=Paper=
{{Paper
|id=Vol-48/paper-2
|storemode=property
|title=Ontological Engineering for Conceptual Modeling
|pdfUrl=https://ceur-ws.org/Vol-48/Raban.pdf
|volume=Vol-48
}}
==Ontological Engineering for Conceptual Modeling==
https://ceur-ws.org/Vol-48/Raban.pdf
Ontological Engineering for Conceptual Modeling
1 2
Ryszard (Richard) Raban , Brian Garner
1
Faculty of Information Technology
University of Technology, Sydney
richard@socs.uts.edu.au
2
School of Computing and Mathematics
Deakin University
brian@deakin.edu.au
Abstract. In acknowledging the importance of ontologies in conceptual
modeling, database integration and business process modeling, this paper
introduces a set of principles for building ontologies. Starting from Guarino's
meta-properties of ontological terms, the paper describes the denotational
semantics of the meta-properties and derives from them some engineering rules
and checks for constructing domain specific conceptual models, based on the
overarching requirement to assign meanings to concepts using tags and labels.
Parallel research by the authors into the use of contextual references and roles
to restrict such meanings will be published elsewhere.
1 Introduction
Ontologies grew out of being a philosophical endeavor of finding the top level
categories of existence (those appear in the works of Aristotle through Kant,
Heidegger to the ontological categories introduced recently by Sowa [1]) into an
important tool in domain knowledge representation, and recently, in information
systems modeling. Whenever a model is built, a certain ontological commitment is
assumed. In most cases, however, this commitment is not explicitly stated. It makes
information exchange, interoperability and integration very difficult. XML [2], XMI
[3] or UML [4], [5], [6], to mention just some of the prominent modeling and
integration tools, will not be able to realize their full potential in the area of
knowledge sharing and integration unless the tags and labels used have ontology-
based semantics.
As ontologies become more and more part of knowledge engineering and modeling
[7], [8], [9], it is imperative to have precise rules for engineering ontlologies
themselves.
A similar problem also arises in managing changing contexts within reasoning
processes which, as argued in [10], often requires dynamic ontology modifications. In
order to be able to manipulate ontologies without loosing their internal consistency,
strict ontology construction rules are required.
This paper aims to advance the basis of ontological engineering by specifying rules
for creating a hierarchy of properties that individuals might have and by exploring
some implications of the rules for conceptual modeling. We start by defining the
denotational semantics of ontological meta-properties, also referred to in this paper as
criteria, and then derive from them rules for properties subtyping. The meta-
properties, which were partially introduced in [11], [12], [13], [14], [15] and have
been recently refined and formalized by Guarino and Welty in [16], were adopted as
the starting point for this research.
2 Extensional semantics of meta-properties.
Let's assume that in a particular Universe of Discourse there are individuals x that
can be dynamically created and destroyed.
Let ωt be the existence predicate defined on all x such that ωt(x) means that an
individual x exits at a point in time t. We assume that each individual might have
exactly one creation time tcx such that
∀t < tcx ¬ωt(x) ∧ ∃t∆∀ tcx ≤ t < tcx + t∆ ωt(x)
and exactly one destruction time tdx such that
∀t > tdx ¬ωt(x) ∧ ∃t∆∀ tdx - t∆ < t ≤ tdx ωt(x).
Let τx = [tcx, tdx] be the period in which an individual x exists or the individual x's
lifetime.
Let Ωt = {x | ωt(x)} be a set of all individuals existing at a point in time t.
First-order properties correspond to monadic predicates over Ωt. If P is a property,
Pt(x) means that an individual x has property P at a point in time t. This, of course,
implies that the individual x must exist at the point in time t to have the property. For
example, individuals of a Universe of Discourse might have properties like PERSON,
EMPLOYEE, RED, SHORT, etc. Note that properties are not attributes like LENGTH,
or COLOR which are functions defined on a domain of individuals and return
attribute values. For example, LENGTH(x) = 175cm or COLOR(y) = 'red'.
A individual x acquires a property P at a point in time tcP(x) such that
∀t < tcP(x) ¬Pt(x) ∧ ∃t∆∀ tcP(x) ≤ t < tcP(x) + t∆ Pt(x)
and discards it at a point in time tdP(x) such that
∀t > tdP(x) ¬Pt(x) ∧ ∃t∆∀ tdP(x) - t∆ < t ≤ tdP(x) Pt(x).
A period of time during which an individual x holds a property P is called an
attribution period of P to x and is defined as τP(x) = [tcP(x), tdP(x)] such that
∀t ∈ τP(x) Pt(x).
In this paper, the discussion is limited to such properties that apply for some period
of time to at least one individual, that is ∀P ∃x tcP(x), < tdP(x).
A property P can have many attribution periods for an instance x. For example, a
person can hold property STUDENT many times in different periods of time.
We call a property P static if;
∀x Pt(x) → (τP(x) = τx )
Otherwise, a property is called dynamic.
A static property is inherent to an individual; it is acquired at its creation time and
holds for its entire lifetime. Properties like PERSON, LIVING-BEING are static. A
dynamic property is acquired by an individual temporarily, and it can be acquired and
discarded many times in an individual's lifetime. The previously mentioned property
STUDENT is an example of a dynamic property.
The denotation of a property P is defined as δPt = {x | Pt(x)} and represents a set of
all individuals that have property P at a point in time t.
It is also valid to use the denotation for the existence predicate - δωt is a set of all
individuals existing at a point in time t.
2.1 Subtyping
If a property Q is a subtype of a property, denoted by Q ≤ P, then
∀t (δQt ⊆ δPt).
If additionally
∃t (δQt ⊂ δPt),
then Q is a proper subtype of P, which we denote by Q < P. If a property Q is a
(proper) subtype of a property P, it can be said that a property P is a (proper)
supertype of a property Q.
There could be two different types of subtyping. Firstly, we can have time
independent or static subtyping. In this case, a static property Q is a subtype of a static
property P. For example, property PERSON is a static subtype of property LIVING-
BEING and it means that a living-being can also be a person, and if it is so, it remains
a person for its lifetime.
Secondly, we can have time dependent subtyping or dynamic subtyping. In this
case, a dynamic property Q is a subtype of a property P, which could be either static
or dynamic. It means that an individual x with the property P might have the property
Q at some periods of time and might not have this property on some other occasions.
For example, property STUDENT is a dynamic subtype of property PERSON as a
person might be a student only for some periods of time. Similarly, properties PART-
TIME-STUDENT and FULL-TIME-STUDENT are dynamic subtypes of property
STUDENT and here too a student can change its status from being a part-time-student
to being a full-time-student, and vice-versa, many times during the period of
enrolment.
Using the above terminology let's define the semantics of the three meta-properties
introduced by Guarino [16]: identity, rigidity and dependence.
2.2 Identity
Following the original definition, we say that a property P has identity, and denote
it by +I, if there is a relation R such that
∀t ∀xy (Pt(x) ∧ Pt(y)) → (R(x,y) ↔ (x = y)).
The relation R is called an identity condition of P. For example, property PERSON
has identity as its instances can be distinguished from each other by their DNA
structure (relation HAS-SAME-DNA) or the makeup of their brains (relation HAS-
SAME-BRAIN). On the other hand, individuals of property THING cannot be
distinguished by any identity condition inherent to all things.
Further we say that a property P has its own identity, and denote it by +O, if there
is a relation R such that
∀t ∀xy (Pt(x) ∧ Pt(y)) → (R(x,y) ↔ (x = y))
and
∀Q (¬(Q < P)) → (¬(∀t ∀xy (Qt(x) ∧ Qt(y)) → (R(x,y) ↔ (x = y))).
In other words, a property P has its own identity, if it does not share its identity
condition defined by the relation R with any property Q which is not a subsumption of
the property P. For example, relation HAS-SAME-DNA allows us to distinguish
between any two individuals having property LIVING-BEING, but it cannot be used
to distinguish between individuals having a property being a supertype of LIVING-
BEING. Thus, property LIVING-BEING has its own identity.
However, property PERSON shares its identity condition HAS-SAME-DNA with all
individuals with property LIVING-BEING. And unless property PERSON introduces
its own identity condition, we say that the property does not have its own identity, and
denote it by –O.
Obviously, if a property has its own identity (+O) it also has identity (+I).
Conversely, not having identity (-I) rules out its own identity, and therefore, implies
lack of own identity (-O). This leaves only three possible identity criteria: -I-O, +I-O,
and +I+O.
Let's explore under what conditions a subtype Q of a property P with given identity
criteria can inherit or change the identity criteria of its supertype.
If a property P has identity, it means that there is an identity condition defined for
its individuals. For any subtype property Q of P, individuals with property Q have
also property P and, therefore, can be distinguished using the property P’s identity
condition. Thus, having identity is always inherited.
If a subtype property Q of P has its own identity, it becomes +I+O irrespective of
what kind of identity criteria the supertype has. If, however, a subtype property Q of
P does not have its own identity, it always becomes +I-O, unless its supertype does
not have identity at all.
These subtyping rules for identity are summarized in TABLE I. The boxes with the
phrase 'not allowed' signify the fact that identity cannot ever be lost in subtypes or
acquired from a subtype, which does not have identity. The symbol I(T) means that
subtyping is allowed under the identity criteria, and the symbol I(⊥) means that
subtyping is not allowed under the identity criteria.
TABLE I. Subtyping Rules for Identity.
Q≤P -I-O +I-O +I+O
-I-O allowed I(T) not allowed I(⊥) not allowed I(⊥)
+I-O not allowed I(⊥) allowed I(T) allowed I(T)
+I+O allowed I(T) allowed I(T) allowed I(T)
2.3 Rigidity
A property P is rigid, which is denoted by +R, if it is a static property. It means
that all individuals with property P meet the rigidity condition
Pt(x) → (τP(x) = τx ).
A property is non-rigid, which is denoted by -R, if
∃t' ∃t" ∃x (Pt'(x) ∧ ωt"(x) ∧ ¬ Pt"(x)).
It means that there is at least one individual that violates the rigidity condition at
some point in time.
A property is anti-rigid, which is denoted by ~R, if
∃t' ∃t" ∀x (Pt'(x) → (ωt"(x) ∧ ¬ Pt"(x)).
Anti-rigidity is a special case of non-rigidity, in which all individuals holding a
property P violate the rigidity condition, and as such is subsumed by non-rigidity.
A rigid property P can have a rigid subtype property Q, if Q holds for its
individuals for their entire lifetime. For example, property LIVING-BEING and its
subtype PERSON. This amounts to static subtyping. But also, a subtype property Q of
a rigid property P can be a result of dynamic subtyping, and then it can be either non-
rigid or anti-rigid, depending whether some or all of its individuals violate the rigidity
condition. Therefore, rigidity is not inherited.
It is possible to have a rigid proper subtype Q of a non-rigid property P, since the
denotation δQt ⊂ δPt could contain only those individuals out of δPt, which fulfill the
rigidity condition. Equally, it is possible that a proper subtype Q of a non-rigid
property P has the denotation δQt ⊂ δPt that contains only those individuals out of δPt,
which violate the rigidity condition, or contains some that do and some that do not.
Hence, non-rigidity is not inherited.
Since all individuals that have an anti-rigid property P hold it for periods of time
always shorter than their lifetimes, any subtype property Q of the property P cannot
hold it longer than P’s lifetime. Therefore, all individuals of any subtype property Q
must violate the rigidity condition, which means that anti-rigidity is inherited.
The summary of subtyping rules of the rigidity conditions is presented in TABLE
II. The symbol R(T) means that subtyping is allowed under the rigidity criterion, and
the symbol R(⊥) means that subtyping is not allowed under the rigidity criterion.
TABLE II. Subtyping Rules for Rigidity
Q≤P +R -R ~R
+R allowed R(T) allowed R(T) not allowed R(⊥)
-R allowed R(T) allowed R(T) not allowed R(⊥)
~R allowed R(T) allowed R(T) allowed R(T)
2.4 Dependence
Following Guarino, we confine this discussion to one type of dependence that is
“notional dependence, which holds for a property if its instances require instances of
another property to exist” [16]. We say that a property P is dependent, which is
denoted by +D, if
∀t∀x (Pt (x) → ∃Q≠P∃y≠x Qt (y)).
In other words, for an individual x to have a property P ,it is required that there
exists an individual having a property Q. In this definition, it is also assumed that Q is
not a part of P. For example, individuals with property PARENT require individuals
with property CHILD to exist.
A property P is independent, which is denoted by -D if it not dependent.
If a property Q is a subtype of a dependent property P, all individuals with the
property Q also have the property P, and are therefore subject to the same dependency
condition, and as such, are dependent. Thus, dependence is inherited by subtypes. On
the other hand, an independent property P can have dependent or independent
subtypes.
The summary of subtyping rules of the dependence criterion is presented in
TABLE III. The symbol D(T) means that subtyping is allowed under the dependency
criterion, and the symbol D(⊥) means that subtyping is not allowed under the
dependency criterion.
TABLE III. Subtyping Rules for Dependence
Q≤P +D -D
+D Allowed D(T) allowed D(T)
-D not allowed D(⊥) allowed D(T)
3 Ontological Engineering Rules
All desirable combinations of the three property criteria give rise to eight property
types (a metalevel classification of properties), which were described in [16]. Three of
them are called Formal as they do not carry identity, and the remaining five are called
sortals as they have either their own or an inherited identity. The property types are
shown in TABLE IV. Note that we have split Category, Type and Merely Rigid
Sortals according to their dependency criterion and Material Role according to its
own identity criterion. This will enable us to have a closer look at subtyping allowed
for those types of properties.
TABLE IV. Property Types Resulting from Property Criteria.
Property Type Property Examples
Criteria
F Category+ -O-I+D+R SOCIAL-ENTITY
O (Cat+)
R Category- -O-I-D+R THING, LOCATION, ENTITY
(Cat-)
M
Formal Role -O-I+D~R PART, PATIENT, ACTOR
A (FRole)
L Atribution -O-I-D-R MALE, RED
(Attr)
S Type-Atribution Mixing -O+I-D-R MALE-PERSON, RED-FLOWER
(ATMix)
O Type+ +O+I+D+R ORGANIZATION
(Type+)
R
Type- +O+I-D+R LIVING-BEING
(Type-)
Phasal Sortal +O+I-D~R CATERPILAR
T
(PSort)
Material Role+ +O+I+D~R STUDENT
A (MRole+)
Material Role- -O+I+D~R FOOD
L (MRole-)
Merely Rigid Sortal+ -O+I+D+R LORD
S (MRSort+)
Merely Rigid Sortal- -O+I-D+R INVERTEBRATE-ANIMAL
(MRSort-)
TABLE V summarizes the allowed subsumptions between property types shown in
TABLE IV. Cells contain three subsumption conditions originating from identity,
dependence and rigidity criteria discussed earlier. These are shown in the table, as
appropriate, for the respective property types. For example, at the intersection of
Formal Attribution (Attr row) and Formal Role (FRole column) there are:
• I(T) indicating that the identity criterion allows the subsumption, as per TABLE I.
• D(⊥) which indicates that the dependency criterion does not allow the subsumption,
as per TABLE III.
• R(⊥) which indicates that the rigidity criterion does not allow the subsumption, as
per TABLE II; and since it is a conjunction of the three conditions, it follows that
the subsumption is not allowed. All allowed subsumptions are highlighted by
shading of the cells.
3.1 Guarino’s ontology engineering rules.
Let us examine subtyping rules given in [16] and assess their coverage in the
discussion so far:
G1. “Antirigid class cannot subsume a rigid class.” This rule has already been
accounted for in the discussion of rigidity.
G2. “ICs cannot be ‘overriden’ by a subclass, merely augmented” (in other words,
sortals cannot subsume formal concepts). This has already been accounted for in
the discussion of identity.
G3. “A dependent class cannot subsume an independent one.” This has already been
accounted for in the discussion of dependence.
G4. “A material role can be subsumed by rigid sortals, since they carry identity ...
They are the roles that normally specialise formal roles… ” In the discussion so
far, a material role is the most flexible of all the property types in terms what it
can subsume (see TABLE V). Except for material roles without own identity,
which cannot be subsumed by formal properties, all the other subsumptions are
allowed. However, the cited rule makes good sense, since it would be desirable
to have in the ontology some indication of what property the role applies to.
Otherwise, the role specification would be somehow incomplete, like saying that
there is a material role STUDENT without any indication that it applies to
PERSON. But there is no reason to make the assumption that a rigid property
must be subsumed by a rigid one; there could be some other material roles or
even phased sortals between the material role and the subsuming rigid property
in the subsumption hierarchy.
G5. “Phased sortals must be subsumed by a type.” This is required to be able to
establish the identity of the changing entity. But since a merely rigid,
independent sortal, type-attribution mixing, material role and phased sortal
should all be subsumed by a type, all of them can directly subsume a phased
sortal.
G6. “Merely rigid sortals ... are always subsumed by at least one type.” This is to
provide an identity condition, as merely rigid sortals do not carry their own
identity condition.
G7. “Types can only be subsumed by categories and strictly non-rigid formal
attributions.” In other words, types sit between formal properties and the rest of
the sortals in the subsumption hierarchy. In fact, it has already been said that the
other sortals should be eventually subsumed by a type. Of course, types can
form an hierarchy and subsume each other before being subsumed by a category
or formal attribution.
TABLE VI summarizes all the conditions discussed so far, and shows when
subtyping of properties of different types is allowed, as indicated by the content of
respective cells. If “not allowed” is written in a cell, it means that there is a restriction
on the subsumption originating from TABLE V. In cases where “G(n) not allowed” is
written, it indicates that one of the Guarino’s rule n has been invoked to prohibit this
subsumption. For example, a formal attribution (Attr row) cannot be subsumed by a
formal role (FRole column) since the cell on the intersection of the two contains
phrase “not allowed” derived from TABLE V.
TABLE V. Conditions for Subtyping Originating from the Three Property Criteria.
F O R M A L S O R T A L S
⊆ Cat+ Cat- FRole Attr ATMix Type+ Type- PSort MRole+ MRole- MRSort+ MRSort-
O-I+D+R -O-I-D+R O-I+D~R O-I-D-R O+I-D-R O+I+D+R O+I-D+R O+I-D~R O+I+D~R O+I+D~R +I+D+R O+I-D+R
F Cat+ I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(⊥)D(T) I(⊥)D(T) I(⊥)D(T) I(⊥)D(T) I(⊥)D(T) I(⊥)D(T) I(⊥)D(T) I(⊥)D(T)
-O-I+D+R R(T) R(T) R(⊥) R(T) R(T) R(T) R(T) R(⊥) R(⊥) R(⊥) R(T) R(T)
O
Cat- I(T)D(⊥) I(T)D(T) I(T)D(⊥) I(T)D(T) I(⊥)D(T) I(⊥)D(⊥) I(⊥)D(T) I(⊥)D(T) I(⊥)D(⊥) I(⊥)D(⊥) I(⊥)D(⊥) I(⊥)D(T)
R -O-I-D+R R(T) R(T) R(T) R(T) R(T) R(T) R(T) R(T)
R(⊥) R(⊥) R(⊥) R(⊥)
M FRole I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(⊥)D(T I(⊥)D(T) I(⊥)D(T) I(⊥)D(T) I(⊥)D(T) I(⊥)D(T) I(⊥)D(T) I(⊥)D(T)
A -O-I+D~R R(T) R(T) R(T) R(T) )R(T) R(T) R(T) R(T) R(⊥) R(⊥) R(T) R(T)
L Attr I(T)D(⊥) I(T)D(T) I(T)D(⊥) I(T)D(T) I(⊥)D(T) I(⊥)D(⊥) I(⊥)D(T) I(⊥)D(T) I(⊥)D(⊥) I(⊥)D(⊥) I(⊥)D(⊥) I(⊥)D(T)
-O-I-D-R R(T) R(T) R(⊥) R(T) R(T) R(T) R(T) R(⊥) R(⊥) R(⊥) R(T) R(T)
S ATMix I(⊥)D(⊥) I(⊥)D(T) I(⊥)D(⊥) I(⊥)D(T) I(T)D(T) I(T)D(⊥) I(T)D(T) I(T)D(T) I(T)D(⊥) I(T)D(⊥) I(T)D(⊥) I(T)D(T)
-O+I-D-R R(T) R(T) R(⊥) R(T) R(T) R(T) R(T) R(⊥) R(⊥) R(⊥) R(T) R(T)
O Type+ I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T)
+O+I+D+R R(T) R(T) R(⊥) R(T) R(T) R(T) R(T) R(⊥) R(⊥) R(⊥) R(T) R(T)
Type- I(T)D(⊥) I(T)D(T) I(T)D(⊥) I(T)D(T) I(T)D(T) I(T)D(⊥) I(T)D(T) I(T)D(T) I(T)D(⊥) I(T)D(⊥) I(T)D(⊥) I(T)D(T)
R
+O+I-D+R R(T) R(T) R(⊥) R(T) R(T) R(T) R(T) R(⊥) R(⊥) R(⊥) R(T) R(T)
PSort I(T)D(⊥) I(T)D(T) I(T)D(⊥) I(T)D(T) I(T)D(T) I(T)D(⊥) I(T)D(T) I(T)D(T) I(T)D(⊥) I(T)D(⊥) I(T)D(⊥) I(T)D(T)
T +O+I-D~R R(T) R(T) R(T) R(T) R(T) R(T)
R(T) R(T) R(T) R(T) R(T) R(T)
MRole+ I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T)
A +O+I+D~R R(T) R(T) R(T) R(T) R(T) R(T) R(T) R(T) R(T) R(T) R(T) R(T)
MRole- I(⊥)D(T) I(⊥)D(T) I(⊥)D(T) I(⊥)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T)
L -O+I+D~R R(T) R(T) R(T) R(T) R(T) R(T) R(T) R(T) R(T) R(T) R(T) R(T)
MRSort+ I(⊥)D(T) I(⊥)D(T) I(⊥)D(T) I(⊥)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T) I(T)D(T)
S -O+I+D+R R(T) R(T) R(⊥) R(T) R(T) R(T) R(T) R(⊥) R(⊥) R(⊥) R(T) R(T)
MRSort- I(⊥)D(⊥) I(⊥)D(T) I(⊥)D(⊥) I(⊥)D(T) I(T)D(T) I(T)D(⊥) I(T)D(T) I(T)D(T) I(T)D(⊥) I(T)D(⊥) I(T)D(⊥) I(T)D(T)
-O+I-D+R R(T) R(T) R(⊥) R(T) R(T) R(T) R(T) R(⊥) R(⊥) R(⊥) R(T) R(T)
TABLE VI. Summary of Subtyping Conditions.
F O R M A L S O R T A L S
⊆ Cat+
O-I+D+R
Cat-
O-I-D+R
FRole
O-I+D~R
Attr
O-I-D-R
ATMix
O+I-D-R
Type+
O+I+D+R
Type-
O+I-D+R
PSort
O+I-D~R
MRole+
O+I+D~R
MRole-
O+I+D~R
RSort+
O+I+D+R
RSort-
O+I-D+R
F Cat+ allowed allowed not allowed not not not not not not not not
-O-I+D+R allowed allowed allowed allowed allowed allowed allowed allowed allowed
O
Cat- not allowed not allowed not not not not not not not not
R -O-I-D+R allowed allowed allowed allowed allowed allowed allowed allowed allowed allowed
M FRole allowed allowed allowed allowed not not not not not not not not
-O-I+D~R allowed allowed allowed allowed allowed allowed allowed allowed
A
Attr not allowed not allowed not not not not not not not not
L -O-I-D-R allowed allowed allowed allowed allowed allowed allowed allowed allowed allowed
S ATMix not not not not allowed not allowed not not not not allowed
-O+I-D-R allowed allowed allowed allowed allowed allowed allowed allowed allowed
Type+ allowed allowed not allowed (G7) not allowed allowed not not not (G7) not (G7) not
O
+O+I+D+R allowed allowed allowed allowed allowed allowed allowed
Type- not allowed not allowed (G7) not not allowed not not not not (G7) not
R +O+I-D+R allowed allowed allowed allowed allowed allowed allowed allowed allowed
PSort not (G5) not not (G4) not allowed not allowed allowed not not not allowed
T +O+I-D~R allowed allowed allowed allowed allowed allowed allowed allowed
MRole+ (G4) not (G4) not allowed (G4) not (G4) not allowed allowed allowed allowed allowed allowed allowed
+O+I+D~R allowed allowed allowed allowed
A
MRole- not not not not (G4) not allowed allowed allowed allowed allowed allowed allowed
-O+I+D~R allowed allowed allowed allowed allowed
L
MRSort+ not not not not allowed allowed allowed not not not allowed allowed
-O+I+D+R allowed allowed allowed allowed allowed allowed allowed
S MRSort- not not not not allowed not allowed not not not not allowed
-O+I-D+R allowed allowed allowed allowed allowed allowed allowed allowed allowed
4 Using Property Types in Conceptual Modeling
In knowledge bases [17], [18] and databases [19], [20], there is a commonly
accepted distinction between definitions of terms, their characteristics and the
relations between them (often referred to as a schema or the TBox), and assertions
about the world stated in instances of those terms (often referred to as a fact base or
the Abox). This section will discuss implications of the taxonomy of properties for
defining domain models, i.e. classes, their characteristics and the relations between
them (the TBox).
In conceptual modeling of an application domain, not only properties are given, but
also all the sufficient and necessary conditions for an individual to carry the specific
property are defined. These property definitions are typically called classes.
Individuals that hold the property defined by a class are called instances of the class.
In order to maintain the distinction between properties and classes, the former will be
denoted by all capital (hyphenated) names (e.g. LIVING-BEING), and the latter by
non-hyphenated names with the first letter of each word capitalized (e.g.
LivingBeing). Classes based on properties will have corresponding names consisting
of the same wording.
A class defines domain specific conditions for the class membership. The
conditions give characteristics that are pertinent to all the class members in the
context of the domain and the purpose for which the modeling is performed.
Properties of type Attribution seems to provide appropriate terminology for
specifying class characteristics. However, property type Attribution, as explained in
[16], is
“refering … to an attribution as the property of having an attribute with certain
value, i.e. having gender MALE or color RED.”
And therefore, while useful to describe characteristic of individuals, attributions
are not suitable for declaring that class Person should have gender stated for its
instances. This requires a relation, which maps instances of the class to a set of
attributions relevant to the characteristic being defined. The sets of attributions will be
called attribution types. This brings us to the first relation type of conceptual
modeling, which has the following format:
Characteristic(Class, AttributionType).
For class Person, this relation type can be instantiated as
Gender(Person, {“Male”, “Female”}) – enumerated attribution type
Height(Person, {x: x is distance measurement in meters}) – measured
attribution type
Address(Person, {x: x is a character string}) – description attribution
type
Dependent properties come into existence in relation to some other properties
holding over different individuals. For example, STUDENT is a property of a person
being enrolled for a university course, or BANK-CUSTOMER is a property of a
person having a bank account. The statements have the following elements in them:
• they tell us that STUDENT and BANK-CUSTOMER are subtypes of property
PERSON, and
• they also point out what properties STUDENT and BANK-CUSTOMER are
dependent on; in this case the properties depend on the existence of respectively, a
UNIVERSITY-COURSE and of a BANK-ACCOUNT.
It is easy to show that there are relationships between classes based on these
properties by creating pairs (Student, UniversityCourse) and (BankCustomer,
BankAccount). What remains to be answered is what type of relationships do they
represent.
In order to answer this question, it is useful to call upon Charles Peirce’s three
basic categories Firstness, Secondness and Thirdness which were described in the
quotation from the original provided in [1]:
“First is the conception of being or existing independent of anything else. Second
is the conception of being relative to, the conception of reaction with, something
else. Third is the conception of mediation, whereby a first and a second are
brought into relation. (1891)”
Obviously, independent properties are related to the Firstness. Dependent
properties relate to the Secondness. The Thirdness, which mediates the relationship,
provides an answer to the original question. The mediating element that brings
STUDENT and UNIVERSITY-COURSE together is ENROLMENT, and the one that
brings BANK-CUSTOMER and BANK-ACCOUNT together is BANK-ACCOUNT-
CONTRACT. In general, dependent properties will result in a conceptual relation type
defined as follows:
DependencyMediator(DependentClass, Class)
which for the two examples is instantiated as:
Enrolment(Student, UniversityCourse)
BankAccountContract(BankCustomer, BankAccount).
The only other issue here is what property type DependencyMediator is based on.
Mediating properties seems to be rigid, dependent and carry their own identity, and
therefore they are of type Type+.
Another type of relationships that can exist between properties is the structural
relationship. In this case, the relations bring about certain arrangement of individuals.
For example, PartOf(Engine, Car), Above(Roof, Basement). This type of relationship
can be defined as
StructuralDependency(Class, Class).
Structural dependencies are properties that seem to be both dependent and non-
rigid. It is the type of properties, which are not included in the taxonomy as they are
“too weak … to capture the rigor … intended” [16]. However, if a structural
dependency is combined with one of the related properties, for example, PART-OF-
CAR or ABOVE-BASEMENT, it becomes independent and non-rigid and therefore is
of type Attribution.
5 Conclusion
This paper critically reviews the application of ontological engineering to
conceptual modeling. The two activities, while related, differ in purpose. Ontological
engineering deals with rules and principles of conceptualization of a problem domain.
Conceptual modeling, on the other hand, is concerned with the problem domain
structuring. While one may accept that no structure exists without underlying
conceptualization, the requisite conceptualization is usually implicit and often derived
on an intuitive, craft basis. Manifestation of an explicit basis for conceptualization
will, in our opinion, not only result in IT solutions of greater integrity, but will also
facilitate system and data integration vital to enterprise application integration,
including semantic web applications.
In the first part, the paper presented denotational semantics of identity, rigidity and
dependence used to define types of properties, and then introduced a set of property
subtyping rules and checks. It established the foundations for creating clean, well-
structured taxonomies. In the second part, the links between ontology engineering
principles and conceptual modeling were explored. In particular, three types of
emergent relationships were discussed.
Further work will concentrate on the development of domain ontologies as the
basis for data and system integration for oceanographic data interchange and
electronic business processes. Parallel work on the rules for context management and
role constraints will also benefit from the explication of property subtyping rules and
constraints.
References
1. Sowa, J.F., Knowledge Representation. 2000, Pacific Grove, CA USA: Brooks/Cole. 593.
2. Connolly, D., Extensible Markup Language (XML). 1997, W3C.
3. Object Management Group, XMI Metadata Interchange (XMI). 1999, OMG.
4. Jacobson, I., G. Booch, and J. Rumbaugh, The Unified Software Development Process.
Object Technology Series. 1999, Reading, MA: Addison-Wesley.
5. Rumbaugh, J., I. Jacobson, and G. Booch, The Unified Modelling Language Reference
Manual. Object Technology Series. 1999, Reading, MA: Addison-Wesley.
6. Booch, G., J. Rumbaugh, and I. Jacobson, The Unified Modelling Language User Manual.
Object Technology Series. 1999, Reading, MA: Addison-Wesley.
7. Zhu, X., et al., Ontology-Based Web Site Mapping for Information Exploration, in
Proceedings of the Eighth International Conference on Information Knowledge
Management. 1999: Kansas City, MO USA. p. 188-194.
8. Embley, D.W., et al., Ontology-based Extraction and Structuring of information from Data-
Rich Unstructured Documents, in Proceedings of the 1998 ACM 7th International
Conference on Information and Knowledge Management. 1998: Washington, USA. p. 52-
58.
9. Valente, A., et al., Building and (Re)Using an Ontology of Air Campaign Planning. IEEE
Inteligent Systems, 1999. 14(1 (Jan/Feb 1999)): p. 27-36.
10.Keyser, D., Ontologically Yours, in Lectures in Artificial Intelligence, M.-L. Mugnier and
M. Chein, Editors. 1998, Springer-Verlag. p. 35-47.
11.Sowa, J.F., Using a Lexicon of Canonical Graphs in a Semantic Interpreter, in Relational
Models of the Lexicon, M.W. Evens, Editor. 1988, Cambridge University Press: Cambridge.
12.Strawson, P.F., Individuals. An Essay on Descriptive Metaphysics. 1959, London:
Routledge.
13.Griffin, N., Relative Identity. 1977, Oxford: Oxford University Press.
14.Guarino, N., M. Carrara, and P. Giaretta, An Ontology of Meta-Level Categories, in
Principles of Knowledge Representation and reasoning: Proceedings of the Fourth
International Conference (KR'94), J. Doyle, E. Sandewall, and P. Torasso, Editors. 1994,
Morgan Kaufman Publishers: San Francisco, CA.
15.Guarino, N., Formal Ontology, Conceptual Analysis and Knowledge Representation.
International Journal of Human-Computer Studies, 1995. 43(5/6): p. 625-640.
16.Guarino, N. and C. Welty, A Formal Ontology of Properties, in Proceedings of EKAW-
2000: The 12th International Conference on Knowledge Engineering and Knowledge
Management, R. Dieng and O. Corby, Editors. 2000, Springer-Verlag. p. 97-112.
17.Brachman, R.J., An Overview of the KL-ONE Knowledge Representation System. Cognitive
Science, 1985. 9(2): p. 171-216.
18.Levesque, H.J. and R.J. Brachman, Knowledge Level Interfaces to Information Systems, in
On Knowledge Base Management Systems: Integrating Artificial Intelligence and Database
Technologies, M.L. Brodie and J. Mylopoulos, Editors. 1986, Springer-Verlag: New York.
19.Abrial, J.R., Data Semantics, in Data Base Management, J.W. Klimbie and K.L. Koffeman,
Editors. 1974, Noth-Holland Publishing: Amsterdam. p. 1-59.
20.Mylopoulos, H.J. and P.A. Bernstein, A Language Facility for Designing Database-
Intensive Applications. ACM Journal on Database Systems, 1980. 5(2): p. 185-207.