Ontologies for the Semantic Web:

Time and Space

Jerry R. Hobbs

USC/ISI

Marina del Rey, CA

DAML-Time

DAML (Semantic Web) Ontology of time for describing

temporal content of web pages temporal properties of web pages temporal properties of web services

Maps easily into other temporal theories/ontologies (e.g., Cyc, SUMO, PSL, ...)

Connects easily with various temporal resources

Supports reasoning about time

Integrated with TimeML for annotation and analysis of NL text

Aims of DAML-Time

Examples

Need bookby next

Tuesday

Ships bookswithin five

business days?

Marriage record for ancestor: year

Find birth records for same name,between 15 and 45 years before

E-Commerce:

Genealogy:

Coverage of Temporal Ontology

1. Topological relations

2. Durations

3. Clock and Calendar

4. Temporal Aggregates

5. Deictic Time

6. Vague Temporal Concepts

Time: Topology

intervalinstants

start endinside

x ybefore(x,y)

before is anti-reflexive, anti-symmetric, transitive

start before inside before end

Interval Relations in Terms of before, starts, ends

(A T1,T2)[int-overlaps(T1,T2) <--> [proper-interval(T1) & proper-interval(T2) & (E t2,t3)[ends(t2,T1) & begins(t3,T2) & before(t3,t2) & (A t1)[begins(t1,T1) --> before(t1,t3)] & (A t4)[ends(t4,T2) --> before(t2,t4)]]]]

T1

T2

t2

t3 t4

t1

The Interval Algebra(Allen & Ferguson, 1997)

before

meets

overlaps

starts

equals

during

finishes

Relationsbetweenthis and

start,end, andbefore

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)]

Events and Time

Temporal ontology is not an ontology of events, e.g., no aspect, event decomposition, etc.

Predicates to interface events with time:

at-time(e,t) during(e,T) time-span-of(T,e)

Or event ontology can provide its own means:

holds(e,t) p(x,t) etc.

Or in temporal ontology, temporal thing that covers both intervals and events.

Events in the Temporal Ontology

Instants InstantEvents Intervals IntervalEvents

EventsTemporalEntities

TemporalThing

IntervalThingsInstantThings

Then temporal predicates are generalized to TemporalThing, InstantThing, IntervalThing

Units of Duration

duration(T, *Second*) = n means interval T is n seconds long

duration(T,*Second*) = 60*duration(T,*Minute*)duration(T,*Minute*) = 60*duration(T,*Hour*)duration(T,*Hour*) = 24*duration(T,*Day*)duration(T,*Day*) = 7*duration(T,*Week*)

duration(T,*Day*) = ??*duration(T,*Month*)

duration(T,*Month*) = 12*duration(T,*Year*)

Duration Descriptions

Interval

DurationDescription: Seconds: Minutes: Hours: Days: Weeks: Months: Years:

durationDescriptionOf

Many equivalent DurationDescriptions

Temporal Arithmetic duration-description(T,y,m,w,d,h,n,s+60) <--> duration-description(T,y,m,w,d,h,n+1,s)

duration-description(T,y,m,w,d,h,n+60,s) <--> duration-description(T,y,m,w,d,h+1,n,s)

duration-description(T,y,m,w,d,h+24,n,s) <--> duration-description(T,y,m,w,d+1,h,n,s)

duration-description(T,y,m,w,d+7,h,n,s) <--> duration-description(T,y,m,w+1,d,h,n,s)

duration-description(T,y,m,w,d+??,h,n,s) <--> duration-description(T,y,m+1,w,d,h,n,s)

duration-description(T,y,m+12,w,d,h,n,s) <--> duration-description(T,y+1,m,w,d,h,n,s)

Canonical description of duration

Concatenation and "Hath"

Hath(n,u,x): n units of type u comprises x

September(x,y) --> Hath(30,*Day*,x)minute(x) --> Hath(60,*Second*,x)

x

u u u u |S|=n

Concatenation(x,S): x is concatenation of intervals in S

Concatenation(T1,{T2,T3}) --> duration(T1,u) = duration(T2,u) + duration(T3,u)

x

S

Clock and Calendar

Time zones: Not geographical regions, but legal entities Property of hours days months years C.E. CE(z) = Common Era in time zone z

Various ways of saying minit(y,n,x) <--> minitFn(n,x) = y <--> clock-int(y,n,*Minute*,x) <--> y is the nth minute in x

A subset of intervals that correspond to clock or calendar designations, e.g., August 2003

Days of the Week

dayofweek(y,n,x) <--> cal-int(y,n,*Day*,x) & (E x1,n1) cal-int(x,n1,*Week*,x1)

dayofweek(d,1,w) <--> Sunday(d,w)

Tuesday(1-Jan-2000) anchors cycle of weeks

Months and Leap Years

cal-int(m,1,*Month*,y) <--> January(m,y)

January(m,y) --> Hath(31,*Day*,m)

leapyear(y) <--> yr(y,n,CE(z)) & 400 | n v [4|n & ~100|n]

February(m,y) & ~leapyear(y) --> Hath(S,28,*Day*,y)

Month as a Unit of Duration

nth day nth day

one month

But: January 31 + 1 month = February 28 January 30 + 1 month = February 28 February 28 + 1 month = March 28 or March 31? January 31 + 2 months = March 31 January 30 + 2 months = March 30

So [January 30 + 1 month] + 1 month =/= January 30 + 2 months

Need months as units of duration since since chargesare often by the month.

Clock and Calendar

weekendday(d,w) <--> Saturday(d,w) v Sunday(d,w)

da(d,4,m) & July(m,y) --> holiday(d,USA)

business-day(d,g) <--> ~(E w)[weekendday(d,w)] & ~holiday(d,g)

Time Stamps

Time Stamps:

time-of(t,y,m,d,h,n,s,z) <--> in-interval(t,secFn(s,minFn(n,hrFn(h,daFn(d,monFn(m,yrFn(y,CE(z))))))))

If t is 4:25:38 pm PDT, January 28, 2003

then time-of(t,2003,1,28,16,25,38,*PDT*)

Mapping onto ISO 8601 standard

Relate to duration descriptions so temporal arithmetic can be done on dates.

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”

Temporal Aggregates

temporal sequence: set of nonoverlapping instants and/or intervals ordered by before

first(s), nth(s,n)

futurep(p,u) = s <--> (A t)[member(t,s) <--> (E t1,t2)[p(t) & now(t1,u) & begins(t2,t) & before(t1,t2)]] (sequence of all the p’s after now)

Deictic Time

now(t,u): instant/interval t is now in utterance/document u

today(d,u) <--> now(t,u) & in-interval(t,d) & day(d,n,x)

past(t,u) <--> now(t1,u) & before(t,t1)

ago(t,T,u) <--> now(t1,u) & interval-betw(t,t1) = T

Vague Temporal Concepts

Vague Temporal Concepts:

recently, soon, a little while, ....

Where text annotation can help immensely: what durations do people intend?

She had recently [3 mos] bought a laptop.

In recent [5 yrs] years farmers have been enjoying record yields.

The recent [1 wk] computer crash was costly.

Need data on what these terms mean.

Convergence

TimeML(ARDA AQUAINT program)Annotation of NL corpora

Development of algorithmsfor annotation

For QA, MT, etc.

DAML-Time(DARPA DAML program)

Expressing temporalcontent and capabilities

of Web sites and services

Most information on the Webis in natural language

TimeML <--> DAML-Time

Example

Query: I want the latest book by John McCarthy by next Tuesday.

Author: John McCarthy et al.Book: Formalizing Common SenseDate: 1998Price: $24.95

Delivery within 5 business days

Author: John McCarthyBook: LISP 1.5 Date: 1962Price: $16.95

Author: John McCarthy et al.Book: Defending AI ResearchDate: 1996Price: $21.95

Example

Query: I want the latest book by John McCarthy by next Tuesday. Price is no object.

Author: John McCarthy et al.Book: Formalizing Common SenseDate: 1998Price: $24.95

Delivery within 5 business days

Author: John McCarthyBook: LISP 1.5 Date: 1962Price: $16.95

Author: John McCarthy et al.Book: Defending AI ResearchDate: 1996Price: $21.95

TimeML

Annotation of time and events in natural language text.

Time stamping of events.

Ordering of events wrt each other.

Anchoring of deictic temporal expressions.

Identifying signals of temporal information.

Facilitates reasoning about persistence of events.

Creation of TIMEBANK, gold standard of 300 articles.

An Annotation

Delivery within five business days.

<EVENT eid="e1" class="OCCURRENCE" tense=”NONE" aspect="NONE">Delivery</EVENT><MAKEINSTANCE eiid="ei1" eventID="e1" signalID="s1" /><SIGNAL sid="s1">within</SIGNAL><TIMEX3 tid="t1" type="DURATION">five business days</TIMEX3><TLINK eventInstanceID="ei1" relatedToTime="t1” relType="IS_INCLUDED"/>

Time Expressions in TimeML

<TIMEX3 tid="t1" type="DURATION">five business days</TIMEX3>

Dates, times, durations

functionInDocument: Creation_Time, ... (Anchors deictic expressions like “now”, “next Tuesday”)

Follows ISO 8601 time standard

Events in TimeML

<EVENT eid="e1" class="OCCURRENCE" tense=”NONE" aspect="NONE">Delivery</EVENT>

Class: Occurrence: delivery State: on order Reporting: announce I-Action: attempt, offer I-State: believe, want Aspectual: begin, continue Perception: see, watch

Tense: Past, Present, Future, None

Aspect: Progressive, Perfective, Perfective_Progressive, None

Links in TimeML

<TLINK eventInstanceID="ei1" relatedToTime="t1” relType="IS_INCLUDED"/>

TLINK: interval relations

SLINK: Modal: could Factive: forgot Counterfactive: prevent Evidential: said, saw Negative evidential: denied Negative: not

ALINK: Initiation: started to read Culmination: finished reading Termination: stopped reading Continuation: kept reading

TLINK Relations

IdenticalSimultaneousBeforeAfterImmediately beforeImmediately afterIncluding

Is IncludedOverlapsHoldingBeginningBegun byEnding Ended by

<TLINK eventInstanceID="ei1" relatedToTime="t1” relType="IS_INCLUDED"/>

TimeML: Annotation Scheme:An Example

The top commander of a Cambodian resistance force said Thursdayhe has sent a team to recover the remains of a British mine removalexpert kidnapped and presumed killed by Khmer Rouge guerrillastwo years ago.

resist

command

sent recover

Thursday

said now

remove kidnap

2 years

presumed

killedremain

Example

“next Tuesday”:

Tuesday(first(futurep(cal-week,u)))

“five business days”:

nth(futurep(business-day,u),5)delivery

5 business daysorder

next Tuesday

?

Summary of DAML-Time/TimeML

TimeML annotation of text

Algorithms for automatic TimeML annotation of text

Interpret annotations in DAML-Time

Reason in DAML-Time to match requests with services

DAML-Space:A Effort towards an

Ontology of Space

with contributions from Rusty Bobrow, Murray Burke, Dan Connolly, Dejing Dou,

George Ferguson, Andrew Gordon, Pete Haglich, Pat Hayes, Adam Pease, Steve Reed, Richard Waldinger and others

Context

The Semantic Web requires common ontologies with wide acceptance and use.

DAML-S: an ontology of services Development began February 2001 About a dozen people in inner circle Some people have explored using it Institutional status at W3C Version 0.9 just released

DAML-Time: a temporal ontology Development began February 2002 Most work by 3 people Abstract theory 90% complete Mapping between DAML-Time and TimeML Several sites “about to” use it

Want to build on this experience for a spatial ontology.

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 of 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 (e.g., OpenCyc, SUMO, ...) and annotation schemes

Link with various standards for geographical information (OpenGIS, GML, ...)

Structure of Effort

Abstract Theoryof Space

(FOL)

Complete or Partial Realization in DAML / OWL /

RuleML / ...

SUMO OpenCyc

Cohn Hayes & Chaudhri

Annotation Standards

etc

Existing Standards NLP ExtractionTechniques

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 by Keeping silent on issue Provide easily exercised options

Use textbook logic for abstract theory; DAML/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 --

Granularity Granularity

Aggregates, distributions Temporal aggregates

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 atHolesNOT open and closed setsNOT pathological topologies

Dimension and Orientation

Abstract characterization of dimension, projections on component dimensionsLinks 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-inSymmetryLinks 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 measuresAlternate descriptions of sizeEnglish-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

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.

Spatial Aggregates

What are the most common ways of describing spatial aggregates?

A qualitative theory of distributions.

? Texture

Geologic/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, ...

Linkages

Exploit the large amount of research on spatial representation and reasoningOpenCyc, SUMO, Cohn, Galton, Hayes & Chaudhri, Hayes, Asher & Vieu, Egenhofer, ForbusAxiomatize best of this work in coherent fashion

Link with existing large ontologies and annotation schemes SUMO, OpenCyc

Ontology should bottom out in existing standards OpenGIS, GML

Target Applications

As drivers for what has to be represented

Flight map system, COA planning, trafficabilityTravel system involving lat/longs, political divisions, weatherAlexandrian Digital Library Geologic and space (NASA) applications (3-D)Cell biology Image interpretation and descriptionRoboticsVirtual reality

For some of these, we are collecting brief descriptions of the requirements for spatial representation and reasoning

Organization

# of participants

degree ofcommunityacceptance

Organization

# of participants

time tocompletion

Organization

# of participants

quality ofontology

Organization

daml-spatial mailing list

Web page - George Ferguson

Coherent construction of abstract theories by small group of people

Committee of interested persons in U.S. and Europe Email for commentary / feedback Telecons every 2 weeks to track issues/progress

Presentations and discussion sessions at relevant workshops

Early realizations of relevant parts of ontology in DAML

Early construction of application-oriented entry subontologies