An Ontology of Time for the Semantic Web
Jerry R. Hobbs and Feng Pan
University of Southern California
/ Information Sciences Institute ________________________________________________________________________
In connection with the DAML project for bringing about the Semantic Web, an ontology of time is being developed for describing the temporal content of Web pages and the temporal properties of Web services. The bulk of information on the Web is in natural language, and this information will be easier to encode for the Semantic Web insofar as community-wide annotation and automatic tagging schemes and the DAML time ontology are compatible with each other.
Categories and Subject
Descriptors: I.2.4 [Artificial Intelligence]: Knowledge Representation Formalisms and Methods - Representations
(procedural and rule-based); Temporal logic; I.2.7
[Artificial Intelligence]: Natural Language Processing - Text
analysis; H.3.5
[Information Storage and Retrieval]: Online
Information Services - Web-based services; H.3.1 [Information Storage and
Retrieval]: Content Analysis and Indexing - Linguistic processing
General Terms: Design, Documentation, Languages, Theory
Additional Key Words and Phrases: ontology, time, semantic web, temporal information, temporal relation, duration, clock and calendar, time zone
________________________________________________________________________
The DARPA Agent Markup Language
(DAML) project is DARPA¹s effort to bring into reality the Semantic Web, in
which Web users and automatic agents will be able to access information on the
Web via descriptions of the content and capabilities of Web resources rather
than via key words. An important part of this effort is the development of
representative ontologies of the most commonly used domains. We have developed
such an ontology of temporal concepts, for describing the temporal content of
Web pages and the temporal properties of Web services. This effort has been
informed by temporal ontologies developed at a number of sites and is intended
to capture the essential features of all of them and make them easily available
to a large group of Web developers and users, embedded in the ontology mark-up
language OWL[1].
The bulk of information on the Web is in natural
language, and this information will be easier to encode for the Semantic Web
insofar as community-wide annotation and automatic tagging schemes and the DAML
time ontology are compatible with each other. Indeed, this compatibility was
explored by Hobbs and Pustejovsky [2003].
In this paper we outline the temporal ontology.
Five categories of temporal concepts are considered, and for each the principal
predicates and their associated properties are described.
A note on notation before we begin: Conjunction
( 
) takes
precedence over implication ( É ) and
equivalence ( º ). Formulas are assumed
to be universally quantified on the variables appearing in the antecedent of
the highest-level implication. Thus,
p
(x) 
p
(y) É q
(x,y) 
q
(y)
is to be interpreted as
(" x,y)[[p
(x) 
p
(y)] É [q
(x,y) 
q
(y)]]
2. Topological Temporal Relations
2.1 Instants and Intervals
There are two subclasses of TemporalEntity: Instant and Interval.
Instant(t) É TemporalEntity(t)
Interval(T) É TemporalEentity(T)
These are the only two subclasses of temporal entities.
(" T)[TemporalEntity(T) É Interval(T) Ú Instant(T)
As we will see, intervals are, intuitively, things with extent and instants are, intuitively, point-like in that they have no interior points. (In what follows, lower case t is used for instants, upper case T for intervals and for temporal-entities unspecified as to subtype. This is strictly for the reader¹s convenience, and has no formal significance.)
The predicates begins and ends are relations between instants and temporal entities.
begins(t,T) É
Instant(t) 
TemporalEntity(T)
ends(t,T) É
Instant(t) 
TemporalEntity(T)
For convenience, we can say that the beginning and end of an instant is itself. The converses of these rules are also true.
Instant(t) É begins(t,t)
Instant(t) É ends(t,t)
The beginnings and ends of temporal entities, if they exist, are unique.
TemporalEntity(T) 
begins(t
,T) 
begins(t
,T) É t
= t
TemporalEntity(T) 
ends(t
,T) 
ends(t
,T) É t
= t
In one approach to infinite intervals, a positively infinite interval has no end, and a negatively infinite interval has no beginning. Hence, we use the relations begins and ends in the core ontology, rather than defining functions beginningOf and endOf, since the functions would not be total. They can be defined in an extension of the core ontology that posits instants at positive and negative infinity.
The predicate inside is a relation between an instant and an interval.
inside(t,T) É
Instant(t) 
Interval(T)
This concept of inside is not intended to include beginnings and ends of intervals, as will be seen below.
It will be useful in characterizing clock and calendar terms to have a relation between instants and intervals that says that the instant is inside or the beginning of the interval.
(" t,T)[beginsOrIn(t,T) º [begins(t,T) Ú inside(t,T)]]
The predicate timeBetween is a relation among a temporal entity and two instants.
timeBetween(T,t
,t
) É TemporalEntity(T)
Instant(t
) 
Instant(t
)
The two instants are the beginning and end points of the temporal entity.
(" t
,t
)[t
¹ t
É (" T)[timeBetween(T,t
,t
) º begins(t
,T) 
ends(t
,T)]]
The ontology is silent about whether the interval from t to t, if it exists, is identical to the instant t.
The ontology is silent about whether intervals consist of instants.
The ontology is silent about whether intervals are uniquely determined by their starts and ends.
The core ontology is silent about whether intervals are uniquely determined by their beginnings and ends.
We can define a proper interval as one whose start and end are not identical.
(" T)ProperInterval(T)
º Interval(T) 
(" t
,t
)[begins(t
,T) 
ends(t
,T) É t
¹ t
]]
The ontology is silent about whether there are any intervals that are not proper intervals.
2.2 Before
There is a before relation on temporal entities, which gives
directionality to time. If temporal entity T
is before temporal entity T
, then the end of T
is before the start of T
. Thus, before
can be considered to be basic to instants and derived for intervals.
(" T
,T
)[before(T
,T
)
º ($ t
,t
)[ends(t
,T
) 
begins(t
,T
) 
before(t
,t
)]]
The before relation is anti-reflexive, anti-symmetric and
transitive.
before(T
,T
) É T
¹ T
before(T
,T
) É Øbefore(T
,T
)
before(T
,T
) 
before(T
,T
) É before(T
,T
)
The end of an interval is not
before the beginning of the interval.
Interval(T) 
begins(t
,T) 
ends(t
,T) É Øbefore(t
,t
)
The beginning of a proper
interval is before the end of the interval.
ProperInterval(T) 
begins(t
,T) 
ends(t
,T) É before(t
,t
)
If one instant is before another,
there is a time between them.
Instant(t
) 
Instant(t
) 
before(t
,t
) É ($ T) timeBetween(T,t