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-

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

 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

. 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

, T

be two ﬁrst-

order theories such that Σ(T

) ⊆ Σ(T

). We say that

is an extension of T

iff for any sentence σ ∈ L (T

if T

|= σ then T

|= σ.

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.

is a conservative extension of T

iff for any sen-

tence σ ∈ L(T

|= σ iff T

|= σ.

is a non-conservative extension of T

iff T

is an

extension of T

and there exists a sentence σ ∈ Σ(T

)

so that

2 σ and T

|= 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

and

is the notion of interpretation, which is a mapping

from the language of T

to the language of T

that

preserves the theorems of T

(Enderton, 1972). The

interpretation is faithful if the mapping also preserves

the satisﬁable sentences of T

One notion of equivalence among theories is mu-

tual faithful interpretability, that is, T

faithfully in-

terprets T

and T

faithfully interprets T

. An even

stronger equivalence relation is that of logical syn-

onymy: Two ontologies T

and T

are synonymous

iff there exists an ontology T

with the signature

Σ(T

)∪Σ(T

) that is a deﬁnitional extension of T

and

If there is an interpretation of T

in T

, then there

exists a set of sentences (referred to as translation

deﬁnitions) in the language L

∪ L

of the following

form, where p

(x) is a relation symbol in L

and ϕ(x)

is a formula in L

(∀x) p

(x) ≡ ϕ(x)

Thus, T

interprets T

if there exists a set ∆ of

translation deﬁnitions such that

∪ ∆ |= T

faithfully interprets T

if T

∪ ∆ is a conservative

extension of T

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

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

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

http://colore.oor.net/psl core/psl core.clif

KEOD2014-InternationalConferenceonKnowledgeEngineeringandOntologyDevelopment

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),

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),

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

. The concepts found within the

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

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

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

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)

∀x∀y∀z (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

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

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

, 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,

l p in f inite end

, 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).

http://colore.oor.net/timepoints/linear point.clif

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)

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

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

, 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

, in-

Additional information about the various relations

found in convex and non-convex intervals can be found in

(Ladkin, 1986).

http://colore.oor.net/combined time/

http://colore.oor.net/combined time/endpoints.clif

http://colore.oor.net/combined time/

vector continuum.clif

MergingtheDOLCEandPSLUpperOntologies

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

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

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

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

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

interval with end points

can be found in COLORE

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-

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

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

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

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

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

We could not modify the axioms found in T

psl core

since

the axioms are standardized in ISO 18629-11:2005.

KEOD2014-InternationalConferenceonKnowledgeEngineeringandOntologyDevelopment

∀x (ob ject(x) ⊃ (∃o∃t participates in(x, o, t))) (7)

∀o∀t (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

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

. 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

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

http://colore.oor.net/psl core/mandatory.clif

http://colore.oor.net/interval psl/

∀x (timeinterval(x) ⊃ ¬(activity(x)∨

activity occurrence(x)∨

timepoint(x) ∨ ob ject(x))) (9)

∀x∀y (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)

∀x∀y∀z (overlay(x, y, z) ≡

(∃i

∃i

(psl interval(x, i

) ∧ psl interval(y, i

)∧

begino f (i

) = begino f (z)∧

endo f (i

) = 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

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

mandatory

. Since we would like to show that

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-

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

val versions of the axioms from T

mandatory

. No addi-

tional axioms are included in this ontology and it can

be found in COLORE

. Essentially this ontology as-

signs time intervals

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 –

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

The DOLCE subtheories of T

dolce participation

and T

dolce time mereology

are able to interpret the

interval mandatory

and T

interval psl core

ontologies in

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

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

(P(t

, t

) ≡ timeinterval(t

)∧

timeinterval(t

)∧

be f oreEq(begino f (t

), begino f (t

))∧

be f oreEq(endo f (t

), endo f (t

))) (12)

Thus, we can say that the time interval t

is part

of time interval t

: the beginning of t

can either be

before or equal to the beginning of t

, and the end of

can either be before or equal to the end of t

http://colore.oor.net/interval psl/interval mandatory.clif

Recall that we did not commit to a particular temporal

construct in T

mandatory

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.

(∀x∀y∀t (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:

∀x∀y 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)

∀x∀y∀z 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

∗

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

is deﬁned to be a part of a time

interval t

if the begin of t

is before or equal to t

and

the end of t

is before or equal to t

. 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

∗

dolce present

Proof. Let ∆

be the set of translation deﬁnitions

KEOD2014-InternationalConferenceonKnowledgeEngineeringandOntologyDevelopment

found in COLORE

. Using Prover9, we show

that

interval psl core

∪ ∆

|= 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

interval mandatory

and T

dolce participation

For the interpretation of T

interval mandatory

and

dolce participation

, we reuse the set of translation

deﬁnitions ∆

from the previous section (because

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.

∀x∀y∀z∀t (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

dolce participation

Proof. Let ∆

be the set of translation deﬁnitions

found in COLORE

. Using Prover9, we show

that

interval mandatory

∪ ∆

|= T

dolce participation

http://colore.oor.net/interval psl/mappings/interval psl

core2dolce present.clif

Proofs can be found at http://colore.oor.net/

dolce present/interprets/output/.

http://colore.oor.net/interval psl/mappings/interval

mandatory2dolce participation.clif

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

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.

REFERENCES

Choi, N., Song, I.-Y., and Han, H. (2006). A Survey on

Ontology Mapping. SIGMOD Record, 35(3):34–41.

Chui, C. (2013). Axiomatized Relationships between On-

tologies. Master’s thesis, University of Toronto.

de Bruijn, J., Ehrig, M., Feier, C., Mart

ın-Recuerda, F.,

Scharffe, F., and Weiten, M. (2006). Ontology Me-

diation, Merging, and Aligning, pages 95–113. John

Wiley & Sons, Ltd.

Enderton, H. B. (1972). A Mathematical Introduction to

Logic. Academic Press.

Euzenat, J. and Shvaiko, P. (2007). Ontology Matching.

Springer-Verlag New York, Inc., Secaucus, NJ, USA.

uninger, M. (2009). Using the PSL Ontology. In Staab, S.

and Studer, R., editors, Handbook on Ontologies, In-

ternational Handbooks on Information Systems, pages

423–443. Springer Berlin Heidelberg.

uninger, M., Hahmann, T., Hashemi, A., Ong, D., and

Ozg

ovde, A. (2012). Modular First-Order Ontologies

via Repositories. Applied Ontology, 7(2):169–209.

MergingtheDOLCEandPSLUpperOntologies

Gruninger, M. and Ong, D. (2011). Veriﬁcation of Time

Ontologies with Points and Intervals. 2011 Eighteenth

International Symposium on Temporal Representation

and Reasoning (TIME), 0:31–38.

Hayes, P. (1996). A Catalog of Temporal Theories. Tech-

nical Report UIUC-BI-AI-96-01, Beckman Institute

and Departments of Philosophy and Computer Sci-

ence, University of Illinois.

Kalfoglou, Y. and Schorlemmer, M. (2005). Ontology

Mapping: The State of the Art. In Kalfoglou, Y.,

Schorlemmer, M., Sheth, A., Staab, S., and Uschold,

M., editors, Semantic Interoperability and Integra-

tion, number 04391 in Dagstuhl Seminar Proceedings,

Dagstuhl, Germany. Internationales Begegnungs- und

Forschungszentrum f

ur Informatik (IBFI), Schloss

Dagstuhl, Germany.

Kutz, O. and Mossakowski, T. (2011). A Modular Consis-

tency Proof for DOLCE. In Burgard, W. and Roth, D.,

editors, Proceedings of the Twenty-Fifth AAAI Confer-

ence on Artiﬁcial Intelligence (AAAI 2011), August 7-

11, 2011, pages 227–234, San Francisco, California,

USA. AAAI Press.

Ladkin, P. B. (1986). Time Representation: A Taxonomy of

Internal Relations. In Proceedings of the 5th National

Conference on Artiﬁcial Intelligence, volume 1, pages

360–366, Philadelphia, PA.

Masolo, C., Borgo, S., Gangemi, A., Guarino, N., and

Oltramari, A. (2003). WonderWeb Deliverable D18

Ontology Library (Final). Technical report, IST

Project 2001-33052 WonderWeb: Ontology Infras-

tructure for the Semantic Web.

Stuckenschmidt, H., Seraﬁni, L., and Wache, H. (2005).

Reasoning about Ontology Mappings. Technical re-

port, ITC-IRST, Trento.

van Benthem, J. (1991). The Logic of Time: A Model-

Theoretic Investigation into the Varieties of Temporal

Ontology and Temporal Discourse. Synthese Library.

Springer.

Zimmermann, A., Kr

otzsch, M., Euzenat, J., and Hitzler, P.

(2006). Formalizing Ontology Alignment and its Op-

erations with Category Theory. In Proceedings of the

Fourth International Conference on Formal Ontology

in Information Systems (FOIS 2006), pages 277–288,

Amsterdam, The Netherlands. IOS Press.

KEOD2014-InternationalConferenceonKnowledgeEngineeringandOntologyDevelopment