Merging the DOLCE and PSL Upper Ontologies
Carmen Chui and Michael Gr
¨
uninger
Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, M5S 3G8, Canada
Keywords:
DOLCE, First-order logic, Ontology Merging, Ontology Repositories, Ontology Verification, PSL, Upper
Ontologies.
Abstract:
In this paper, we examine the relationships between the axiomatization of participation in two upper ontolo-
gies, the Process Specification Language (PSL) and the Descriptive Ontology for Linguistic and Cognitive
Engineering (DOLCE). We discuss the obstacles faced to formalize the relationships between these ontologies
and provide an overview of the methodology undertaken to merge the ontologies together. We introduce new
ontologies that serve to bridge the PSL and DOLCE ontologies together to allow us to specify the mappings
between them. We illustrate how ontology verification is used to show faithful interpretations between the two
upper ontologies.
1 INTRODUCTION
In order to understand how two ontologies are related
to each other, there is a need to explicitly identify the
potential relationships between them, and we cannot
understand such relationships without analyzing the
axioms of the ontologies. In this paper, we explore the
relationships between two upper ontologies – the Pro-
cess Specification Language (PSL) and the Descrip-
tive Ontology for Linguistic and Cognitive Engineer-
ing (DOLCE). Our objective is to determine whether
one upper ontology can be interpreted in the other by
using techniques from ontology verification to exam-
ine the model-theoretic properties of both ontologies.
In particular, we examine how the theories found in
DOLCE can be mapped to the PSL ontology by using
existing ontologies found in the COmmon Logic On-
tology REpository (COLORE), and then discuss the
steps needed to bridge these ontologies together.
With respect to ontology mapping, the research
community is often interested in determining whether
two contextually equivalent ontologies contain the
same, or similar, axioms and descriptions of concepts.
The intent of ontology mapping is to make semantic
matches between the ontologies and to utilize these
matches to aid us in reasoning tasks (Kalfoglou and
Schorlemmer, 2005). Ontology merging allows the
creation of a new ontology from two, possibly over-
lapping, ontologies (Euzenat and Shvaiko, 2007; Choi
et al., 2006). Additionally, in this work, we utilize on-
tology mapping along with ontology merging to iden-
tify similarities and conflicts between the ontologies
(Choi et al., 2006).
Our approach to ontology mapping is based on on-
tology verification, which is concerned with the re-
lationship between the intended models of an ontol-
ogy and the models of the axiomatization of the on-
tology. In particular, the models of an ontology are
characterized up to isomorphism and then shown to
be equivalent to the intended models of the ontology.
The objective is the construction of the models of one
ontology from the models of another ontology by ex-
ploiting the metatheoretic relationships (such as faith-
ful interpretation and definable equivalence) between
these ontologies and existing theories in COLORE.
In this paper, we begin by examining the funda-
mental ontological commitments of the DOLCE and
PSL ontologies with respect to the notion of partic-
ipation. We selected these two ontologies because
they appeared to have several commonalities in their
axiomatizations of time, process, and participation.
However, when we examine the fundamental ontolog-
ical commitments of these ontologies, we can identify
two major obstacles to their integration they differ
on their time ontologies (time points vs. time inter-
vals) and they make different assumptions about how
objects participate in activity occurrences. We intro-
duce sets of ontologies that combine both time points
and intervals, and which can serve as a bridge be-
tween the time ontologies of DOLCE and PSL. We
also extend the PSL ontology with new axioms re-
garding the notion of participation. Figure 1 illus-
16
Chui C. and Grüninger M..
Merging the DOLCE and PSL Upper Ontologies.
DOI: 10.5220/0005027100160026
In Proceedings of the International Conference on Knowledge Engineering and Ontology Development (KEOD-2014), pages 16-26
ISBN: 978-989-758-049-9
Copyright
c
2014 SCITEPRESS (Science and Technology Publications, Lda.)
trates the bridges that are created to formalize the re-
lationships between the DOLCE and PSL ontologies.
Finally, we show that the resulting extensions of PSL
can faithfully interpret the DOLCE ontology, with an
emphasis on the semi-automatic verification of these
ontologies.
2 ONTOLOGY MERGING
THROUGH VERIFICATION
Two key techniques used in this paper are ontology
mapping and the design of ontologies through the
merging of existing ontologies. In this section, we
discuss the notion of ontology verification and how
it is used to support ontology mapping. We also re-
view existing ontology merging techniques and dis-
cuss how these are related to our approach.
2.1 Ontology Verification
Verification is concerned with the relationship be-
tween the intended models of an ontology and the
models of the axiomatization of the ontology
1
. In
particular, we want to characterize the models of an
ontology up to isomorphism and determine whether
or not these models are equivalent to the intended
models of the ontology. In practice, the verification
of an ontology is achieved by demonstrating that it
is equivalent to another logical theory whose models
have already been characterized up to isomorphism.
We therefore need to understand the different relation-
ships among logical theories, which will also lead us
to specify the mappings between ontologies.
A fundamental property of an ontology is the
range of concepts and relations that it axiomatizes.
Within the syntax, this is captured by the notion of
the signature of the ontology. The signature Σ(T ) of
a logical theory T is the set of all constant symbols,
function symbols, and relation symbols that are used
in the theory. The simplest relationships between log-
ical theories are the different notions of extension, in
which the signature of one theory is a subset of the
signature of another theory. Let T
1
, T
2
be two first-
order theories such that Σ(T
1
) Σ(T
2
). We say that
T
2
is an extension of T
1
iff for any sentence σ L (T
1
),
if T
1
|= σ then T
2
|= σ.
1
A first-order ontology is a set of first-order sentences
(axioms) that characterize a first-order theory, which is the
closure of the ontology’s axioms under logical entailment.
In the rest of the paper we will simply drop the term first-
order and assume ontologies and theories to be first-order.
T
2
is a conservative extension of T
1
iff for any sen-
tence σ L(T
1
),
T
2
|= σ iff T
1
|= σ.
T
2
is a non-conservative extension of T
1
iff T
2
is an
extension of T
1
and there exists a sentence σ Σ(T
1
)
so that
T
1
2 σ and T
2
|= σ.
Non-conservative extension plays a key role in
COLORE. Ontologies within the repository are orga-
nized into sets of ontologies with the same signature
known as hierarchies. The set of ontologies within a
hierarchy are ordered by non-conservative extension;
an ontology is a root theory of hierarchy if it is not
extended by any other ontology within the same hier-
archy.
If the logical theories have different signatures,
there is a range of fundamental metalogical relation-
ships which are used in ontology verification. All
of them consider mappings between the signatures of
the theories that preserve entailment and satisfiabil-
ity. The basic relationship between theories T
A
and
T
B
is the notion of interpretation, which is a mapping
from the language of T
A
to the language of T
B
that
preserves the theorems of T
A
(Enderton, 1972). The
interpretation is faithful if the mapping also preserves
the satisfiable sentences of T
A
.
One notion of equivalence among theories is mu-
tual faithful interpretability, that is, T
1
faithfully in-
terprets T
2
and T
2
faithfully interprets T
1
. An even
stronger equivalence relation is that of logical syn-
onymy: Two ontologies T
1
and T
2
are synonymous
iff there exists an ontology T
3
with the signature
Σ(T
1
)Σ(T
2
) that is a definitional extension of T
1
and
T
2
.
If there is an interpretation of T
A
in T
B
, then there
exists a set of sentences (referred to as translation
definitions) in the language L
A
L
B
of the following
form, where p
i
(x) is a relation symbol in L
A
and ϕ(x)
is a formula in L
B
:
(x) p
i
(x) ϕ(x)
Thus, T
B
interprets T
A
if there exists a set of
translation definitions such that
T
B
|= T
A
T
B
faithfully interprets T
A
if T
B
is a conservative
extension of T
A
.
2.2 Existing Merging Techniques
Within the applied ontology community, there exist
various terms used to describe the notion of ontol-
ogy merging; some of these terms have slight dif-
ferences in the notion of merging but all agree that
MergingtheDOLCEandPSLUpperOntologies
17
a new ontology is created from two ontologies. In
(Choi et al., 2006), the authors indicate that ontology
merging is the process of generating a new ontology
from two or more existing and different ontologies
that contain similar notions of a given subject. In (Eu-
zenat and Shvaiko, 2007), the notion is similar, where
the new merged ontology contains the knowledge of
the source ontologies. Other notions of merging dis-
cussed in (de Bruijn et al., 2006; Zimmermann et al.,
2006) indicate that ontology merging results in a new
ontology that is a union of two source ontologies, and
captures all of the knowledge found in the source on-
tologies.
Bridge axioms are another term used to describe
axioms that relate the terms of two or more ontologies
together, and serve as the basis for ontology merg-
ing when the ontologies are expressed in the same
language (Euzenat and Shvaiko, 2007; Zimmermann
et al., 2006). They are often written in the form
of subsumption axioms (Zimmermann et al., 2006;
Stuckenschmidt et al., 2005); we make the distinction
here that the notion of ‘bridging’ used in our approach
is not restricted to subsumption axioms, but of the cre-
ation of an ontology (resulted from the merge) and the
usage of translation definitions to illustrate faithful in-
terpretations between theories.
Ontology mappings are used to formalize the cor-
respondences between the entities of one ontology
with the entities of another (Euzenat and Shvaiko,
2007). There are several notions of mappings which
will not be discussed in this section; we direct the
reader to (Choi et al., 2006) for such distinctions. In
this work, we utilize translation definitions to specify
the mappings between the theories.
Our approach to ontology merging is distinct from
these existing techniques as it utilizes ontology verifi-
cation in the process to ensure that the source theories,
along with the new intermediary theory, are faithfully
interpretable with one another. As well, we provide
direct mappings between the concepts in the ontolo-
gies through the use of translation definitions which
are first-order axiomatizations of the interpretations
between the ontologies.
3 BACKGROUND
DOLCE is often known as an ontology of endurants
(objects) and perdurants (processes). Similarly, the
PSL ontology also axiomatizes classes and properties
of objects and activity occurrences. In this section, we
briefly review these two upper ontologies, and we re-
view the different ontological commitments that they
make. It will be these differences which will become
the focus for the design of new bridge ontologies in
the remainder of the paper.
3.1 PSL-Core
The Process Specification Language (PSL) is an on-
tology designed to facilitate the correct and complete
exchange of process information among manufactur-
ing systems (Gr
¨
uninger, 2009). These applications
include scheduling, process modelling, process plan-
ning, production planning, simulation, and project
management. The PSL ontology is organized into a
core theory, PSL-Core
2
and a set of partially ordered
extensions; the core ontology consists of four disjoint
classes: activities can have zero or more occurrences,
activity occurrences begin and end at time points, time
points constitute a linear ordered set with end points
at infinity, and objects are elements that are not activ-
ities, occurrences, or time points (Gr
¨
uninger, 2009).
In PSL, the ternary relation, participates in(x, o, t), is
used to specify that an object x participates in an ac-
tivity occurrence o at a time point t. In other words, an
object can participate in an activity occurrence only at
those time points at which both the object exists and
the associated activity is occurring.
There are five additional modules within the PSL
ontology T
occtree
(which is closely related to situa-
tion calculus), T
subactivity
(which axiomatizes the com-
position relation on activities), T
atomic
(which axiom-
atizes concurrent activities), T
complex
(which axioma-
tizes complex activities), and T
actocc
(which axioma-
tizes the composition relation on occurrences of com-
plex activities). However, none of these notions corre-
spond to concepts within DOLCE, so the only part of
the PSL ontology considered in this paper is restricted
to PSL-Core.
3.2 DOLCE
As the first module of the WonderWeb library of
foundational ontologies, the Descriptive Ontology for
Linguistic and Cognitive Engineering (DOLCE) aims
to capture the categories which underlie natural lan-
guage and human common sense (Masolo et al.,
2003). DOLCE is based on the distinction between
enduring and perduring entities, referred to as con-
tinuants and occurrents, where the fundamental dif-
ference between the two is related to their behaviour
in time (Masolo et al., 2003). Endurants are wholly
present at any time: they are observed and perceived
as a complete concept, regardless of a given snapshot
of time. Perdurants, on the other hand, extend in time
2
http://colore.oor.net/psl core/psl core.clif
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18
by accumulating different temporal parts, so they are
only partially present at any given point in time.
Based on the distinction between endurants
and perdurants, DOLCE has been partially mod-
ularized into the following modules in (Chui,
2013): T
dolce taxonomy
(which axiomatizes the sub-
sumption and disjointness of DOLCE categories),
T
dolce mereology
(which axiomatizes parthood for atem-
poral entities), T
dolce time mereology
(which axioma-
tizes a mereology on time intervals), T
dolce present
(which axiomatizes an entity’s existence in time),
T
dolce temporary parthood
(which axiomatizes the time-
indexed parthood of entities), T
dolce constitution
(which
axiomatizes the co-location of different entities in the
same space-time), and T
dolce participation
(which ax-
iomatizes the participation of entities).
The authors of (Kutz and Mossakowski, 2011)
have shown that the first-order axiomatization of
DOLCE is consistent and have provided an alterna-
tive modularization of ontology; we have adapted
their axioms in the results of this paper and included
them in COLORE
3
. The concepts found within the
T
dolce participation
, T
dolce time mereology
, and T
dolce present
theories are considered in this work as they corre-
spond with concepts found in PSL-Core and other
time ontologies in COLORE.
3.3 Relationships among the Ontologies
In order to understand how the PSL ontology is re-
lated to DOLCE, we begin by outlining some obser-
vations of both ontologies. As shown on the left-hand
side of Figure 1, the various subtheories of DOLCE
are depicted as modules in the ontology. There are
no relations in the PSL ontology that intuitively cor-
respond to the concepts of temporary parthood, con-
stitution, or dependence within DOLCE. On the other
hand, the PSL ontology focuses on relations between
activity occurrences, objects, and time points. In
this paper, we therefore focus on the three subtheo-
ries of DOLCE that axiomatize relationships between
perdurants, endurants, and time intervals: participa-
tion T
dolce participation
, being present T
dolce present
, and
time mereology T
dolce time mereology
. In DOLCE, time
intervals are used to describe temporal objects in
T
dolce participation
and T
dolce present
, all of which con-
tain T
dolce time mereology
. DOLCE does not contain an
ordering on time, but has a time mereology. In con-
trast, the T
psl core
PSL-Core ontology uses time points
to describe the temporal aspects of objects and activ-
ity occurrences, as well as uses an ordering on time,
but does not contain a time mereology. From this ob-
servation, both ontologies appear to have intuitions of
3
http://colore.oor.net/dolce/
perdurants/endurants and activity occurrences/objects
being present and participating in some time con-
struct, yet these intuitions seem to be quite different,
and the relationship between the two ontologies is not
obvious.
The second DOLCE module that we consider is
T
dolce participation
; this subtheory contains the follow-
ing axiom (Ad35 in (Masolo et al., 2003)) which indi-
cates every endurant participates in some perdurant at
a given time object:
x ED(x) (y, t) PC(y, x, t) (1)
A similar axiom is found in T
psl core
that indicates
activity occurrences require an object to participate
in them. From these observations, we can hypothe-
size that perdurants and endurants from DOLCE are
equivalent to activity occurrences and objects in PSL,
respectively. We can further conjecture that the notion
of participation PC(x, y, z) in DOLCE is equivalent to
the participates in(x, y, t) relation in PSL: for any ob-
ject x, activity occurrence y, and time interval z, there
exists a time construct t that is equivalent to the time
interval z, where x participates in y during t. We write
these equivalences as the following translation defini-
tions:
x PD(x) activity occurrence(x) (2)
x ED(x) ob ject(x) (3)
x T (x) timeinterval(x) (4)
xyz (PC(x, y, z) ob ject(x)
activity occurrence(y)timeinterval(z)
(tbe f oreEq(begino f (z), t) be f oreEq(t, endo f (z))
participates in(x, y, t))). (5)
The DOLCE ontology also contains a taxonomy
of classes of perdurants and endurants. The PSL on-
tology does not contain a corresponding taxonomy of
activities, activity occurrences, or objects. Neverthe-
less, DOLCE does not provide additional axioms that
distinguish among the different classes of perdurants,
apart from the taxonomic axioms. We therefore do
not pursue a mapping from this part of the DOLCE
ontology to the PSL ontology.
We can extract the following obstacles from our
observations:
1. PSL-Core utilizes a time point ontology, which
has an ordering but not a mereology.
2. DOLCE utilizes a time interval ontology, which
has a mereology but no ordering.
3. Both PSL-Core and DOLCE make different on-
tological commitments on how objects/endurants
participate in activity occurrences/perdurants.
MergingtheDOLCEandPSLUpperOntologies
19
dolce present
dolce mereology
dolce participation
interval with endpoints
DOLCE Hierarchies
Combined Time Hierarchy
dolce temporary parthood
dolce time mereology
dolce constitution
dolce taxonomy
dolce dependence
periods root
Periods Hierarchy
lp infinite end
Timepoints Hierarchy
periods
finite periods
cem periods
lp ordering
linear point
sim vc end
endpoints
psl coremandatory
PSL Hierarchy
psl core root
finite sim vc end
interval mandatory
interval psl core
Interval PSL Hierarchy
Figure 1: Relationships between DOLCE modules and theories in COLORE. Solid lines indicate conservative extensions,
dashed lines indicate non-conservative extensions, and the bolded dash-dot-dotted lines indicate faithful interpretations be-
tween ontologies.
In the sections that follow, we address how to
overcome these obstacles by creating new ontologies
to integrate the ontologies describing time points and
orderings with ontologies describing time intervals
and mereologies. In order to identify the specific
relationship between the two ontologies of DOLCE
and PSL, it should be possible to add a mereology of
time intervals to PSL, or add an ordering to DOLCE,
and then determine whether the resulting extensions
of DOLCE and PSL faithfully interpret each other.
COLORE contains numerous mathematical theories
that can assist us in this regard – the Combined Time
hierarchy H
combined time
contains time ontologies that
utilize both time point and time interval constructs,
and are able to interpret a mereology on time points
and time intervals. Figure 1 illustrates the bridges that
can be created to formalize the relationships between
the ontologies.
It may be noted that there are two different in-
tuitions about bridging ontologies that are being ex-
plored here. We first consider new ontologies which
are created as either nonconservative extensions of
ontologies in existing hierarchies, or as merged on-
tologies, that is, they are conservative extensions of a
set of other ontologies from different hierarchies. We
will see this in the role played by the ontologies in the
Combined Time and Interval PSL hierarchies. An al-
ternative intuition is that a bridging ontology is strong
enough to faithfully interpret one ontology while con-
servatively extending another, thus providing a way
of embedding the two ontologies within the bridging
ontologies. We will see this in the role played by on-
tologies in the Interval PSL hierarchy.
It is also interesting to see how this approach to
bridging ontologies is related to the notion of bridge
axioms. For bridging ontologies which are the merge
of other ontologies, there exist sentences whose sig-
nature is the union of the signatures of the merged
ontologies. For example, we will see that there exist
axioms in the ontologies of the Combined Time hi-
erarchy which use relations on both time points and
time intervals. Such axioms correspond to the bridge
axioms in (Stuckenschmidt et al., 2005; Euzenat and
Shvaiko, 2007). On the other hand, for bridging on-
tologies which faithfully interpret an ontology, we do
not find such sentences. Instead, the translation defi-
nitions that specify the interpretation play the role of
bridge axioms between the two ontologies.
4 MERGING TIME POINT AND
INTERVAL ONTOLOGIES
To address the first obstacle, we utilize existing com-
bined time ontologies to integrate time points and
KEOD2014-InternationalConferenceonKnowledgeEngineeringandOntologyDevelopment
20
time intervals, and mereologies and orderings. In this
way, existing temporal ontologies found in COLORE
can be used to analyze the interpretations between the
DOLCE and PSL. Here we briefly outline the time
point and time interval ontologies used. We then ex-
amine a set of time ontologies from COLORE which
merge the time point ontologies with the time interval
ontologies.
4.1 The Time Points Hierarchy
Within this hierarchy are ontologies that describe time
in terms of time points and that introduce a par-
tial ordering on the set of time points using the bi-
nary relation be f ore(x, y). We are particularly inter-
ested in two of these ontologies, based on the roles
they play as modules of other ontologies. The lin-
ear point theory, T
linear point
4
, derived from axioms
found in (Hayes, 1996), is a simple ontology whose
axioms state that time points infinitely extend a time-
line in both forward and backward directions. The
linear time points with endpoints at infinity theory,
T
l p in f inite end
5
, derived from axioms found in (Hayes,
1996), also represents a linear ordering on time points
that infinitely extends in both forward and backward
directions, but it contains axioms that enforce the ex-
istence of endpoints at infinity in both directions.
4.2 The Periods Hierarchy
The axioms for the periods hierarchy, H
periods
, were
proposed in (van Benthem, 1991), and additional in-
formation about other ontologies in this hierarchy can
be found in (Gr
¨
uninger et al., 2012). We are in-
terested in the in the weakest theory of this hier-
archy, T
periods
, since it is used by T
end points
, which
is described in Section 4.3. The Minimal Theory
of Periods, T
periods
, constitutes the minimal set of
conditions that must be met by any period struc-
ture (van Benthem, 1991). It contains two relations,
precedence(x, y) and inclusion(x, y), and two conser-
vative definitions, glb(x, y, z) and overlaps(x, y), as its
non-logical lexicon. Every element in the domain is
considered a time interval, and there are transitivity
and irreflexivity axioms for the precedence(x, y) re-
lation, making it a strict partial order; similarly, the
transitivity, reflexivity, and anti-symmetry axioms for
the inclusion(x, y) relation make it a partial order. As
well, the axiom, glb(x, y, z), guarantees the existence
of greatest lower bounds between overlapping inter-
vals defined by overlaps(x, y).
4
http://colore.oor.net/timepoints/linear point.clif
5
http://colore.oor.net/timepoints/lp infinite end.clif
An interesting property in these ontologies is the
convexity of time intervals. Intuitively, convex inter-
vals are those which have no gaps (Ladkin, 1986)
6
.
The convexity of time intervals requires an ordering
over time intervals and a mereology, and hence it
can be defined by ontologies in the H
periods
hierar-
chy. However, convexity is not definable in DOLCE
since it lacks an ordering on time intervals.
4.3 The Combined Time Hierarchy
Given that we want to merge ontologies from the
time points hierarchy with ontologies from the pe-
riods hierarchy, we need to consider ontologies that
include both time points and time intervals as primi-
tives, and define a set of functions and relations spec-
ifying the interactions between them. These time on-
tologies
7
are derived from the theories presented in
(Hayes, 1996), and have been modified and verified in
(Gruninger and Ong, 2011). Depending on the rela-
tions and functions used, these theories can represent
time in very different ways. For example, the theory
of endpoints, T
end points
, defines time points only as the
boundary of time intervals, where every interval is as-
sociated with exactly two time points: the begin of
and end of the interval. In contrast, the theory of time
point continuum, T
point continuum
, defines intervals by
the set of adjacent time points in which they are con-
tained; another theory, T
vector continuum
introduces the
concept of directionality by allowing ‘backward in-
tervals’ where the end of point is before the begin of
point in the timeline.
The theory of endpoints, T
end points
8
, combines the
language of intervals and points by defining the begi-
nof, endof, and between functions to relate time inter-
vals to time points and vice-versa. In this hierarchy,
this theory imports axioms from T
linear point
that de-
fine a binary be f ore(x, y) relation between time points
as transitive and irreflexive, and asserts that all time
points are linearly ordered and infinite in both direc-
tions. As well, this theory includes axioms that define
the meets at(i, x, j) relation as one between two inter-
vals and the point at which they meet along, restrict
begino f (i) to always come before the endo f (i) func-
tion, and states that intervals are between two points
if they are properly ordered.
The vector continuum theory, T
vector continuum
9
, in-
6
Additional information about the various relations
found in convex and non-convex intervals can be found in
(Ladkin, 1986).
7
http://colore.oor.net/combined time/
8
http://colore.oor.net/combined time/endpoints.clif
9
http://colore.oor.net/combined time/
vector continuum.clif
MergingtheDOLCEandPSLUpperOntologies
21
troduces the notion of orientation of intervals, and
also imports T
linear point
. It contains the same three
functions (begino f (i), endo f (i), and between(x, y))
that transform time intervals into time points and vice-
versa, but differs in its definition of between(x, y) by
allowing the formation of intervals whose endof point
is equal to or before its beginof. Thus, every inter-
val in T
vector continuum
has a ‘reflection’ in the opposite
direction via the back(i) function; intervals oriented
in the forward direction are defined normally where
begino f (i) is before endo f (i). As well, single-point
intervals, known as moments, are defined as intervals
whose begino f (i) and endo f (i) points are the same.
4.4 Composing the Theory of Intervals
with Endpoints
The combined time hierarchy contains ontologies
whose models combine structures for time points
and time intervals. These ontologies were first pro-
posed in (Hayes, 1996), and assume an import of the
T
end points
theory, where every time interval is associ-
ated with two time points. However, T
psl core
contains
a time point ontology that axiomatizes a linear order-
ing with endpoints at infinity, whereas T
end points
ax-
iomatizes a time point ontology in which the linear
ordering does not have such maximum and minimum
time points. Consequently, we need to create a new
theory, T
interval with end points
, in H
combined time
that con-
tains the time interval axioms of T
end points
with a dif-
ferent time point ontology. It is this new time ontol-
ogy which will be used to extend T
psl core
to make it
compatible with the existence of time intervals.
The new intervals with endpoints the-
ory, T
interval with end points
, imports axioms from
T
f inite sim vc end
from H
combined time
and T
l p in f inite end
from H
timepoints
. The primary difference between
the T
f inite sim vc end
and T
sim vc end
ontologies within
H
combined time
is that different time point ontologies
are used in each theory; while both ontologies share
a common set of axioms (T
l p ordering
) additional
axioms in T
linear point
make T
sim vc end
different from
T
f inite sim vc end
, as depicted in Figure 1. Conse-
quently, T
interval with end points
non-conservatively
extends T
f inite sim vc end
since it contains the same
time interval axioms as T
f inite sim vc end
, but different
time point axioms from T
l p in f inite end
. The axioms of
T
interval with end points
can be found in COLORE
10
.
Recall that the DOLCE ontology has a mereology
on time intervals, but that there is no ordering rela-
tion on time intervals; on the other hand, the com-
10
http://colore.oor.net/combined time/
interval with endpoints.clif
bined time ontologies have an ordering over time in-
tervals by which an mereology can be defined. In
this way, the periods hierarchy bridges DOLCE and
combined time hierarchies together since T
periods
is
the common theory between them. We note that the
dash-dot-dotted arrows in Figure 1 outline the faith-
ful interpretations between H
dolce
and H
periods
, and
H
periods
and H
combined time
; however, these are faith-
ful interpretations are conjectured and proofs will be
addressed in future work. In this paper, we only dis-
cuss the composition of theories needed to prove the
faithful interpretations between DOLCE and PSL.
5 EXTENDING T
PSL CORE
To address the second obstacle, we extend the PSL-
Core theory with time intervals and interpret DOLCE
in this new ontology. Within PSL, activity occur-
rences are considered to be occurrents, while objects
are represented by continuants (Gr
¨
uninger, 2009).
The relation participates in(x, o, t) is used to specify
that an object x participates in activity occurrence o
at time point t. Since DOLCE does not utilize time
points but time intervals in its time mereology, an
extension of T
psl core
11
must be created in order to
map the participates in(x, o, t) relation to a relation
on time intervals.
5.1 Theory of PSL-Core Root
A subset of the axioms in T
psl core
were extracted to
create the T
psl core root
theory. The following closure
axiom from T
psl core
was removed
x (activity(x) activity occurrence(x)
timepoint(x) ob ject(x)) (6)
We need a theory which can incorporate both time
points and time intervals, and it is easy to see how
such a closure axiom is problematic, since it precludes
the existence of time intervals as a distinct class. In
other words, there can be no extension of T
psl core
that
contains an axiomatization of time intervals. It is easy
to see that T
psl core
is a non-conservative extension of
T
psl core root
. All new theories that incorporate time
intervals into the PSL ontology are conservative ex-
tensions of T
psl core root
.
5.2 Theory of Mandatory Participation
The original T
psl core
contains a weak axiomatization
of the participates in(x, o, t) relation, and does not
11
We could not modify the axioms found in T
psl core
since
the axioms are standardized in ISO 18629-11:2005.
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22
x (ob ject(x) (ot participates in(x, o, t))) (7)
ot (activity occurrence(o) is occurring at(o, t)
(x participates in(x, o, t))) (8)
Figure 2: Axioms found in T
mandatory
.
impose any conditions beyond requiring that an activ-
ity is occurring at the same time that the object exists.
There are no requirements that an object must partic-
ipate in some activity occurrence, or that an activity
occurrence always have some object participating in
it. We can therefore define a new non-conservative
extension of T
psl core root
called T
mandatory
to take into
account the mandatory participation of PSL objects
in a temporal construct. The axioms found in this
extension import T
psl
core root
and do not include the
between(x, y, z) and be f ore(x, y, z) relations found in
T
psl core
since they involve the usage of time points,
not time intervals, to describe the participation of ob-
jects in activity occurrences and time objects. Fig-
ure 2 lists all of the axioms found in T
mandatory
, and
the axioms can be found in COLORE
12
. Axiom 7 in-
dicates that every object x has to participate in some
activity occurrence o at a time object t, and Axiom 8
indicates that, for every activity occurrence o that oc-
curs during the time object t, there exists an object
that also participates in that time object.
In T
mandatory
, we do not commit to a specific type
of temporal object for object participation, but we
note that there needs to be a ‘bridge’ of sorts to con-
nect the DOLCE and PSL ontologies together. Conse-
quently, we are interested in creating a new bridge on-
tology that contains the PSL constructs that are used
with time intervals. We discuss this new H
interval
psl
hierarchy in the next section.
5.3 The Interval PSL Hierarchy
Since the PSL ontology only describes object and ac-
tivity occurrences with respect to time points, we need
to create a time interval version of the PSL ontol-
ogy. This leads to a new hierarchy, called H
interval psl
,
with T
interval psl core
as its root theory. This hierarchy
contains the time interval versions of the T
psl core
and
T
mandatory
ontologies which are named T
interval psl core
and T
interval mandatory
, respectively, and are depicted in
Figure 1. Each of these ontologies is briefly described
below, and can be found in COLORE
13
.
12
http://colore.oor.net/psl core/mandatory.clif
13
http://colore.oor.net/interval psl/
x (timeinterval(x) ¬(activity(x)
activity occurrence(x)
timepoint(x) ob ject(x))) (9)
xy (psl interval(x, y) (ob ject(x)
activity occurrence(x))timeinterval(y)
begino f (x) = begino f (y)
endo f (x) = endo f (y)) (10)
xyz (overlay(x, y, z)
(i
1
i
2
(psl interval(x, i
1
) psl interval(y, i
2
)
begino f (i
2
) = begino f (z)
endo f (i
1
) = endo f (z)))) (11)
Figure 3: Axioms of T
interval psl core
.
The ontologies in this hierarchy import axioms
from T
psl core root
and T
interval with end points
. In order
to ensure that the time interval version of T
psl core root
contains axioms that describe time intervals, and not
time points, T
interval with end points
is used to describe
the time objects found in this compiled ontology.
Three axioms are added to T
interval psl core
in ad-
dition to the imported ontologies and are outlined in
Figure 3. Axiom 9 indicates that a time interval is
not an activity, activity occurrence, object, or time
point. In Axiom 10, the relation, psl interval(x, y), is
introduced to relate a time interval with the begin of
and end of an activity occurrence or object. Finally,
the overlay(x, y, z) relation is introduced in Axiom 11
to describe a time interval z that overlays
14
activity
occurrences x and y. However, it may not necessar-
ily be the case that both activity occurrence/object y
overlays an activity occurrence/object x, or vice versa.
This axiom is included in case such overlaying of in-
tervals does occur.
5.4 Theory of Mandatory Intervals
Finally, we have the theory of mandatory inter-
vals which imports axioms from T
interval psl core
and
T
mandatory
. Since we would like to show that
T
dolce participation
can faithfully interpret the time in-
terval versions of PSL ontologies from T
interval psl core
,
we extended T
interval psl core
to include the time inter-
14
The terms overlap and intersect were not used to de-
scribe this relation since they are used in mereology on-
tologies. To be consistent with PSL, we decided to use the
term overlay to describe the relationship where time inter-
vals may overlay one another.
MergingtheDOLCEandPSLUpperOntologies
23
val versions of the axioms from T
mandatory
. No addi-
tional axioms are included in this ontology and it can
be found in COLORE
15
. Essentially this ontology as-
signs time intervals
16
to T
interval psl core
to indicate the
mandatory participation of PSL over a time interval.
The right side of Figure 1 summarizes the relation-
ships between the Interval PSL, PSL, and Combined
Time hierarchies.
6 INTERPRETATIONS BETWEEN
DOLCE AND PSL
In order to determine whether PSL can faithfully in-
terpret the subtheories of DOLCE, we first need to
modify T
dolce present
. This module of DOLCE con-
tains class Q(x) of qualities, which is problematic
T
psl core root
is unable to define what a quality is be-
cause it is unable to discern which ob ject(x) is an
endurant ED(x) or a quality Q(x). We must there-
fore specify a subtheory of T
dolce present
that does not
include qualities for this portion of the interpreta-
tion. The axioms of this subtheory T
dolce present
can
be found in COLORE
17
.
The DOLCE subtheories of T
dolce participation
and T
dolce time mereology
are able to interpret the
T
interval mandatory
and T
interval psl core
ontologies in
H
interval psl
, respectively. This is graphically depicted
in Figure 1, where the dashed arrows depict the inter-
pretations from the DOLCE ontology to the Interval
PSL ontology.
6.1 Interpretations between
T
interval psl core
and T
dolce present
From our brief discussion of the theories found in
COLORE, we make the observation that the concept
of parthood in DOLCE is equivalent to the inclusion
of time intervals in T
interval psl core
:
t
1
t
2
(P(t
1
, t
2
) timeinterval(t
1
)
timeinterval(t
2
)
be f oreEq(begino f (t
2
), begino f (t
1
))
be f oreEq(endo f (t
1
), endo f (t
2
))) (12)
Thus, we can say that the time interval t
1
is part
of time interval t
2
: the beginning of t
2
can either be
before or equal to the beginning of t
1
, and the end of
t
1
can either be before or equal to the end of t
2
.
15
http://colore.oor.net/interval psl/interval mandatory.clif
16
Recall that we did not commit to a particular temporal
construct in T
mandatory
.
17
http://colore.oor.net/dolce present/dolce present star.clif
Furthermore, we can state that the concept of be-
ing present in DOLCE is equivalent to the concept of
an object or activity occurrence that exists in a given
time interval, where the beginning of the time interval
is the time point in which an object or activity occur-
rence starts, and that the end of the time interval is the
time point in which the object or activity occurrence
ends.
(xyt (PRE(x, t) (ob ject(x)
activity occurrence(x))timeinterval(t)
be f oreEq(begino f (x), begino f (t))
be f oreEq(endo f (t), endo f (x)))). (13)
We note that, in psl interval(x, y), a unique time
interval is associated with an object or activity occur-
rence in PSL. Similarly, the time interval associated
in PRE(x, t) in DOLCE need not be a time interval at
which an endurant or perdurant is present. The trans-
lation definition for the sum of time intervals is based
on the definition of the overlaps relation in DOLCE:
xy overlaps(x, y)
(be f ore(begino f (x), begino f (y))
be f ore(endo f (x), endo f (y)))
(be f ore(begino f (y), begino f (x))
be f ore(endo f (y), endo f (x))). (14)
xyz SUM(z, x, y)
timeinterval(x) timeinterval(y)
timeinterval(z)
(w (overlaps(w, z)
(overlaps(w, x) overlaps(w, y)))). (15)
To show that T
interval psl core
interprets
T
dolce present
, we define endurants and qualities
in DOLCE to be equivalent to objects in PSL,
perdurants to equivalent to activity occurrences, and
time intervals in DOLCE to be equivalent to time
intervals in Interval PSL. In regards to mereology,
a time intervals t
1
is defined to be a part of a time
interval t
2
if the begin of t
2
is before or equal to t
1
and
the end of t
1
is before or equal to t
2
. The PRE(x, t)
relation in DOLCE is defined to be equivalent to an
object or activity occurrence that occurs during a time
interval. Finally, the SUM(z, x, y) relation in DOLCE
is defined to be a time interval z is the sum of the time
intervals of two activities x and y in Interval PSL.
Theorem 1. T
interval psl core
faithfully interprets
T
dolce present
.
Proof. Let
1
be the set of translation definitions
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24
found in COLORE
18
. Using Prover9, we show
19
that
T
interval psl core
1
|= T
dolce present
It should be noted that, if we consider their en-
tire sets axioms, DOLCE and PSL are not compa-
rable with respect to definable interpretations. Nev-
ertheless, we can identify subtheories of each ontol-
ogy for which we can specify interpretability. For
PSL, we needed to weaken the closure axiom and, for
DOLCE, we needed to consider the subtheory which
omits qualities from the domain.
6.2 Interpretations Between
T
interval mandatory
and T
dolce participation
For the interpretation of T
interval mandatory
and
T
dolce participation
, we reuse the set of translation
definitions
1
from the previous section (because
T
interval mandatory
imports T
interval psl core
), along with
the additional translation definition described below.
Since the DOLCE ontology contains axioms for
participation, we make the observation that the
participation relation, PC(x, y, z), is similar to the
participates in(x, y, t) relation found in PSL. Thus,
we can state that any x and y that participate in z in
DOLCE is equivalent an object x that participates in
an activity occurrence y in a given time interval z and,
at every time point in that interval, x participates in y.
xyzt (PC(x, y, z) ob ject(x)
activity occurrence(y) timeinterval(z)
(be f oreEq(begino f (z), t) be f oreEq(t, endo f (z))
participates in(x, y, t))) (16)
Theorem 2. T
interval mandatory
faithfully interprets
T
dolce participation
.
Proof. Let
2
be the set of translation definitions
found in COLORE
20
. Using Prover9, we show
21
that
T
interval mandatory
1
2
|= T
dolce participation
18
http://colore.oor.net/interval psl/mappings/interval psl
core2dolce present.clif
19
Proofs can be found at http://colore.oor.net/
dolce present/interprets/output/.
20
http://colore.oor.net/interval psl/mappings/interval
mandatory2dolce participation.clif
21
Proofs can be found at http://colore.oor.net/
dolce participation/interprets/output/.
7 SUMMARY
In cases where direct mappings cannot be specified
between ontologies, one can design new ontologies
that can serve as bridges between the ontologies, and
which then allow mappings to be specified. In this pa-
per we have explored how this can be done with the
DOLCE and PSL ontologies. In particular, faithful
interpretations specified between the DOLCE ontol-
ogy and ontologies within the Common Logic Ontol-
ogy Repository (COLORE) have shown that multiple
‘bridges’ were needed before any analyses with the
T
dolce
participation
and T
dolce present
theories could be car-
ried out with theories in COLORE. Firstly, we saw that
the Combined Time hierarchy bridges the Time Points
and Periods hierarchies together to allow us to merge
ontologies of time points and time intervals. Secondly,
the Interval PSL hierarchy bridges both the PSL and
DOLCE ontologies together to allow us to do the map-
ping between them and to identify the faithful inter-
pretations of mereology and orderings in both time
points and time intervals. This exercise in bridging
ontologies together demonstrates how we can axiom-
atize the relationships between theories and compose
new theories that are required for the bridging task.
The methodology presented in this paper is based
on techniques for ontology verification that use an
ontology repository to specify faithful interpretations
among ontologies. It should therefore be applicable to
any set of ontologies which have been verified. Nev-
ertheless, ontologies which have not been explicitly
modularized still pose a challenge, and the interplay
between ontology merging and decomposition merit
further exploration.
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