIndistinguishability 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.

ScalesSet 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

Levels of Structure on Scalesokaynot okay

-- 0 +

orders of magnitude

half orders of magnitude

integers

reals

qualitative amounts

LoMd

Hi

Other Perspectives on Granularity

Composite Entities can be viewed structurally: with their internal structure visible functionally: undecomposed, with their relations to the environment visible

. ...

.

...

.

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.

Other Perspectives on GranularityRefining granularity thru transitivity axioms:

change(e1,e2) & change(e2,e3) --> change(e1,e3)

subevents of this

out(v,c) --> in(v,c)viruscell

virus

cell

out(v,c) --> penetrating(v,wl(c)) --> in(v,c)

wallLooking at

components ofcell

Outline

Time Ontology (OWL-Time)

Event Ontology

“DAML-Space”/“OWL-Space”

Topics and Requirements

A Sketch of Topology

Granularity

Half Orders of Magnitude

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

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)

Some Examples

Cash: 1 cent, 5 cents, 10 cents, 25 cents, $1, $5, $10, $20, $100

Volume: 1cup, 1pint, 1 quart, 1 gallon, 1 peck, 1 bushel

Time: 1 minute, 1 quarter hr, 1 hr, morning..., 1 day, 1 week, 1 month, 1 quarter/semester/season, 1 year, Olympiad/pres.admin...., 1 decade

Opposing Tensions

We want a rough logarithmic categorization scheme for sizes in which the categories arelarge enough that Aggregation operations have reasonably predictable results, Normal variation does not cross category boundariesBut small enough that Our interactions with objects is predictable from their category.

Natural HOMsLinear extent: Examples: 6 feet person, door, chair, table, desk can be moved by one person, can accommodate one person 2 feet TV set, dog, basket, watermelon, sack can be held in two arms 8 inches book, football, cantelope can be held in one hand, manipulated with difficulty in one hand 3 inches pen, mouse, hamburger,orange, cup can be held with the fingers

1 inch french fry, eraser, peppermint candy can be bitten, can be manipulated easily with two fingers and thumb

1/4 inch M&M, thumb tack, diamond handled with care between two fingers

Natural HOMsLinear extent: Examples: 6 feet person, door, chair, table, desk can be moved by one person, can accommodate one person 18 feet office, room one person can move around can accommodate several people 20 yards house, restaurant, small yard, class 60 yards commercial building, large yard 200 yards small factory, field 600 yards large factory, large bridge, dam 1 mile town, airport 3 miles small city 10 miles large city, small county 30 miles large county 100 miles small state 300 miles large state, small nation 1000 miles typical large European nation 3000 miles the United States, China

Summary

An “inter-theory” of the geospatial domain explicating its core concepts would enable use of multiple geographic databases; link to multiple geospatial reasoning engines; link to natural language

(and should be fairly straightforward to do)