A Semantic Representation of Time Intervals in OWL 2
Noura Herradi, Fayc¸al Hamdi and Elisabeth M
´
etais
Cedric Lab, Conservatoire National des Arts et M
´
etiers (CNAM), Paris, France
Keywords:
Ontologies, OWL 2, Temporal Representation.
Abstract:
Representing time over the Semantic Web has always been a challenging issue that many scientific works
were interested to address. To the best of our knowledge, the most important ones focused on models, whereas
Semantic Web and especially OWL 2 offers semantics that can be efficiently used to describe qualitative
diachronic information (i.e. information evolving in time and which start and/or end time is unknown). In this
work, we show the relationship between the OWL 2 semantics and the representation of time intervals; then
we introduce a qualitative representation of temporal information based on a set of SWRL rules, that allows a
sound and complete reasoning mechanism.
1 INTRODUCTION
OWL2 (Motik et al., 2009) allows users to write ex-
plicit, formal conceptualizations of domains models.
It is build upon RDF and RDFS and has the same
kind of syntax. As the main primitives of RDF/RDFS
are related to the organization of the vocabularies
in typed hierarchies using subclass and subprop-
erty relationships, OWL 2 brings more language
primitives besides those presented in its previous
version to allow richer expressiveness. For example,
in addition to the property unqualified cardinality
restrictions available in OWL 1, in OWL 2, even the
qualified cardinality restrictions are possible. Also,
the assertions that an object property is symmetric or
transitive provided by OWL 1 was supplemented in
OWL 2 by the reflexive, irreflexive and asymmetric
object properties assertions. Moreover, the powerful
property chain inclusion implemented in OWL 2
allows a property to be defined as the composition of
several properties, etc. Formal semantics provided
by OWL 2 allows users to describe precisely the
meaning of knowledge; they permit to reason about
this knowledge, besides.
In the 4D-fluents approach (Welty and Fikes,
2006), any time interval can be related with every
other time interval with one basic Allen relation
(Allen, 1983), and all the thirteen Allen relations (cf.
Figure 2) are thus possible. Therefore, the following
Allen operators are all supported: BEFORE, AFTER,
MEETS, METBY, OVERLAPS, OVERLAPPEDBY,
DURING, CONTAINS, STARTS, STARTEDBY,
ENDS, ENDEDBY and EQUALS.
In this work, we introduce a continuity of what
was made before by exploiting the semantics pro-
vided by OWL 2 to give more precision to time
interval representation. We use for this purpose
language constructs provided by the OWL-TIME
ontology (Cox and Little, 2017) which is a W3C
candidate recommendation ontology of concepts
of time. The Tbox classes and properties times
dimensions will be those introduced in (Batsakis
et al., 2017).
The paper is organized as follows. In the next sec-
tion, we present a motivating example to show the im-
pact of properties characteristics on qualitative infor-
mation representation. In section 3 we present our
approach supported by examples of use and the cor-
responding sets of SWRL rules. Background and re-
lated work on time representation in Semantic Web is
discussed in section 4. Finally, we conclude and give
some perspectives in section 5.
2 MOTIVATING EXAMPLE
The 4D-Fluents modeling approach allows represent-
ing individuals through time slices, i.e. captures of an
individual at specific times. And time slices sharing
the same relation have the same time interval (cf. Fig-
ure 1). Moreover, all time intervals of the same quali-
Herradi N., Hamdi F. and MÃl’tais E.
A Semantic Representation of Time Intervals in OWL 2.
DOI: 10.5220/0006518402690275
In Proceedings of the 9th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (KEOD 2017), pages 269-275
ISBN: 978-989-758-272-1
Copyright
c
 2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

Figure 1: An example of time slices in the 4D-Fluents ap-
proach sharing the same time interval.
Figure 2: Allen’s Relations.
tative relation could be linked to each others with one
of the thirteen Allen relations (cf. Figure 2) no matter
the relation occurring within this interval. However,
this solution creates a significant representation prob-
lem. Since the use of Allen’s relations between time
intervals depends on the semantics of properties as it
will be showed in our motivating examples below.
Because time slices could be captures of the same
individuals in different time intervals, linking be-
tween these time intervals with some Allen’s relations
could not be possible, since the object property be-
tween their time slices could have restrictions, limit-
ing thereby the Allen’s relations using possibilities.
We use for expressing our motivating examples,
object properties coming from PersonLink
1
, an OWL
2 ontology representing family relationships. We
chose this ontology due to the rigorous and precise
axioms definitions it provides through OWL 2 seman-
tics.
As a motivating example, We consider the follow-
ing sentences coming from a questionnaire on how
does people express their relationships
2
:
(1) John was married to Sarah.
(2) John was married to Nicole.
These two sentences clearly indicate that John
was married twice, once to Sarah and the other time
to Nicole. Because we have no further information
about these relationships, two specific personLink
1
Available at: http://cedric.cnam.fr/isid/
ontologies/PersonLink.owl
2
The names were changed to keep the anonymity of the
people questioned
Figure 3: Representation in 4D-Fluents of an example of
straight husband relation.
Figure 4: Representation in 4D-Fluents of an example of
polygynous husband relation.
object properties are then possible to express these
sentences. If the (1) and (2) relations hold within a
monogamous heterosexual marriage, then John has
the right to have only one wife at a time interval, and
the object property used to express this relationship
is ”plink:straightHusbandOf” (cf. Figure 3) which is
functional (i.e. accepts only one value in its range).
That means that the two time intervals of (1) and (2)
must be strictly disjoint.
But if John is polygynous and his marriages
with Sarah and Nicole were within a polygynous
heterosexual context, he can have several wives at
intersected time intervals (cf. Figure 4). Thus, using
personLink, the maximum n number of permitted
wives will be expressed using the maximal cardinal-
ity restriction of the ”plink:polygynousHusbandOf”
object property, entailing the time intervals n inter-
sections possibilities.
More examples are presented with every OWL 2
characteristic of interest in the section 3.

3 APPROACH
In our approach, we consider that relations between
time intervals in 4D-Fluents depend on the property
used to relate the two time slices having a relation-
ship within the same time interval (i.e. the time
interval during which the property holds between
two time slices). For our examples, we may use both
quantitative relations (i.e. involving known temporal
instants or intervals) and qualitative ones (i.e. the
exact values of temporal instants or intervals are
unknown). Some OWL 2 property restrictions have
a direct impact on time intervals, and each property
restriction determines the possible Allen relation and
thus gives us precisely the possible Allen relation to
use to relate between time intervals.
OWL 2 is essentially the description logics
SR OI Q (D) (Horrocks et al., 2006) which define
concept descriptions inductively by a set of con-
structors, starting with a set N
C
of concept (or class)
names, a set N
R
of role (or property) names, and a
set N
I
of individual names. The semantics of the
concept descriptions in S R OI Q (D) are defined in
terms of an interpretation I such as I=(4
I
,
.I
) where
4
I
its domain which consists of a non-empty set
of individuals and
.I
is its function of interpretation
which maps concepts names A ∈ N
C
to a subset A
I
⊆ 4
I
, role names R ∈ N
R
to a binary relation R
I
⊆
4
I
× 4
I
, and each individual name a ∈ N
I
to an
individual a
I
⊆ 4
I
. The interpretation of complex
concepts and roles follows from the interpretation of
the basic entities showed in Table 1.
For the rest of the article, we will use the following
notations:
• tsTimeSliceOf ∈ N
R
;
• x, y, z, a, b, c individuals from the range of
tsTimeSliceOf;
• TimeSlice ∈ N
C
;
• TimeInterval ∈ N
C
;
• ∀ i ∈ IN, TimeSlice(ts
i
);
• ∀ i ∈ IN, TimeInterval(I
i
);
• r ∈ N
R
such as ∃ r.> v TimeSlice (Domain), > v
∀ r.TimeSlice (Range);
• s ∈ N
R
such as ∃ s.> v TimeSlice (Domain), > v
∀ s.TimeSlice (Range);
• C ∈ N
C
;
• D ∈ N
C
;
In the next subsections, we will show the result
of each OWL 2 object property characteristic having
impact on topological (ordering) relations among
time intervals. For that purpose, we will use the
OWL-TIME ontology
3
temporal concepts.
Reasoning over temporal information is done us-
ing a set of DL-safe rules (Motik et al., 2006) ex-
pressed in SWRL (Horrocks et al., 2004), as it is the
only solution in accordance with current OWL spec-
ifications while maintaining decidability. These rea-
soning rules are based on the basic Allen’s relations
provided by the OWL-TIME ontology and are spe-
cific to each property. SWRL rules were added for all
object properties of PersonLink having restrictions,
and reasoning was done using Pellet (Sirin et al.,
2007) as it is, to the best of our knowledge, one of
the reasoners supporting SWRL and the only reasoner
supporting date/time comparisons needed for quanti-
tative representations.
3.1 Functional Property
A functional property is a property that can have
only one value in its range (> v ≤ 1r), i.e. each
instance x can have only one unique instance y at a
time for a given functional property. So, if a property
is functional, time slices participating in the relation
represented by this property share the same time
interval but all time intervals they are sharing outside
this relationship with the same functional property
must be disjoints with this time interval. Therefore,
the relation between this time interval and new time
intervals of the same functional property will be
one of the following Allen relations: AFTER or
BEFORE.
If:
tsTimeInterval(ts
1
, I
1
), tsTimeInterval(ts
2
, I
1
),
tsTimeInterval(ts
3
, I
2
), tsTimeInterval(ts
4
, I
2
),
tsTimeSliceOf(ts
1
, a) and tsTimeSliceOf(ts
3
, a)
Then:
> v after(tsTimeInterval(ts
1
, I
1
),
tsTimeInterval(ts
3
, I
2
))
t before(tsTimeInterval(ts
1
, I
1
),
tsTimeInterval(ts
3
, I
2
))
SWRL:
r(?ts
1
, ?ts
2
) ∧ r(?ts
3
, ?ts
4
) ∧
tsTimesSliceO f (?ts
1
, ?a) ∧
tsTimesSliceO f (?ts
3
, ?a) ∧
tsTimesSliceO f (?ts
2
, ?b) ∧
tsTimesSliceO f (?ts
4
, ?c) ∧
3
available at: https://www.w3.org/TR/owl-time/

Table 1: The description logic S R OI Q (D) basic Syntax and semantics.
Name Syntax Semantics
individual name a a
I
atomic role R R
I
inverse role R
−
{(x, y) | (y, x) ∈ R
I
}
universal role U 4
I
× 4
I
atomic concept A A
I
intersection C u D C
I
∩ D
I
union C t D C
I
∪ D
I
complement ¬C 4
I
\ C
I
top concept > 4
I
bottom concept ⊥ ∅
existential restriction ∃ R.C {x ∈ 4
I
| ∃y ∈ 4
I
: (x, y) ∈ r
I
∧ y ∈ C
I
}
universal restriction ∀R.C {x ∈ 4
I
| ∀y ∈ 4
I
: (x, y) ∈ r
I
∧ y ∈ C
I
}
at-least restriction >nR.C {x ∈ 4
I
| atleastny ∈ 4
I
: (x, y) ∈ r
I
∧ y ∈ C
I
}
at-most restriction 6 {x ∈ 4
I
| atmostny ∈ 4
I
: (x, y) ∈ r
I
∧ y ∈ C
I
}
local reflexivity ∃R.Self {x | (x, x) ∈ R
I
}
nominal {a} {a
I
}
tsTimeInterval(?ts
1
, ?I
1
) ∧
tsTimeInterval(?ts
2
, ?I
1
) ∧
tsTimeInterval(?ts
3
, ?I
2
) ∧
tsTimeInterval(?ts
4
, ?I
2
) →
intervalDis joint(?I
1
, ?I
2
)
Example 1: John is a straightHusbandOf Sarah in a
time interval t
1
and a straightHusbandOf Nicole in a
time interval t
2
, the time intervals t
1
and t
2
are distinct
which means that t
1
takes place before or after t
2
.
3.2 Inverse Functional Property
In this type of property, the object determines the
subject, i.e. the property can accept only one and
unique value in its domain at a time for a given object.
Therefore, if a relation r(x, y) of inverse func-
tional type links between two individuals x and y
at a time interval t
1
, and this same relation r links
between x and another individual z at another time
interval t
2
, this time interval t
2
must be BEFORE or
AFTER t
1
. This could be written as following:
If:
r(ts
1
, ts
2
), r(ts
3
, ts
4
),
tsTimeSliceOf(ts
2
, x), tsTimeSliceOf(ts
4
, x),
tsTimeInterval(ts
2
, I
1
) and tsTimeInterval(ts
4
, I
2
)
Then:
> v after(tsTimeInterval(ts
1
, I
1
),
tsTimeInterval(ts
3
, I
2
))
t before(tsTimeInterval(ts
1
, I
1
),
tsTimeInterval(ts
3
, I
2
))
SWRL:
r(?ts
1
, ?ts
2
) ∧ r(?ts
3
, ?ts
4
) ∧
tsTimesSliceO f (?ts
1
, ?a) ∧
tsTimesSliceO f (?ts
2
, ?b) ∧
tsTimesSliceO f (?ts
3
, ?c) ∧
tsTimesSliceO f (?ts
4
, ?b) ∧
tsTimeInterval(?ts
1
, ?I
1
) ∧
tsTimeInterval(?ts
2
, ?I
1
) ∧
tsTimeInterval(?ts
3
, ?I
2
) ∧
tsTimeInterval(?ts
4
, ?I
2
) →
intervalDis joint(?I
1
, ?I
2
)
Example 2: James is the direct supervisor of Thomas
at a period of time t
1
, and Carlos is the direct supe-
rior of Thomas another period of time t
2
. Since the
relation hierarchical superior is of type inverse func-
tional, the time intervals t
1
and t
2
must be disjoint, i.e.
t
1
happens before or after t
2
.
3.3 Symmetric Property
A time slice x connected to another time slice y by a
symmetric property at a specific time interval means
that the time slice y is linked to the time slice x by the
same object property within the same time interval.
By definition, the symmetric relations have thus
equal time intervals:
Let r ∈ N
R
such as r is symmetric r = r
−
;
If:
r(ts
1
, ts
2
), r(ts
3
, ts
4
),
tsTimeSliceOf(ts
1
, x), tsTimeSliceOf(ts
4
, x),
tsTimeSliceOf(ts
2
, y), tsTimeSliceOf(ts
3
, y),
tsTimeInterval(ts
1
, I
1
) and tsTimeInterval(ts
3
, I
2
)

Then:
> v Equals (I
1
, I
2
)
SWRL:
r(?ts
1
, ?ts
2
) ∧ r(?ts
3
, ?ts
4
) ∧
tsTimesSliceO f (?ts
1
, ?a) ∧
tsTimesSliceO f (?ts
2
, ?b) ∧
tsTimesSliceO f (?ts
3
, ?b) ∧
tsTimesSliceO f (?ts
4
, ?a) ∧
tsTimeInterval(?ts
1
, ?I
1
) ∧
tsTimeInterval(?ts
2
, ?I
1
) ∧
tsTimeInterval(?ts
3
, ?I
2
) ∧
tsTimeInterval(?ts
4
, ?I
2
) → intervalEquals(?I
1
, ?I
2
)
Example 3: Marta is the partner of Trevor at a time
interval t
1
. Because the partner of relationship is sym-
metric, Trevor is also partner of Marta at a time inter-
val t
2
and the time intervals t
1
and t
2
are equal.
3.4 Transitive Property r ◦ r v r
A transitive relation is a relation which binds
between a succession of individuals, and which
consequently allows to bind the first individual
to the last one. In this type of relation, the time
interval linking between the first individual and
the last one is at least equal to the intersection of
the other time intervals of the individuals’ succession.
For the transitive diachronic property r :
If:
r(ts
1
, ts
2
), r(ts
3
, ts
4
),
tsTimeSliceOf(ts
1
, x), tsTimeSliceOf(ts
2
, y),
tsTimeSliceOf(ts
3
, y), tsTimeSliceOf(ts
4
, z),
tsTimeInterval(ts
2
, I
1
), tsTimeInterval(ts
3
, I
2
),
TimeInterval(I), during(I, I
1
) and during (I, I
2
)
Then:
r(ts
0
1
, ts
0
4
) with tsTimeInterval(ts
0
1
, I),
tsTimeSliceOf(ts
0
1
, x), tsTimeSliceOf(ts
0
4
, z)
This means that the time interval of the deduced
relation using transitivity will be at least equal to the
period representing the intersection of time intervals
of relations from which the relation is deduced.
Otherwise, none of Allen relations could be used,
because there is no interval intersection.
SWRL:
r(?ts
1
, ?ts
0
1
) ∧ r(?ts
2
, ?ts
0
2
) ∧ r(?ts
3
, ?ts
0
3
) ∧
tsTimesSliceO f (?ts
1
, ?a) ∧
tsTimesSliceO f (?ts
0
1
, ?b) ∧
tsTimesSliceO f (?ts
2
, ?b) ∧
tsTimesSliceO f (?ts
0
2
, ?c) ∧
tsTimesSliceO f (?ts
3
, ?a) ∧
tsTimesSliceO f (?ts
0
3
, ?z) ∧
tsTimeInterval(?ts
1
, ?I
1
) ∧
tsTimeInterval(?ts
0
1
, ?I
1
) ∧
tsTimeInterval(?ts
2
, ?I
2
) ∧
tsTimeInterval(?ts
0
2
, ?I
2
) ∧
tsTimeInterval(?ts
3
, ?I
3
) ∧
tsTimeInterval(?ts
0
3
, ?I
3
) ∧
intervalDis joint(?I
3
, ?I
1
) ∧
intervalDis joint(?I
3
, ?I
2
) → Nothing
Example 4: Stefan is the hierarchical superior of
Monica in a time interval t
1
and Monica is the hier-
archical superior of Peter in a time interval t
2
. The
”hierarchical superior” is a transitive relation, so Ste-
fan is therefore the hierarchical superior of Peter in a
time interval t
3
, and this time interval is at least equal
to the intersection of the t
1
and t
2
time intervals.
3.5 Inverse of Property
An inverse of property is a property that inverses
another property, which means that both of these
properties concern the same individuals x and y at
two time intervals t
1
and t
2
. Intuitively, these time
intervals are equal:
Let r ∈ N
R
and s ∈ N
R
such as r = s
−
;
If:
r(ts
1
, ts
2
), s(ts
2
, ts
1
),
tsTimeSliceOf(ts
1
, x), tsTimeSliceOf(ts
2
, y),
tsTimeInterval(ts
1
,I
1
)and tsTimeIntervalOf(ts
2
, I
2
)
Then:
Equals (I
1
, I
2
)
SWRL:
r(?ts
1
, ?ts
2
) ∧ r(?ts
3
, ?ts
4
) ∧
tsTimesSliceO f (?ts
1
, ?a) ∧
tsTimesSliceO f (?ts
2
, ?b) ∧
tsTimesSliceO f (?ts
3
, ?b) ∧
tsTimesSliceO f (?ts
4
, ?a) ∧
tsTimeInterval(?ts
1
, ?I
1
) ∧
tsTimeInterval(?ts
2
, ?I
1
) ∧
tsTimeInterval(?ts
3
, ?I
2
) ∧
tsTimeInterval(?ts
4
, ?I
2
) → intervalEquals(?I
1
, ?I
2
)
Example 5: John is the straight husband of Sarah in a
time interval t
1
and Sarah is the straight wife of John
in a time interval t
2
. The ”husband of” property is the

inverse of the ”wife of” one thus their time intervals
t
1
and t
2
are equal.
3.6 Properties Cardinality Restrictions
OWL 2 allows both qualified and unqualified cardi-
nality restrictions, i.e. it gives the users the ability to
put restrictions on the number of instances a property
may have. In the sections 3.6.1 and 3.6.2, we will
present the repercussions the max and min cardinality
restrictions have on the representation of time inter-
vals relations.
3.6.1 Max Cardinality Restriction
≤ nr, n ∈ IN
For a property with n maximal cardinality restriction,
any new (n + 1) relation using this property must
have a time interval which has no intersection with
the previous (n) time intervals:
Let r(ts
i1
, ts
i2
) ∀ i ∈ [1, n+1],
If:
tsTimesSliceOf(ts
i1
, x) and tsTimeInterval(ts
i1
, I
i
)
and TimeInterval(I) ∀ i ∈ [1,n] during (I, I
i
)
Then :
> v before (I
n+1
, I) t after(I
n+1
, I)
SWRL:
r(?ts
1
, ?ts
0
1
) ∧ r(?ts
n
, ?ts
0
n
) ∧
tsTimesSliceO f (?ts
1
, ?a) ∧
tsTimesSliceO f (?ts
n
, ?a) ∧
tsTimesSliceO f (?ts
n+1
, ?a) ∧
tsTimeInterval(?ts
1
, ?I
1
) ∧
tsTimeInterval(?ts
n
, ?I
n
) ∧
tsTimeInterval(?ts
n+1
, ?I
n+1
) ∧
notIntervalDis joint(?I
n+1
, ?I
1
) ∧
notIntervalDis joint(?I
n+1
, ?I
n
) → Nothing
Example 6: Neil is the polygynous husband of Car-
ole, and he is also the polygynous husband of Nadia
and Maya in the context of a culture that permits the
polygamy and allows to a man to get married to two
women at the most. The time interval of one of these
three relations is disjoint (i.e. before or after) with the
intersection of the two other relations time intervals
left.
3.6.2 Min Cardinality Restriction
≥ nr, n ∈ IN
In the case of a minimal cardinality restriction, an in-
dividual x, participates in a relation with a minimal
limitation n in it’s range value, witch means that this
individual x must have the same relation with at least
n other individuals, and that all time intervals con-
cerning each of these relations must be intersected.
It seems intuitive when it concerns the natural lan-
guage. However, this temporal information cannot
be introduced because of the Open-World Assump-
tion (Drummond and Shearer, 2006).
4 BACKGROUND AND RELATED
WORK
Different approaches have been proposed to repre-
sent time evolution in Semantic Web. Some of them
like Temporal Description Logics (TDLs) (Artale and
Franconi, 2000) relies on the standard Description
Logics (Baader et al., 2008) which represent the ba-
sics of OWL, they provide further additional con-
structs and then offer more expressiveness over stan-
dard DLs while maintaining DLs decidability. How-
ever, they require extending OWL syntax and se-
mantics with the additional temporal concepts. On
the other hand, an other work approach (Klein and
Fensel, 2001) proposes to make versions of the ontol-
ogy, whenever a change occurs, even if it is a small
one. In this approach, all the versions of the ontology
remain independent from each others since there is no
relation between evolving concepts.
Reification (Gomez et al., 2000) is also an
approach that permits to add the time dimension
in OWL, since it allows the representation of n-ary
relations. However, this approach doesn’t make the
predicate characteristics reachable since it’s consid-
ered as a new object of the reified relation rather
than a predicate of the relation. The 4D-Fluents
approach and its alternative one (n-ary relations (Noy
et al., 2006)) represent time through a 4-Dimensional
model, where each concept has its own time slices
(i.e. images at specific times), making the changes
occur only on the temporal parts and keeping there-
fore the static part unchanged. The n-ary relations
approach is an alternative of the 4D-fluents one since
it permits less proliferation of objects than the 4D-
fluents approach does. The 4D-Fluents approach (and
consequently the n-ary relations) keeps the semantics
of all TBOX components and makes available their
OWL 2 characteristics and restrictions. All these
research activities represented above were made

with the aim of creating models and frameworks
introducing the temporal dimension into ontologies
conception.
(Batsakis et al., 2017) proposes a representation
and reasoning over qualitative relations following the
4D-Fluents model and using a set of SWRL rules to
represent Allen’s relations between time intervals. In
this paper, we present OWL 2 properties and charac-
teristics which semantics have direct impact on time
intervals representation using appropriate Allen’s re-
lations.
5 CONCLUSION AND FUTURE
WORK
We have shown in this work through a motivating
example that relations between time intervals of 4D-
Fluents ontologies depend on OWL 2 semantics, also
that Allen’s relations linking between qualitative time
intervals of the same properties are restricted and are
determined by the property’s characteristics and se-
mantics. For each OWL 2 property of interest, we
defined and made a representation of the impact of its
characteristics and restrictions on time interval rela-
tions. We have also given examples of use for each
of these characteristics, and then we proposed a set
of SWRL rules to allow reasoning over time intervals
relations while retaining decidability.
We plan to apply this work to two applications:
the storage and the retrieval of the entourage of el-
derly people in the Captain Memo memory prosthe-
sis (Herradi et al., 2015), and the representation and
study of prosopography in historical data bases.
ACKNOWLEDGMENTS
This paper has been partially supported by the QUAL-
HIS (CNRS-Mastodons) French project.
REFERENCES
Allen, J. F. (1983). Maintaining Knowledge about Temporal
Intervals. Communications of the ACM, 26:832–843.
Artale, A. and Franconi, E. (2000). A survey of temporal
extensions of description logics. Ann. Math. Artif. In-
tell., 30(1-4):171–210.
Baader, F., Horrocks, I., and Sattler, U. (2008). Description
logics. Foundations of Artificial Intelligence, 3:135–
179.
Batsakis, S., Petrakis, E. G. M., Tachmazidis, I., and Anto-
niou, G. (2017). Temporal representation and reason-
ing in OWL 2. Semantic Web, 8(6):981–1000.
Cox, S. and Little, C. (2017). Time ontology in
OWL. Candidate recommendation, W3C.
https://www.w3.org/TR/2017/CR-owl-time-
20170606/.
Drummond, N. and Shearer, R. (2006). The open world
assumption. In eSI Workshop: The Closed World of
Databases meets the Open World of the Semantic Web,
volume 15.
Gomez, C., Lopez, J. R., and Olive, A. (2000). Evolv-
ing temporal conceptual schemas: the reification case.
In International Workshop on Principles of Software
Evolution, pages 78–82.
Herradi, N., Hamdi, F., M
´
etais, E., Ghorbel, F., and
Soukane, A. (2015). Personlink: An ontology repre-
senting family relationships for the CAPTAIN MEMO
memory prosthesis. In ER Workshops, volume 9382
of Lecture Notes in Computer Science, pages 3–13.
Springer.
Horrocks, I., Kutz, O., and Sattler, U. (2006). The even
more irresistible SROIQ. In KR, pages 57–67. AAAI
Press.
Horrocks, I., Patel-Schneider, P. F., Boley, H., Tabet, S.,
Grosof, B., and Dean, M. (2004). Swrl: A semantic
web rule language combining owl and ruleml. W3c
member submission, W3C.
Klein, M. and Fensel, D. (2001). Ontology versioning on
the semantic web. In Cruz, I. F., Decker, S., Euzenat,
J., and McGuinness, D. L., editors, Proceedings of the
1st International Semantic Web Working Symposium,
pages 75–91, Stanford University, CA, USA.
Motik, B., Horrocks, I., Rosati, R., and Sattler, U. (2006).
Can OWL and logic programming live together hap-
pily ever after? In International Semantic Web Con-
ference, volume 4273 of Lecture Notes in Computer
Science, pages 501–514. Springer.
Motik, B., Patel-Schneider, P. F., Parsia, B., Bock, C., Fok-
oue, A., Haase, P., Hoekstra, R., Horrocks, I., Rutten-
berg, A., Sattler, U., et al. (2009). Owl 2 web ontology
language: Structural specification and functional-style
syntax. W3C recommendation, 27(65):159.
Noy, N., Rector, A., Hayes, P., and Welty, C. (2006). Defin-
ing n-ary relations on the semantic web. W3C working
group note, 12(4).
Sirin, E., Parsia, B., Grau, B., Kalyanpur, A., and Katz, Y.
(2007). Pellet: A practical OWL-DL reasoner. Jour-
nal of Web Semantics, 5(2):51–53.
Welty, C. A. and Fikes, R. (2006). A reusable ontology for
fluents in OWL. In FOIS, volume 150 of Frontiers
in Artificial Intelligence and Applications, pages 226–
236. IOS Press.