Classifying Paths in ER Schemas by Using a Description Logic
for Investigating Query Answering Capability
Kaibo Xu and Junkang Feng
Traditional approaches to the study of queries, such
as using views and integrity constraints, reply upon
natural semantics of the data values of a database.
And contemporary approaches to query answering
capability such as view rewritings and query
containment mappings appear to have focused on
literal meanings of data, but not information (we will,
following semantic information theories, distinguish
between meaning and information, and define them
respectively). With this particular ‘information’
perspective, the notion of ‘classes of a path in an
Entity-Relationship (ER) data schema’ was put
forward as a characterization of the capability of a
schema of accommodating data instances whereby to
provide information for answering a query. Thus far
though, criteria with which a process of classifying
paths can be systematically carried out are yet to be
found and formulated. To this end, one possible
approach seems to first all accurately and formally
describe paths so that we can reason about them, and
then to examine the characteristics of the formal
representations of the paths with a view to finding
useful clues and indications. We propose to use
Description Logics (DL) for this task. In this paper,
we show how to use Description Logics to formulate
paths in an ER schema whereby to find desirable
criteria. We also address related reasoning problems
by discussing a number of reasoning algorithms.
Keywords:
Description Logics, Query Answering
Capability, Classes of Paths, Information Bearing
Capability
1. INTRODUCTION
Following (Dretske, 1981), we define the ‘meaning’ of
a piece of data to be the literal and/or conventional
meaning of the linguistic signs (Mingers, 1995)
involved. And we define the information that a piece
of data bears to be what one could get to know what
happens to be true by consulting the data (Floridi,
2003). Under the general issue of ‘data bear
information’, the notion of ‘classes of a path in an
Entity-Relationship (ER) data schema’ in (Feng and
Crowe, 1999) has been proposed as a means of
identifying and formalizing the capability of a
database in answering a query. To put briefly, in
relation to a query, namely a piece of information that
is required, any path in an ER schema is one of seven
possible classes, and it was found that only certain
classes are useful for answering queries.
The classes are arrived at by following the two
conditions described below, which we believe are
sensible and therefore taken as given:
For a token level data construct, say t, to be capable of
representing an individual real world object or an
individual relationship between some real world
objects, say s, which is neither necessarily true nor
necessarily false (Floridi, 2002), two conditions must
be satisfied:
1) Information content containment
The information content of t when it is considered
in isolation must include s, the simplest case of
which is that the literal or conventional meaning
of t is part of its information content, and the
literal or conventional meaning of t is s;
2) Data construct distinguishability
And t must be distinguishable from the rest of the
data constructs in a system, say Y, that manages
data including t.
In our previous work, we intuitively demonstrated
how to classify individual paths in an ER schema
(Feng and Crowe, 1999). However that work does not
cover how to systematically and precisely classify
individual paths in an ER schema, which would seem
to be the next step of research in this direction. To this
end, to accurately and formally describe paths so that
we can reason about them, and then to examine the
characteristics of the formal representations of the
paths with a view to finding useful clues and
indications seems a sensible approach, which might
well lead to much desired solutions. In this paper, we
propose to use DL to identify and reason about the
meanings represented by the whole of a path in an ER
schema.
DL have found their way into many areas such as
conceptual modeling (Calvanese et. al. 1998),
information integration and so on. However, few DL
based approaches to query answering capability
appear in the literature. Our motivation shown through
this paper is to find out whether the approach just
described above works, and in particular whether DL
is helpful for the classification of paths and the role
DL play in it. We re-iterate our approach as follows.
First, we accurately express the literal meaning and
reason about implicit meanings of paths of an ER
schema by using a Description Logic. Second, we
analyze these DL expressions to identify possible
criteria for identifying the classes to which a particular
path belongs. To this end, we make use of the
reasoning capability of DL systems, among others.
The paper is organized as follows. In the next section,
we review some relevant literature. In Section 3 we
describe briefly the ideas of the ‘classes of a path’.
Section 4 shows how ‘classes of a path’ in ER
schemas can be identified by extending and using a
Description Logic. Section 5 and Section 6 discuss
two types of popular reasoning algorithms, namely the
structural subsumption algorithms and the tableaubased subsumption algorithm to reason about the
subsumption and satisfiability relationships in classes
of paths. The final section contains some concluding
remarks on our findings.
2. LITERATURE REVIEW
The literature on database design, for example, (Batini
et. al. 1992) and (Elmasri and Navathe, 2000) does not
seem to have addressed this problem of query
answering adequately. Studies of query languages
such as SQL, DQL and XQL focus on the expressivity
of the languages themselves but not the answering
capability of sources (i.e., a database) with regard to
given queries.
Some papers do propose the notion of ‘query
(answering) capability’, for example, (Alon, et al,
1995), (Calvanese et. al. 1999) and (Calvanese et. al.
2000), and acknowledge that such a capability is
essential for a database system. This capability is
discussed in view rewriting (Alon et. al. 1995) and
capability-based mediation (Li et. al. 1998), in which,
query answering capability seems to be seen as
equivalent to the simple question of whether data
elements (tuples, attributes, etc) and their connections
that are required by a query exist in the database or not
(Calvanese et. al. 1999). These approaches to query
answering capability can be divided roughly into two
categories: capability-based (Li et. al. 1998) and viewbased (Alon et. al. 1995; Calvanese et. al. 1999;
Calvanese et. al. 2000; Li and Chang, 2001).
Capability-based approaches consider only the
semantics of attributes set when they describe the
capability of sources (Li et. al. 1998). View-based
approaches also use the semantics of attributes set to
describe pre-defined views (Alon et. al. 1995;
Calvanese et. al. 1999; Calvanese et. al. 2000).
The weaknesses of these approaches appear to be the
following. The first is that semantics represents the
literal meaning which is not necessarily information
(Dretske, 1981, Chapter 2), let alone the whole
information that a source contains. Semantics is
useless if it provides no information. Secondly, it
would seem that these approaches consider at most the
semantics of connections of entities whose
relationships are explicitly specified by the referential
integrity rule.
As a result, problems occur. For example, a common
problem in constructing an ER schema, in deriving
information by querying a database, and in entering
data into a database in order for it to be able to
represent certain information is that a database is
mistakenly taken to be able to represent or to have
represented some information that it is unable to
represent. This includes misinterpretation of the
meaning of some connection structures in the ER
schema. The term connection trap has been used to
label this type of errors. For example, fan trap and
chasm trap (Feng and Crowe, 1999). These relatively
earlier works were largely based upon intuitive rather
than formal approaches.
It is also recognized in the literature, for example, in
(Baader et. al. 2003), that network-based modeling
formalisms are informal (i.e., based upon intuition)
and therefore inadequate in defining semantics
formally. One promising intellectual tool for this task
would appear to be the Description Logics. A number
of various Description Logics have been proposed
such as ALCQI, CLASSIC, BACK, LOOM, KRIS, and
CRACK.
3. THE NOTION OF ‘CLASSES OF A PATH’
To study what determines whether a query to a
database would be satisfied by a database, it seems
necessary to first all conceptually find out whether the
database is capable of storing data that would give the
information that the query is after. The approach to
such a capability in (Feng and Crowe, 1999) is to look
at the ER schema on the level of paths, namely part of
an ER schema, all the elements in which are
connected. Here we first introduce some definitions
that we use for our purposes in an ER schema.
Topological connections are the connections made
possible by the topological structure of an ER schema.
Semantic relations are the relationships between
objects in the ‘real world’, which are independent of
an ER schema or any other modeling formalism. If a
topological connection satisfies the aforementioned
‘information content containment’ condition in
relation to a semantic relation, we say that the former
is relevant to the latter. Otherwise it is an irrelevant
topological connection to the semantic relation. Note
that a path might enable irrelevant topological
connections to exist as well as relevant ones.
It was observed in (Feng and Crowe, 1999) that in
relation to a given query, a path can only be one of
seven possible classes. In Fig. 1, we show the
definitions for the seven classes, namely a, b1, b2, c1,
c2, d, and e. Note that in the diagram, A represents the
‘topological connections’ made possible by a path,
and B ‘semantic relations’ between entities, which
formulates an information requirement. C is ‘relevant
connections’ in A in that they are useful for
representing (possibly part) of B. And D is ‘irrelevant
connections’ in A (i.e., irrelevant to representing
(possibly part) of B). E is the subset of B that is not
represented by A.
A
A
D
c1)
B  A.
Elements of D are not elements of B. D are ‘false
semantic relations that may exist’, which may be
caused by a fan trap or ‘true but irrelevant semantic
relations that can be represented by elements of A’.
Elements of D and elements of B cannot be
differentiated. Any element of B has a corresponding
element of A. There is no chasm trap.
B
A
a)
c2)
A  B = .
Given a set of true semantic relations B and a path A,
no true semantic relation in B is captured by A.
B
A
b1)
C
D
Elements of F are not elements of B. F are ‘irrelevant
connections’ in A. Elements of F and elements of B
can be differentiated.
B
Elements of D are not elements of B. D are ‘false
semantic relations that may exist’, which may be
caused by a fan trap or ‘true but irrelevant semantic
relations that can be represented by elements of A’.
Elements of D and elements of C cannot be
differentiated. E are elements of B that can not be
represented by A, which we call ‘true semantic
relations that cannot be captured’. E may be caused by
a chasm trap.
F
d)
A
E
A  B.
Any element of A is an element of B, so there is no
‘false semantic relations that may exist.’
E are elements of B that cannot be represented by A,
i.e., there are ‘‘true semantic relations that cannot be
captured.’ E may be caused by a chasm trap.
A, B
B
C
B
B  A.
A  B = C  , A  B, and B  A.
b2)
F
Any element of B can be represented by element(s) of
A, i.e., there is no ‘true semantic relations that cannot
be captured.’ There is no chasm trap.
E
A
B
e)
E
A = B.
A  B = C  , A  B, and B  A.
Elements of F are not elements of B. F are ‘irrelevant
connections’ in A. Elements of F and elements of C
can be differentiated.
E are elements of B that cannot be represented by A,
which we call ‘true semantic relations that cannot be
captured’. E may be caused by a chasm trap.
Any element of A is an element of B, so there are no
‘false semantic relations that may exist.’ There is no
fan trap.
Any element of B can be represented by element(s) of
A, i.e., there are no ‘true semantic relations that cannot
be captured.’ There is no chasm trap.
Fig. 1. Classes of a path
For example, in Class b1, A  B = C  , A  B, and
B  A. Elements of D are not elements of B. D are
‘false semantic relations that may exist’, which may
be caused by a fan trap or ‘true but irrelevant semantic
relations that can be represented by elements of A’.
Elements of D and elements of C cannot be
distinguished from each other. E are elements of B
that cannot be represented by A, which we call ‘true
semantic relations that cannot be captured by A’. E
may be a result of the chasm trap in a path. Other
classes can be interpreted in the same way.
Each of the classes has been given a meaningful name,
such as ‘mutual exclusion’ (which is Class a) and
‘total inclusion’ (which is Class e), in order to indicate
the relationship between what a path is capable of
representing and what a query requests. In relation to a
particular query, as long as it is capable of
representing something that the query requests, then a
path is said to be ‘sound’; If it is capable of
representing all that the query requests, then a path is
said to be ‘complete’. Here are the definitions of
‘Soundness’ and ‘Completeness’.
Soundness: With respect to a set of true semantic
connections between some entities within a path, if
some or all distinguishable topological connections
that are made possible by a path represents at least a
proper subset of the set of true semantic connections,
then the path is said to be sound.
Completeness: With respect to a set of true semantic
connections between some entities within a path, if
some or all distinguishable topological connections
that are made possible by a path represents the whole
set of true semantic connections, then the path is said
to be complete.
Table 1 shows the meaningful names for the classes
and their ‘soundness’ and ‘completeness’ or the lack
of them. The reader is referred to (Feng and Crowe,
1999) for more details about the notion of ‘classes of a
path’.
Table 1. The 'soundness' and 'completeness' of the classes of a
path
Class of a path
Class a
(mutual exclusion)
Class b1
(partial and nondifferentiable inclusion)
Class b2
(partial and differentiable
inclusion)
Class c1
(total and non-differentiable
inclusion)
Class c2
(total and differentiable
inclusion)
Class d
(partial representation)
Soundness
Completeness
no
no
no
no
Class e
(total representation)
yes
yes
4. IDENTIFYING CLASSES IN ER SCHEMAS
BY DESCRIPTION LOGICS
In relation to different sets of true semantic relations
between entities, which formulate an information
requirement, a path can be of different classes. It has
been shown that how Description Logics can be used
to help define the semantics of a path by redefining a
translation  from ER schemas and information
requirements to knowledge bases (Xu and Feng,
2004). In Description Logics, a knowledge base
includes a finite set of assertions of the following
forms:
A C (inclusion assertion)
A ≐ C (equality assertion)
The semantics of a knowledge base is specified
through the notion of satisfaction of assertions. Here is
an example.
Fig. 2. A path of ‘Class b1’ in relation to ‘which
lecturer is involved in the teaching of which courses’
with implied ER-relationship and implied ER-roles
The ER schema in Fig. 2 can be described as follows:
U1:
Bof¯.Belongs_to ⊓ ≥0Bof¯⊓
Lecturer
≤1Bof¯
Department
Bin¯.Belongs_to ⊓ Rby¯.Runs
Rof¯.Runs ⊓ =1Rof¯
Course
Belongs_to
Bof.Lecturer ⊓ =1Bof ⊓
Bin.Department ⊓ =1Bin
Runs
Rby.Department ⊓ =1Rby ⊓
Rof.Course ⊓ =1Rof
yes
no
no
no
yes
yes
U2:
yes
no
Lecturer
The information requirement is ‘which lecturer is
involved in the teaching of which courses’, which can
be expressed by Description Logic:
Tby¯.Teaches ⊓ ≥1Tby¯
Tof¯.Teaches ⊓ ≥1Tof¯
Course
Department
Tin¯.Teaches ⊓ ≥1Tin¯
Tby.Lecturer ⊓ =1Tby ⊓
Teaches
Tof.Course ⊓ =1Tof ⊓ Tin.Department ⊓
=1Tin
Rof¯.Runs ⊓ =1Rof¯ ⊓ Tof¯.Teaches
Course
⊓ ≥1Tof¯
Runs
Rby.Department ⊓ =1Rby ⊓ Rof.Course
⊓ =1Rof
Tby.Lecturer ⊓ =1Tby ⊓ Tof.Course
Teaches
Here Teaches is the implied ER-relationship, Tby and
Tof are implied ER-roles because we know the rule
that if a lecturer belongs to a department which runs a
course then he may teach this course.
⊓ =1Tof ⊓ Tin.Department ⊓ =1Tin
Intuitively, if there is no rule in the real world that if a
lecturer does NOT belong to a department which runs
a course then he teaches the course, then we cannot
⊓ Tby¯.Teaches ⊓ ≥1Tby¯
say U1 ⇒ U2. Namely the ER schema cannot represent
the information requirement of ‘which lecturer is
involved in the teaching of which courses’.
Tin¯.Teaches ⊓ ≥1Tin¯
C.
Bof¯.Belongs_to ⊓ ≥0Bof¯⊓ ≤1Bof¯
Lecturer
Department
Rof¯.Runs ⊓ =1Rof¯ ⊓ Tof¯.Teaches
Course
In this example, let
⊓ ≥1Tof¯
A = ‘A lecturer belongs to a department, and a
department runs a course’,
Belongs_to
B = ‘A lecturer is involved in the teaching of a
particular course run by a particular department’,
Runs
C = ‘A lecturer who belongs to a department is
involved in the teaching of a particular course run by
this department’,
D = ‘A lecturer who belongs to a department is not
involved in the teaching of a particular course run by
this department’,
E = ‘A lecturer who does not belong to a department is
involved in the teaching of a particular course run by
this department’,
Now we translate the above into DL expressions:
A.
Bof¯.Belongs_to ⊓ ≥0Bof¯⊓ ≤1Bof¯
Department
Bin¯.Belongs_to ⊓ Rby¯.Runs
Rof¯.Runs ⊓ =1Rof¯
Course
Belongs_to
Bof.Lecturer ⊓ =1Bof ⊓
Bin.Department ⊓ =1Bin
Runs
Rby.Department ⊓ =1Rby ⊓ Rof.Course
⊓ =1Rof
Department
≥1Tin¯
⊓
=1Bof
Tby¯.Teaches ⊓ ≥1Tby¯
Rby¯.Runs ⊓ Tin¯.Teaches ⊓
⊓
Rby.Department ⊓ =1Rby ⊓ Rof.Course
⊓ =1Rof
Tby.Lecturer ⊓ =1Tby ⊓ Tof.Course
Teaches
⊓ =1Tof ⊓ Tin.Department ⊓ =1Tin
D.
Bof¯.Belongs_to ⊓ ≥0Bof¯⊓ ≤1Bof¯
Lecturer
⊓ ¬Tby¯.Teaches ⊓ ≥1Tby¯
Department
Bin¯.Belongs_to ⊓ Rby¯.Runs ⊓
¬Tin¯.Teaches ⊓ ≥1Tin¯
Rof¯.Runs ⊓ =1Rof¯ ⊓
¬Tof¯.Teaches ⊓ ≥1Tof¯
Belongs_to
Bof.Lecturer ⊓ =1Bof ⊓
Bin.Department ⊓ =1Bin
Runs
Rby.Department ⊓ =1Rby ⊓ Rof.Course
⊓ =1Rof
Teaches
Tby.Lecturer ⊓ =1Tby ⊓ Tof.Course
⊓ =1Tof ⊓ Tin.Department ⊓ =1Tin
E.
B.
Lecturer
Bof.Lecturer
Bin.Department ⊓ =1Bin
Course
Lecturer
Bin¯.Belongs_to ⊓ Rby¯.Runs ⊓
Lecturer
¬Bof¯.Belongs_to ⊓ ≥0Bof¯⊓
≤1Bof¯ ⊓ Tby¯.Teaches ⊓ ≥1Tby¯
Department
¬Bin¯.Belongs_to ⊓ Rby¯.Runs ⊓
Tin¯.Teaches ⊓ ≥1Tin¯
Rof¯.Runs ⊓ =1Rof¯ ⊓ Tof¯.Teaches
Course
⊓ ≥1Tof¯
Belongs_to
Bof.Lecturer ⊓ =1Bof ⊓
Bin.Department ⊓ =1Bin
Runs
Rby.Department ⊓ =1Rby ⊓ Rof.Course
⊓ =1Rof
Teaches
Tby.Lecturer ⊓ =1Tby ⊓ Tof.Course
⊓ =1Tof ⊓ Tin.Department ⊓ =1Tin
A is the union of C and D. B is the union of C and E.
C corresponds to some connections in A. But they
cannot be differentiated from the connections of D
because we cannot distinguish several interpretations
such as (Tby¯.Teaches) and (¬Tby¯.Teaches),
which are concerned with the implied ER-role Tby on
implied ER-relationship teaches. That is, we cannot
derive the appropriate information from all the mixed
instances by comparing the implied ER-roles or
implied ER-relationships.
This example illustrates how DL helps the
classification of a path. As for the two conditions
mentioned in the Introduction Section of this paper,
i.e., the Information Content Containment condition
and the Distinguishability condition, DL helps us
identify criteria for them.
The Information Content Containment Condition
In Description Logics, a knowledge base  is a set of
assertions (including inclusion assertions and equality
assertions), which contains atomic concepts and
concept expressions. Let (A) be the relevant
information content of path A in an ER schema, which
has been formulated by using the description language
of a Description Logic. Let (B) be a set of semantic
relations, which formulates an information
requirement or a query, formalized by the description
language of a Description Logic. In the following
examples, (A) and (B) are captured by concept
expressions. The inclusion relationship between A and
B is expressed in the form like (B)  (A) which
means the relevant information content of A includes
the other of B.
That is to say, If (B)  (A), then condition one is
satisfied. After transforming these Description Logics
expressions of (A) and (B) to a normal form
(Baader et. al. 2003), we can easily compare them to
find out whether one includes another. For example,
for the path in Fig. 2, condition one is not satisfied
because (U1)  (U2). The path is therefore in
‘partial inclusion’.
The Distinguishability Condition
For this condition we observe the following criteria
for verifying whether a path in an ER schema is
distinguishable from the rest data constructs in the
database system. If all the differences between
concept expressions of (I) and (J) with regard to
every atomic concept in them are the different
quantifiers which restrict the same pairs of ERrelationship, ER-role, attribute or domain symbols
except implied ER-relationship or implied ER-role
symbols, then (I) and (J) can be distinguished.
Otherwise they cannot.
That is to say, if there is any difference between the
quantifiers that restrict the same pairs of implied ERrelationship or implied ER-role symbols, then these
two concept expressions cannot be distinguished.
5. REASONING
PATHS
IN
CLASSIFICATION
OF
To apply the criteria identified above, paths need to be
expressed in DL. If a path is long, complex, and lack
of ‘locality’ (Leonid, 2000; Vardi, 1997), then
inferences with DL would be needed.
Providing a formalization of ER schemas in terms of a
DL language facilitates reasoning to be performed on
the schemas. It is well known that checking
satisfiability of concepts and moreover the concept
subsumption problem is the key inference in
Description Logics reasoning tasks. Unfortunately one
type of the popular reasoning algorithms, namely the
structural subsumptions algorithms fail to complete
because they are unable to handle DL languages that
include complex constructors such as disjunction, full
negation, and full existential restriction. For these
languages, the tableau-based subsumption algorithm
has turned out to be quite useful.
Here is an example concerning the tableau-based
subsumption algorithm. There is an ER schema that
shows two relationships Belongs_to between entity
Lecturer and Department, Run between entity
Department and Course respectively. A lecturer
belongs to a department, which runs a course.
In brief, the concept description of Lecturer is:
Lecturer ○ Belongs_to.(Department ⊓
Runs.Course)
There is another statement that a lecturer is involved
in the teaching of a particular course.
Lecturer ○ Teaches.Course
To check whether (1)
(3) is unsatisfiable.
⇒
(2), we must verify whether
Belongs_to.(Department ⊓ Runs.Course) ⊓
 Teaches.Course
After transforming (3) by using the usual rules for
quantifiers, we obtain:
Belongs_to.Department ⊓
Belongs_to.(Runs.Course) ⊓  Teaches.Course
There must exist an individual, say b, that satisfies
each of the conjuncts:
b  Belongs_to.Department
b  Belongs_to.(Runs.Course)
b   Teaches.Course
From (6) we can deduce that there must exist an
individual c such that (b, c)  Belongs_toI and
c(Runs.Course)I. Analogously, c(Runs.Course)I
implies the existence of an individual f with (c, f)
RunsI and fCourseI.
From (7) we can deduce that there must NOT exist an
individual d that (b, d)  TeachesI and dCourseI.
Here we introduce the notion of composition
constructor ○, which is one of the role-forming
constructors. If R, S are role descriptions, then R○S
(composition) is also a role description. A given
interpretation I can then be extended to complex role
descriptions as follows:
(R ○ S)I = {(a, c)  I  I  b.(a, b)  RI  (b, c)
 SI } [1];
Assume Teaches = Belongs_to ○ Runs, we obtain that
(b, f)  (Belongs_to ○ Runs)I = TeachesI and
fCourseI, which has an contradiction. This algorithm
proves that (1) ⇒ (2) when Teaches is the composition
role of Belongs_to and Runs.
6. UNDECIDABILITY
The interesting reasoning problems such as
subsumption and satisfiability are, in most small
description logics, effectively decidable. However,
unfortunately not all the satisfiability and subsumption
of reasoning in Description Logics is decidable. For
example, subsumption in FL (○,) and FL (○, =) is
undecidable (Baader et. Al. 2003).
One of the reasons why satisfiability and subsumption
in many Description Logics are undecidable is that
there exist some unlocal (Baader et. al. 2003)
problems. However, most of the concept/role
constructors in these Description Logics can express
only local properties about elements. That is to say,
these Description Logics do not satisfy locality
(Leonid, 2000; Vardi, 1997).
In Description Logics, the notion of locality restricts
that the elements that are linked to a concept cannot be
arbitrarily far with respect to role links from this
concept. If there is a Description Logic language that
does not satisfy locality, then it is too hard for us to
use this language to compute and reason about the
satisfiability and subsumption relationships. Therefore
it is undecidable.
The capability for data of bearing information has the
same kind of problems. If a data construct is rather
complex, then satisfiability and subsumption
relationships become undecidable. It is also
impossible for us to automatically derive all the
information borne by this rather complicated data
construct. Therefore we divide the subsumption check
in reasoning about this type of capabilities (i.e., data’s
bearing information) into two parts: local problems
and unlocal problems.
We use reasoning services of those small and less
expressive but decidable Description Logics such as
ALCtrans, which is one kind of ALC extended by
agreements and disagreements to automatically check
whether a data schema is subsumed by an information
requirement. That is, we perform reasoning algorithms
during the subsumption checking to derive those
simple implicit meanings, which are the meanings
implied by concept/role constructors that are only
concerned with local properties of concept elements.
Similarly, a complex implicit meaning is the meaning
implied by concept/role constructors that are
concerned with unlocal properties of concept
elements, for example, the meanings that are implied
by the constructor role-value-maps. In such a case,
namely, when we meet some complex unlocal
problems, which are complex and undecidable, we use
role-value-maps or other complex and more
expressive constructors in the Description Logic
languages to manually check the subsumptions.
7. CONCLUSIONS
In this paper we have shown how to use Description
Logics to help classify paths of an ER schema. We
have given our findings, in particular the criteria
identified through examining DL expressions of paths
of an ER schema, which would help the process of
classifying a path. We have also made suggestions on
how to tackle undecidability problems in reasoning
about the paths.
Our conclusion is that our approach to the
identification of criteria for classifying paths seems
working, and Description Logics is a suitable
modeling formalism to capture and reason about the
meanings of paths of an ER schema and the usefulness
of paths in answering a query for information.
ACKNOWLEDGE
I would like to thank my friend, Mr.HongWei Xu and
other members of this database research group, for
their help and wise advices.
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