Computing and Information Systems
© University of Paisley 2005
Beyond Semantics: Verifying Information Content Containment
of Conceptual Data Schemata by Using Channel Theory
Yang Wang and Junkang Feng
There is an ever-growing need to consider semantics
in various research fields. Although numerous
methods and solutions have been proposed and used
along this line, some fundamental issues that need to
be addressed still remain. The one that we are
particularly interested in is how something that has
semantics could have impacts on its receiver. It would
seem that the impacts results from the capability of
yielding knowledge. And by Dretske’s notion of ‘to
know’, an essential component of this capability is
information provision. Semantics has a role to play
only if it contributes to the provision of information.
Our approach to addressing this issue is therefore to
use a number of theories that address the problem of
information flow. In this paper we focus on the
problem of ‘information content’ of some informationbearing objects or events, such as a piece of data that
are constructed in some particular way, which we call
‘data construct’.
To verify whether the information content of a given
data construct contains a given piece of information
systematically is not easy, particularly so when the
information is beyond the literal meaning of the data.
In this paper, we describe how a sophisticated theory
about information flow, namely the Channel Theory,
can be used for such a task. The main point we make
in the paper is that this task can be accomplished
through identifying nested information channels that
cover both some intra-properties and inter-properties
of a schema.
Our work so far seems to show that this is a promising
avenue. Such an approach introduces mathematical
rigor into the study, and results in a sound means for
the verification. This in turn provides the practice of
conceptual modeling and validation with a desirable
and reliable guidance.
1. INTRODUCTION
Semantics has become an increasingly significant
factor in various information system (IS) research
fields such as system integration, knowledge
representation and management, and semantic web
services. In order to develop sound semantics-based
approaches and methods, the need for solid theoretical
bases cannot be overlooked. Our interest resides in
1
how semantics of something could have impact on its
receiver. It would seem that the impact results from
the capability of yielding knowledge. And by
Dretske’s notion of ‘to know’ (Dretske 1981, p.92), an
essential component of this capability is information
provision.
Therefore we have been exploring the relevance of
semantic information and information flow theories,
such as Dretske’s work (1981), Devlin’s work (1991)
and the Information Flow theory (also called
Information Channel Theory, CT for short) put
forward by Barwise and Seligman (1997), to
information systems. In this paper, we present our
thinking on what we call ‘information content
containment’, i.e., how an information-bearing object,
such as a data construct, conveys information that
constrains a given piece of information. Such a
concept is put forward as an essential part of the
notion of ‘Information Bearing Capability’ (IBC) by
Feng and his colleagues in (Feng 1999, Xu and Feng,
2002, and Hu and Feng, 2002). This notion and many
associated ideas are a result of observations through
years of experience. There are four conditions
identified that enable a data construct to represent a
particular piece of information (which is called ‘the
IBC Principle’ for convenience and will be given
shortly), one of which is called the ‘information
content containment’ condition. To verify whether
these conditions hold of a particular system is not
straightforward, as it is not simply a matter of
checking the literal meaning of the data. To this end,
we have been making considerable effort and achieved
some preliminary yet encouraging results. Among
what have been achieved, it was found that employing
a sophisticated theory of information flow within a
notional distributed system, namely the Channel
Theory (CT) introduces much needed rigor into this
work and can serve as a sound means for verifying
whether the ‘Information Content Containment’
condition is satisfied over any given pair of two
elements, one of which is a data construct and the
other a piece of information. That is, whether the
‘information content' of the data contains the
information. In this paper we describe our approach by
using examples in conceptual data modeling, and
avoid any lengthy description of the CT per se.
The rest of the paper is organized as follows. In the
next section, the IBC Principle is introduced. After
that, the reasons why we choose the Channel Theory
as our intellectual tool for the job in hand are
described. In Section 5, we present details on how we
verify the ‘Information Content Containment’
condition by using the method of CT summarised in
section 4. In Section 6, some related works that are
concerned with ‘information content preserving’ in
schema transformation and with contributions of CT
to semantic interoperability and ontology mapping are
briefly summarised. Finally, we give conclusions and
indicate directions for further work.
2. THE ‘IBC’ PINCIPLE AND ITS RELEVANCE
In practice, due to the lack of understanding of the
difference and link between information and data,
problems can occur. For example, it is difficult to
identify
redundant
or
conflict
information
requirements; the transformation from human level
models to machine level design and implementation
may not be information content preserving; a query to
a system may receive unsound and/or incomplete
answers. An underlying reason for this could be that
the system’s capability of bearing information is overestimated or mis-interpreted. Some of such problems
were recognized as ‘connection traps’ by Codd (1970)
and Howe (1989), and discussed in detail in Feng and
Crowe’s work (1999). We envisage that the ideas of
‘Information Bearing Capability’ should help.
The notion of IBC and the work around it were
developed over a number of years as shown in series
of works (Feng 1999; Xu and Feng 2002 and Hu and
Feng, 2002). The version of it that we present here is
that which takes into account the three major parties
that are involved in information flow, namely
information source (S), information bearer (B), and
information receiver (R). We call such a thought the
framework of SBR for simplicity and convenience
purposes. The IBC Principle (Feng, 2005) is now
specified as follows:
This Principle is concerned with token level (in
comparison with the ‘type level’) data (or media)
constructs’ representing individual real world objects
and individual relationships between some real world
objects.
 For a token level data construct (or a ‘media
construct’ in general), say t, to be capable of
representing an individual real world object or an
individual relationship between some real world
objects (or a ‘referent construct’ in general), say s,
which is neither necessarily true nor necessarily
false1,
1
See Floridi (2002).
2
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;
And t must be distinguishable (identifiable)
from the rest of the data constructs in a system,
say Y, that manages data including t (or from the
rest of the media constructs in a system Y that
manages media constructs including t, in general).
The above two conditions were formulated from the
viewpoint of the relationship between S and B under
the SBR framework.
 For a data construct (or a ‘media construct’ in
general) t that is capable of representing an
individual real world object or an individual
relationship between some real world objects (or a
‘referent construct’ in general) s to actually provide
information about s,
t must be accessible by the only means
available to system Y;
In the case that t has neither literal nor
conventional meaning and in the case that neither
the literal nor the conventional meaning of t is s,
the information receiver, i.e., the R in the SBR
framework, must be provided with means by Y to
infer s from t.
The above two conditions were formulated from the
viewpoint of R’s obtaining information about S via B
under the SBR framework.
This Principle is scalable to more (i.e., t could be an
instance of an entire system among many related
systems, for example) or less (e.g., an instance of a
simple attribute of an entity in an ER schema)
complex cases, and hence flexible in terms of
applicability.
We call the first condition of the above four the
‘Information Content Containment’ condition. And
the concept of ‘information content’ of a sign/message
can be defined as follows (Dretske 1981, p.45):
‘A state of affairs contains information about X
to just that extent to which a suitably placed
observer could learn something about X by
consulting it.’
In this paper, we focus on how we could verify
whether a state of affairs contains information about
X. And our approach is to make use of theories on
information flow.
3.
SOME THEORIES ON INFORMATION
FLOW
3.1 Dretske’s Semantic Theory of Information
Dretske put forward a theory (Dretske, 1981), which
not only captures, following Shannon (Shannon and
Warren, 1949), the quantitative aspect of
communication of information, but also addresses the
information content of an individual message. These
form an account of how information can flow from its
source to a cognitive agent, i.e., the receiver. Although
his theory has been widely cited, we also note its
objections. Firstly, as Dretske’s theory is based upon
probability, certain conditions must be maintained for
a probability distribution to occur. In the ‘real world’,
this might be a stringent requirement. Secondly,
Dretske includes the ‘internal’ contribution of the
prior knowledge k and the ‘external’ contribution of
objective probabilities to the conceptualisation of
information flow. However, Dretske has to accept that
different ways of determining relevant possibilities
and precisions give different probability measures and
therefore different information flow and knowledge
(Barwise and Seligman, 1997). Finally, Dretske goes
beyond Shannon’s work (1949) that concerns solely
the quantitative aspect of communication with many
messages (Devlin, 2001), and tackles explicitly the
content of information that an individual message
bears. And yet it is difficult to identify the information
content of an individual message.
3.2 Devlin’s ‘Infon’ and Situation Theory
To model information flow, the mechanism used by
Devlin (1991) is made up of situation types and
constraints, which connect situation types. This theory
seems to emphasise the ‘soft’ aspect of information
flow, i.e., what is going on in people’s mind.
Moreover, it does not seem to address the issue of how
a constraint gets established, which would not rule out
the possibility of them being arrived at subjectively.
3.3 The Information Channel Theory
Taking into consideration the shortcomings of the
above two theories on modelling information flow, we
choose the Channel Theory (Barwise and Seligman,
1997) as a tool to verify whether a given data
construct satisfy the ‘information content containment
condition’ of the aforementioned IBC Principle. The
reasons why we think that this is appropriate are
summarised below.
In general, saying that ‘B bears information about S’
is the same as saying ‘there is information flow from S
to B’. And the latter is in the language of CT, which is
a systematic approach to mathematically modelling
and analysing information flow.
3
With CT, information flow is possible only because
what is involved in information flow can be seen as
components of a distributed system. That is to say, the
notion of ‘distributed system’ provides us with a way
to model and formulate, if possible, an ‘information
channel’ within which information flows.
Information flow requires the existence of certain
connections (which may be abstract or concrete)
among different parts that are involved in information
flow. Following Dretske (1981, p.65), such a
‘connection’ is primarily made possible by the notion
of ‘conditional probability’ where the condition is the
Bearer. However, this is perhaps only a particular way
for ‘connections’ to be established. It would be
desirable to see in general how a connection becomes
possible. The notion of ‘information channel’ in CT
helps here. In CT terms, information flow is captured
by ‘local logics’ (which are roughly conditionals
between ‘types’) within a distributed system. Most
frequently, information connections lie with ‘partial
alignments’ (Kalfoglou and Schorlemmer, 2003)
between system components. CT is capable of
formulating such alignments by using concepts of
‘infomorphisms’ ‘state space’, and ‘event
classification’. The property of ‘state space’ enables
every instance and state relevant to the problem to be
captured. Consequently, informational relationship
between components connecting through the whole
system can be modelled as the inverse image of
projections between their corresponding state spaces.
Such inverse images are also known as
‘infomorphisms’ between event classifications. This
is exactly how the ‘infomorphisms’ for the ‘core’
(which is a classification for the whole distributed
system) of an information channel can be found. We
ask our readers, who are not familiar with CT, to bear
with us here as we will use example to show the basics
of CT shortly.
4. A METHOD OF USING CT TO VERIFY
INFORMATION CONTAINMENT
We have developed a method for the task at hand,
which consists of a series of steps below. The reader is
referred to the appendix for those numbered terms:
 Identify component classifications[1] relevant to the
task at hand and then use them to construct a
distributed system;
 Validate the existence of infomorphisms[2] between
the classifications and construct an information
channel[3] relevant to the task at hand;
 Construct the core of the channel by identifying
those parts of the component classifications
(including normal tokens[4]) that contribute to the
desired information flow;
 Find the local logic[5] on the core, i.e., the
entailment relationships between types of the
classification for the ‘core’ that is directly relevant
to the information flow, i.e., the information content
containment at hand;
 Arrive at desired system level’s theory
applying the f-Elim rule
core.
[7]
[6]
by
on the local logic on the
We describe this method in detail by means of
examples in the next Section.
5.
VERIFYING
CONTAINMENT
INFORMATION
We believe that to verify whether the information
content of the schema contains something about a
specific ‘real world’ application domain takes two
steps, which can be roughly seen as corresponding to
the syntactic level and the semantic level of
(Organisational) Semiotics (Stamper, 1997; Liu, 2000
and Anderson 1990). We use Figure 1 to show our
points.
has
has
Marks
(0,n)
(1,1)
finished
student
(1,1)
(1,n)
Qualifications
added
Figure 1 Topological connection t
5.1 Semantic Level
On this level, the problem being addressed is
‘meaning, propositions, validity, signification,
denotations,…’ (Stamper, 1997) Accordingly, what
should be looked at is how a topological connection,
which is a connection between entities made possible
by an Entity-Relationship (ER) schema, is able to
represent a real world relationship. That is to say, this
level is concerned with the relationship between a
conceptual data schema and the ‘real world’ that the
schema models. Specifically, we want to see whether
and how information flows from the ‘real world’ to
the schema. In other words, the information content of
the schema includes something about a specific ‘real
world’ application domain.
In the world of CT, information flow is ever possible
only within a distributed system, i.e., a system made
up of distinct components, the behaviour of which is
government by certain regularities. Within such a
system, ‘what’ flows is captured by the notion of
4
‘local logics [5]’ and ‘why’ information can flow is
explained by the concept of ‘information channel [3]’.
Therefore, it is essential to construct relevant and
appropriate ‘distributed systems’. Considering the
condition of ‘information content containment’ of the
IBC Principle under the SBR framework, the
information source is the ‘individual real world object
or individual relationship between some real world
objects (or a ‘referent construct’ in general) s’, and the
information bearer is the ‘topological relation t’.
On this level then, to make sure that a conceptual data
schema is capable of representing some particular real
world individuals involves constructing a distributed
system justifiably that supports information flow
between these two different types of things. The
‘connections’ between them, which are instances of
the distributed system, are crucial.
We view the process of constructing a conceptual
schema for representing some particular real world as
a ‘notional system’.2 It is interesting to note that the
notion of ‘distributed system’ in CT is similar to the
concept of ‘notional system’ in Soft Systems
Methodology (SSM) (Checkland, 1981). In addition,
sometimes we use the term ‘semantic relations’ to
refer to something in the ‘real world’ in contrast to
‘topological connections’, which are elements within a
data schema and can be seen as something on the
syntactic level. Semantic relations are not unlike the
notions of ‘objects in the “reality”’ and ‘social
conventions’ in semiotics (liu, 2000).
In such a distributed system (It is called
‘representation system [8]’in particular), the semantic
relations and the conceptual schema can be seen as
components. Using the notions of CT, the conceptual
model is our source classification (not to be confused
with the ‘information source’ in aforementioned
SBR), and the semantic relation is target
classification. The tokens of the schema consist of all
the instances of data constructs, i.e., the topological
connections between data values. The types of this
classification are different data construct types. An
entity, a relationship or a path in a conceptual model
can all be different ‘types’.
As the process of ‘constructing a schema’ is modelled
as a distributed system, the classification that serves as
the core of our information channel is made up of
connections that are causal links between our
conceptual model (i.e., the schema) and what it
models for and types that are ways of classifying these
links. The logic on this classification captures the
reasoning of the schema construction. That is, the
2
See Checkland (1981)
constraints made up the logic on the ‘core’ of the
system represent the rules employed by the database
designer about how to modeling real world objects to
the conceptual model. The normal tokens of the logic
are the links that must satisfy the constraints, among
all possible tokens of the system.
Now let us use the example in Figure 1 to illustrate
our ideas. Assume that there is a semantic relation s,
say ‘After having successfully passed all required
modules, a student receives a new qualification (a
degree or diploma)’. We show how the topological
connection t (as shown in Figure 1) comes to represent
the semantic relation s. The information channel and
infomorphisms for justifying this are shown in Figure
2.
f1 (topological connection between ‘student’, ‘marks’
and ‘qualifications’) ├ ζ C
f2 (semantic relation between ‘student’, ‘marks’ and
‘qualifications’)
In the above entailment relation, f1 (topological
connection between ‘student’, ‘marks’ and
‘qualifications’) is the result on the core of applying
function f1 to a type of the classification CM, namely
topological connection between ‘student’, ‘marks’ and
‘qualifications’. f2 (semantic relation between
‘student’, ‘marks’ and ‘qualifications’) can be
interpreted the same way.
The f-Elim Rule allows us to move from this
constraint in the logic on the core of the channel to the
component level, and we have:
topological connection between ‘student’, ‘marks’ and
‘qualifications’ ├CM+SR
semantic relation between ‘student’, ‘marks’ and
‘qualifications’.
Figure 2 Information channel diagram 1
In this diagram, C is the ‘core’ of the information
channel that is the process of constructing a schema
like the one in Figure 1; CM and SR are
classifications of the conceptual model (e.g., a data
schema) and a real world application domain
respectively. Infomorphisms f1: CM C and f2:
SR C enable the causal relations between these two
component classifications and the core, which is also a
classification. Combining these two infomorphisms,
we obtain an infomorphism f = f1 + f2 from CM+SR
to C. All of them formulate, following BS97
(Barwaise and Seligman, 1997, p.235), a
representation system R. In the example, business
constraint that ‘if a student has passed all required
modules, he/she is awarded a new qualification’ can
be captured as part of the local logic ζ on the core,
namely:
Note that this move is only valid for those tokens that
are actually connected by the channel. This is
determined by the properties of the f-Elim Rule,
namely it preserves non validity (i.e., ‘completeness’)
but not validity (i.e., not ‘soundness’).
The local logic ζ that holds on the core, i.e., the
distributed system involving topological connections
within the schema and semantic relations within the
real world application domain takes, as a prerequisite,
the tokens of the classification CM (Conceptual
Model, i.e., the schema) that are required for linking to
those of the classification SR (Semantic Relation, i.e.,
the ‘real world’) in order to form the instances of the
core do exist. This would rely upon the inner
relationship within the model, which may be captured
as information flow on a lower level – what we call
syntactic level. That is to say, syntactic level
information flow supports that of semantic level.
5.2 Syntactic Level
topological connection between ‘student’,
‘marks’, and ‘qualifications’ R
semantic relation between ‘student’, ‘marks’ and
‘qualifications’
To formulate it in CT terms results in an entailment
relation between types of the ‘core’ classification:
5
On this level, we look at the inside of a schema (it is
the source system as mentioned above) and find out
whether and how a part of the schema may bear
information about another, namely if information
flows between parts of the schema. This is a type of
constrains that the schema must adhere to, and
eventually the database that is constructed according
to the schema must also. Therefore information flow
within a schema and a database plays a role in
determining what a conceptual schema is capable of
representing. For the example shown in Figure 1, the
problem to be addressed here is what information flow
must exist within the path as a necessary condition in
order to enable the aforementioned information flow
on the semantic level. In CT terms, this is a matter of
making sure that the tokens of the classification CM
(Conceptual Model, i.e., the schema) that are required
for linking to those of the classification SR (Semantic
Relation, i.e., the ‘real world’) in order to form the
‘connections’ (i.e., the instances of the core) do exist.
As above, the task is to find out whether it is possible
to construct an appropriate ‘distributed system’ and an
associated information channel that would support the
desired logics. We will use the same example in
Figure 1. But this time, we will look at ‘informational
relationships’ between parts of the schema rather than
that between the real world and the schema as a
whole. Specifically, we examine whether and how the
entity ‘mark’ actually provides information about
entity ‘qualifications’ by both connecting to the entity
of ‘student’. On this level, the idea of ‘information
source’ and ‘information bearer’ still applies. The
relationship ‘marks-student’ is now the information
bearer, t, while the relationship ‘student-qualification’
is the information source, s. The notional relevant
distributed system will be constructed by using these
two relationships accordingly.
‘There are many ways to analyze a particular system
as an information channel’, and ‘if one changes the
channel, one typically gets different constraints and so
different information flow’ (Barwise and Seligman,
1997, p.43). We will use entity ‘student’ to illustrate
how to construct a distributed system and information
channel for a particular purpose. To help this, the
schema is now extended as shown in Figure 3.
The tokens a, a’….of A are individual ‘markstudent’ relationships at various times. There are
many ways to classify the tokens. The way
adopted here is ‘a student receives his/her final
mark for a module’. For example, there are marks
for ‘SPM’ (‘Software Project Management’
module), ‘ISTP’ (‘Information Systems Theory
and Practice’), etc. These then become the types
of the classification.
Classification B: for relationship ‘studentqualification’.
Like classification A, the tokens b, b’ …of B
consist of individual ‘student-qualification’
relationships at various times. To classify these
tokens we use types like ‘a student is awarded a
particular qualification’. Examples of the
qualifications are ‘BSc IT’, ‘BA BA’, etc.
State space [9] SA: for classification A.
The tokens x, x’… of SA consist of individual
‘mark-student’ relationships at various times. The
states consist of 0 and 1 for each model. The state
of si (i is the name of a model.) is 1, if ‘a student
receives his/her final mark that is no less than 50
for a module’. Otherwise it is 0. For example, if
MSPM ≥ 50, then sSPM = 1SPM, otherwise sSPM =
0SPM. Consequently, the set of state rA for SA
should consist of each state of every included
module, namely rA = {{0SPM,, 0ISTP …, 0OAD}…
{1SPM , 1ISTP…,1OAD}}. If there are altogether 8
modules, the cardinality of rA is 28 = 64.
Event classification [10] Evt(SA ).
The event Classification A associated with SA,
namely Evt(SA) has the same tokens as SA, but
the types of it will be all the subsets of rA, for
instances, {Φ}, {0SPM , 0ISTP,…, 0OAD}, …, {{0SPM ,
0ISTP…, 0OAD}, {0SPM , 0ISP …, 1OAD}},…, {{0SPM ,
0ISTP…, 0OAD}, {0SPM , 0ISTP…, 1OAD}, …, {1SPM ,
1ISTP…, 1OAD}}. That is, Evt(SA) is the power set of
SA. The total number of types of Evt(SA) is
therefore 264. The relationships between the types
and the tokens of A and Evt(SA) follow the tokenidentical infomorphism gA: A
Evt(SA ) (Barwise
and Seligman, 1997, p.55)
State space SB: for classification B.
Figure 3 Extanded Schema
Now, we can define the ‘classifications’ involved.
Classification A: for relationship ‘markstudent’.
6
The tokens y, y’… of SB consist of individual
‘student-qualification’ relationships at various
times. Like SA, the states are also 0 and 1 for each
qualification. The state of sj (j is the name of a
qualification.) is 1, if the ‘degree’ attribute of
‘student-qualification’ is set to an appropriate
degree name. The state of sj is 0 if there is no new
degree is added. For example, if degree, BSc BIT,
is added, the state SBSc BIT = 1, otherwise, SBSc BIT =
0. Therefore, the set of state rB for SB should
consist of each state of every added degree, such
as rB = {1BSc BIT, 0BA BA …}. If there are altogether
two possible added degrees, the cardinality of rB is
22 = 4.
Event Classification Evt (SB ).
The same tokens are present in the event
classification Evt(SB). Similarly, the types of it are
also all the possible subsets of rB. For example,
{Φ}, {0BSc BIT }, {0BA BA }, …, {0BSc BIT , 1BA BA },…,
{1BSc BIT , 0BA BA},…, {0BSc BIT , 0BA BA , 1BSc BIT , 1BA
BA}. If there are totally two degrees, the number of
types for Evt(SB) will be 24. Also, there is a
natural infomorphism gB: B
Evt(SB ).
We define a classification, say W, on which a desired
local logic lives, which is the sum of Classification A
and Classification B[11], namely W = A + B. Any
token of this classification consists of two parts, <a,
b>, where a and b are instances of the ‘mark-student’
relationship,
and
the
‘student-qualification’
relationship respectively. The types of W are the
disjoint union of the types of classification A and B. It
is important to notice that there are no one-to-one
relationships between tokens of classifications A and
B. Although W connects A and B, not all tokens of W
represents meaningful and useful connections between
their tokens. For example, a student might have marks,
which will not relate to a certain degree if he changes
his stream of a course in the middle of a semester.
That is to say, only a subset of the tokens of W
actually participates in the actual information flow.
Therefore, classification W is not the information
channel that we are after. Our aim is to find the partial
alignment (Kalfoglou and Schorlemmer, 2003) for the
core of channel.
To this end, we define state space S for classification
W. The tokens c, c’…. of S are arbitrary instances of
the classification W at various times. The set of states
of S is {rA, rB}. An instance, say w, of classification W
is in state <rA1, rB1>, if the state of w’s ‘mark for a
module’ part is rA1, and the state of w’s ‘qualification
awarding’ part is rB1. There are natural projections [12]
associated with state space S, i.e., pA: S SA, pB: S
SB. In order to find the real informational relationship,
i.e., that a student has passed all required modules for
a course bears the information that the student is
awarded a certain degree, we need to restrict the state
space by eliminating those invalid states, such as
7
<{0SPM, 1ISTP, …1OAD }, {1BSc BIT }>. As a result, we
have a subspace S*of S. This subspace inherits all the
properties of space S including the natural projections.
As we did above regarding Evt(SA ) and Evt(SB), we
can find the event classification Evt(S*) for S*. Such
an event classification enables the existence of partial
relationships between tokens of Evt(SA ) and Evt(SB ).
This is what we want to model as the core of the
information channel. According to a proven
proposition, i.e., Proposition 8.17[13] (Barwise and
Seligman, 1997, p.109), there are infomorphisms
between event classifications Evt(SA), Evt(SB) and
Evt(S*) on inverse directions of the natural
projections between them.
The
infomorphisms
from
the
component
classifications to the core of the information channel
C are defined as follows.
The infomorphism fA: A
C is the
composition of the infomorphisms
gA: A
C.
Evt(SA) and Evt(pA ) : Evt(SA )
The infomorphism fB: B
C is the
composition of the infomorphisms
gB: B
C.
Evt(SB) and Evt(pB) : Evt(SB)
The relationship between information channel C,
component classifications A and B can now be seen in
Figure 4.
Figure 4 Information channel diagram 2
The core Classification C supports a local logic LC,
which is concerned with entailment relations between
sets of states of state space S. Here, as shown in the
conceptual schema diagram, following a regulation in
this particular organisation, there is a system level
constraint, namely ‘if having passed all required
modules like SPM, ISTP …(5), OAD , the student
obtains a new degree, BSc BIT’. Resulted from this,
there should be a constraint supported by the LC:
fA (a student gets final marks that are no less than
50 for SPM, ISTP …(5),OAD) ├Lc
fB (a student is awarded BSc BIT degree)
If we apply the f-Elim Rule to infomorphisms, fA and
fB, this logic can be moved (translated) from the core
to the level of the component classifications A + B as
a regular theory:
a student gets final marks that are no less than 50
for SPM, ISTP …(5), OAD├ Ls
a student is awarded BSc BIT degree
This constraint is valid only under the condition that
relationships
‘marks-student’
and
‘studentqualification’ are satisfied through the channel C.
We would like to point out before we leave this
section that the information channels on the ‘syntactic’
level are conceptualisation of some particular ‘intra
properties’ of a schema, which are actually nested
inside the channels on the ‘semantic level’ that
involve the schema and the real world that it models.
And the latter captures what might be called ‘inter
properties’ of some kind of the schema.
6. RELATED WORKS
Sophisticated concepts stemming from CT were
formulated for explorations on semantic information
and knowledge mapping, exchanging, and sharing
among separate systems. Kent (2002b; 2002a) exploits
semantic integration of ontologies by extending firstorder-logic-based approach (Kent, 2000) based on CT.
An information flow framework (IFF) has been
advocated as a meta-level framework for organising
the information that appears in digital libraries,
distributed databases and ontologies (Kent, 2001).
Based on Kent’s work, Kalfoglou and Schorlemmer
developed an automated ontology mapping method
(Kalfoglou and Schorlemmer, 2003a) by using
concepts of CT in the field of knowledge sharing.
Furthermore, they extended their thoughts into
developing a mechanism for enabling semantic
interoperability (Kalfoglou and Schorlemmer, 2003),
which seems to be a mathematically sound application
of CT. All these research results show that CT is a
powerful intellectual tool for finding relationships
between items with semantics. In this paper, we have
shown how CT might be used in conceptual modeling
in terms of determining whether a conceptual model is
capable of ‘containing’ certain required information.
7. CONLUSIONS AND FUTURE WORK
The work we present here draws on a number of
works and is a result of addressing something that they
seem to have missed. Conceptual modelling is
considered as a valuable tool in IS development.
However, it would seem that fundamental questions,
such as ‘what enables conceptual models to be what
they are, and why they are capable of providing
required information’, have not been answered
convincingly. Hull (1986), Miller et al (1993; 1994)
and Kwan and Fong (1999) advocate a theory
concerning the ‘information capacity’ (IC) of a data
schema, which is close to our ideas. Their works focus
on schema transformation and integration by using the
mathematical notion of mapping and developing
correctness criteria (1993). Measures of equivalence
or dominance of schemas based on the preservation of
the information content of schemas are offered (Batini
et al., 1992; Miller, 1994). In addition to IC, other
relevant works are in the area of analysing
relationships between entities during conceptual
modelling of real-world applications (Dey et al., 1999)
and meanings of relationships on ontological aspects
of investigation (Wand et al., 1999). One thing that
seems in common among these theories and
approaches is that they concentrate on the syntactic
aspect of the problem. The notion of ‘information
content’ seems to be defined intuitively and concerned
only with the data instance level. We believe that it
would be worth extending our attention beyond data,
and looking at sufficient conditions that might exist
that enable data constructs to represent information.
8
Why does a conceptual model that uses meaningful
building blocks have potential impacts on its user? We
observe that the potential impacts come from the
information provision (bearing) capability of the
conceptual model. The semantics of the building
blocks do have a role to play but it is so only when it
contributes to the provision of information. We have
not gone into details to argue for this observation in
this paper, rather we have provided a way for
verifying whether the information content of a data
construct contains a given piece of information about
something. The main finding presented in this paper is
that by identifying and articulating nested information
channels that cover both some intra-properties and
inter-properties of a schema this task can be
accomplished systematically.
Due to space constraints, we are unable to present our
work on other conditions under the umbrella of the
IBC Principle. But our aspirations in pursuing it and
our approach have been described in this paper. The
ideas embodied by the IBC Principle do seem to make
sense, helpful, and moreover justifiable not only by
using Dretske’s theory (1981) and Devlin’s theory
(1991), on which the Principle is based, but also by
using Channel Theory (Barwise and Seligman, 1997).
This work also extends the application scope of
Channel Theory into conceptual modeling for
information systems. This is encouraging. We will
continue our investigation along this line to further
develop our theoretical thinking and to consolidate
and further explore the practical relevance of our
theoretical thinking, for example, in the areas of
schema optimization and query answering capability
of a schema.
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Appendix
1. A classification is a structure A = <U, ∑A, ╞A >
where U is the set of objects to be classified (the
tokens of A), ∑A the set of objects used to classify
the tokens (the types of A), and ╞A is a binary
relation between U and ∑A determining which
tokens are of which type.
2. Let A and C to be two classifications. An
infomorphism between them is a pair f = <f, f >
of functions. For all tokens c of C and all types α of
A, it is true that
f  (c) ╞A α iff c ╞C f  (α)
This is also to say that two function f and f are in
opposite directions: f: A C. In it, f-up maps
tokens form A to C. f-down maps types from C to
A.
3. Information channel consists of an indexed family
C= {fi: Ai
C} i I of infomorphisms with a
common co-domain C, the core of the channel.
4. A subset of tokens that really participate in the
information flow are called normal tokens.
5. A local logic L = <A,├L , NL> consists of a
classification A, a set of sequent ├L involving the
types of A, the constraints of L, and a subset NL 
U, the normal tokens of L, which satisfy ├L.
6. Theory T = <typ(T), ├ > consist of a set typ(T) of
types, and a binary relation ├ between subsets of
typ(T). Pairs <Γ, Δ> of subsets of typ(T) are called
sequents. If Γ├ Δ, for Γ, Δ  type(T), then the
sequent Γ├ Δ is a constraint. T is regular if for all α∈
typ(T) and all sets Γ, Γ’, Δ, Δ’, ∑’, ∑0 , ∑1 of type:
1. Identity: α├ α,
2. Weakening: if Γ├ Δ, then Γ, Γ’├ Δ,
Δ’,
3. Global Cut: if Γ, ∑0 ├ Λ, ∑1 for each
partition <∑0 , ∑1> ( ∑0 ∪ ∑1 = typ(T)
and ∑0 ∩ ∑1 = Φ), then Γ├ Λ.
7.
10
These rules consider mappings of types. f-Intro
preserves validity but not non-validity. f-Elim does
not preserve validity but preserves non-validity.
8. Representation system R = <C, ζ> consists of a
binary channel C = {f: A C, g: B C}, with
one of the classifications designated as source (say
A) and the other as target, together with a local
logic ζ on the core C of this channel.
The representations of R are the tokens A. if
a∈ tok(A) and b∈ tok(B), a is a representation of
b, written a
R
b, if a and b are connected by some
c ∈ C. The token a is an accurate representation of
b if a and b are connected by some normal token,
that is, some c ∈ Nζ.
A set of types Γ of the source classification
indicates a type β of the target classification,
written Γ R β, if the translations of the types into
the core gives us a constraint of the logic ζ, that is,
if the translations of the types into the core
gives us a constraint of the logic ζ, that is, if
f[Γ]╞ζ g(β). The content of a token a is the set of
all types indicated by its type set. The
representation a represents b as being of type β if a
represents b and β if a represents b and β is in the
content of a.
9. State Space is a classification S for which each
token is of exactly one type. The types of a state
space are called states, and we say that a is in state
δ if a╞ S δ. The state space S is complete if every
state is the state of some token.
10.Event Classification Evt(S) associated with a state
space S has as tokens the tokens of S. its types are
arbitrary sets of states of S. The classification
relation is given by a╞Evt(S) α, if and only it stateS (a)
∈ α.
11. Sum A+B of classification has as set of tokens the
Cartesian product of tok(A) and tok(B) and as set of
types the disjoint union of type(A) and typ(B), such
that for α ∈ typ(A) and β ∈ typ(B), <a, b>╞A+B α
iff a╞A α, and <a, b>╞A+B β iff b╞B β.
12. A (state space) Projection f: S1 S2 from state
space S1 to state space S2 is given by a covariant pair
of functions such that for each token a ∈ tok(S1),
f(stateS1 (a)) = statesS2 (f(a)).
13. Proposition 8.17. Given state space S1 and S2, the
following are equivalent:
(1). f: S1 S2 is a projection;
(2). Evt(f) : Evt(S2)
infomorphism.
Evt(S1) is an
Wang.Y is a Researcher and Dr. J. K. Feng a Senior
Lecturer at the University of Paisley
11