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of the domain: in the previous example, the time point 4 has the maximum membership degree
1, whose meaning is that 4 is fully possible as value of the defined approximate time point, while
3 and 5 have membership degrees 0.8 and 0.5 respectively, indicating that they are also possible
values of the approximate time point, but to a lower extent than 4.
A duration in time, i.e. a time span , is a pair [Δt, G] and can be denoted by either a set or a range
of time points. A fuzzy time span example is [Δt ={0.8/3, 1./4, 0.7/5}, year ] that means a duration
of about 4 years.
A temporal distance from the origin, i.e. a time distance , is defined as a pair [d, G] in which d is
a positive or negative value, indicating the distance in time granules on G from the origin. In this
case [d=2, day ] means two days after the origin. As t, also d can be a fuzzy set indicating a fuzzy
time distance.
A time interval is a triple [t, Δd, G]; in a crisp case [t=1991, Δd=3, year ] means a range of 3 years
from 1991.
A composite span is a union of spans [Δt i , G i ], not necessarily adjacent and on the same basic
domain G.
An aperiodic time element is a union of time intervals [t i , Δd i , G i ]. The crisp example [t=1-11-
2008, Δd=28, day ] [t=30-11-2008, Δd=31, day ] means 28 days from 1-11-2008 and 31 days
from 30-11-2008.
Finally, a periodic time element is a union of time intervals separated by time distances: [t i , Δd i ,
G i ], [d k , G k ]. For example [t=1-8-2000, Δd=31, day ], [d=1, year ] means every August from year
2000. An example of approximate periodic time element is [t=1-2000, Δd={0.2/1, 0.8/2, 1./3,
0,8/4}, week ], [d=1, year ] that means around the third week of every January from year 2000.
Since in the context of metadata compilation we may have time series that are related to finite repeti-
tions of observations or events, a finite periodic time element is defined as composed of a periodic time
element and a time point:
[t i , Δd i , G i ], [d k , G k ][ t, G]
in which the time point t specifies the end of the repetition.
An example of finite periodic time element is “ every autumn from 2000 to 2005 ” that is formally
expressed as:
[21-09-2000, 91, day ], [1, year ][21-12-2005, day ].
TimeML for Expressing Imperfect Time Indications in Temporal Metadata
TimeML is a markup language of the XML family for describing events, signals and temporal expres-
sions into a text written in natural language. It is designed to address four situations:
1. Time stamping of events (identifying an event in time, instant or interval of validity).
2. Ordering events with respect to one another (relative ordering).
3. Reasoning with contextually underspecified temporal expressions (temporal functions such as 'last
week' and 'two weeks before').
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