IF Based Semantic Interoperability for Distributed Digital Museums
Hongzhe Liu1, Hong Bao2, Junkang Feng3
1, 2Institute
of Information Technology, Beijing Union University, Beijing, 100101, China
86-10-64900942
{xxtliuhongzhe, baohong}@buu.com.cn
3School
of Computing, University of Paisley, Paisley, PA1 2BE, UK
[email protected]
Abstract
The inter-operability between participating systems
within a distributed environment is a problem, which
needs to be addressed, when we observe an ever-growing
need for inter-operation and integration across
heterogeneous knowledge organization. The proliferation
of ontologies and other similar knowledge rich and
labour intensive structures exposed to a distributed
environment like the Web demonstrate the need. Many
solutions have been proposed and used. But problems
remain. For example, often it is syntactic interoperability,
rather than semantic interoperability, that is tackled. We
introduce a sophisticated theory concerning semantic
information and information flow (IF) put forward by
Barwise and Seligman in 1997 and we describe a
scenario of how we approach semantic interoperability
between two different antique classification structures by
mainly following the work of Kalfoglou and
Schorlemmer that is concerned with achieving semantic
interoperability based upon IF.
Keywords
Information flow, semantic interoperability, digital
museum, ontology
1 Introduction
Within China there are hundreds of digital heritage
archives of special scientific and cultural information.
They are available electronically, but are diverse both in
content and in form from museum to museum. For
example, one of the semantic heterogeneity is that
different museums may choose different antique
classification standards; therefore it is very common that
the same antique category may contain different sub
category structure, and even if they happen to adopt the
same antique classification structure, they may name the
same category differently. Museum organizations
frequently need to communicate with other galleries, for
example, it is useful to retrieve conservation techniques
used for objects held in other museums that are similar to
their own. Successful communication among museums
poses a challenge in those semantic heterogeneities,
which are common both within and between
organizations. Successful communication means that they
understand each other and there is a guaranteed accuracy.
This is a requirement for complete semantic integration
in which the intended models of both agents are the same,
that is, all the inferences that hold for one agent, should
also hold when translated into the other agent’s ontology
[14]. The nature of the work is ontology mapping, as it
has been shown in the recent literature that the ontology
mapping mechanisms are mainly based on the
ontological correspondence between the participant
parties. There ought to be, beyond the usual ontological
correspondence between the communicating systems, a
correspondence between the inference engines in terms
of their operators and deduction rules. We tackle the
problem of semantic heterogeneity from a theoretical
standpoint with attainable practical applications in a
variety of knowledge sharing structures, including
ontologies. In our view, in order to be semantically
integrated among multiple local digital museums
presupposes to be semantically inter-operable, and that’s
the focus of this paper. Semantic interoperability as a
1
prerequisite for semantic integration, our aim is to
capture semantic interoperability between separate
systems and to represent and model it in formal structures
in order to reason over those in subsequent integration
steps. Having achieved that, we will then be able to
establish semantic preserving exchange of information
between the communicating systems, which is the first,
and arguably, the most crucial step in achieving the kind
of inferential knowledge sharing [14].
morphism respectively based on the knowledge sharing
ideas of IFF and the role that instances (tokens) play in
the reliable flow of information. All these works provide
us with a theoretical foundation for ontology mapping for
semantic interoperability or knowledge sharing; we
mainly follow Kalfoglou and Schorlemmer’s works in [9]
and apply it to digital museum real world scenarios.
2 Related works
Information-centered ideas and notions are abundant:
Information
management,
information
systems,
information integration and information super highway…
to name just a few. The talk of information seems
everywhere. It is said that we are in an ‘information age’
and we are experiencing a revolution determined/caused
by information.
But it has been observed that ‘the current revolution
appears to be primarily technological, with people
discovering new and more efficient ways to transform
and transmit information’ ([1], p.4). A technological
revolution should be guided by relevant science. But in
our view there is yet any proper science of information.
Serious attempts have been made though in establishing
one, such as the work of Dretske [6], Devlin [4][5], and
Floridi [7] (who concentrates on the development of the
philosophy of information); the most recent one of which
however is that of Barwise and Seligman [1]. They had
presented ‘two mathematical models of information flow
(IF) in distributed systems, information channels, and
local logics’.
The first attempt to apply the results of recent efforts
towards a mathematical theory of information and
information flow in order to provide a theoretical
framework for describing the mapping and merging of
ontologies is probably the Information Flow Framework
(IFF) [11][12]. Kent exploits the central distinction made
in channel theory between types and tokens, and he
promotes a two-step process that determines the core
ontology of community connections capturing the
organization
of
conceptual
knowledge
across
communities. The process starts from the assumption that
the common generic ontology is specified as a logical
theory and that the several participating community
ontologies extend the common generic ontology by
means of the notion of theory interpretation. However
Kent’s framework is purely theoretical and no method for
implementing his two-step process is given. Very close to
IFF in spirit and in the mathematical foundations,
Schorlemmer [13] studies the intrinsic duality of
channel-theoretic constructions, and gives a precise
formalization to the notions of knowledge sharing
scenario and knowledge sharing system. His central
argument is that formal analysis of knowledge sharing
and ontology mapping has to take a duality between
syntactic types (concept names, logical sentences, and
logical sequents) and particular situations (instances,
models, semantics of inference rules) into account.
Drawing from the theoretical ideas of Kent’s IFF and
Schorlemmer’s analysis of duality in knowledge sharing
scenarios, Kalfoglou and Schorlemmer [9] [10] propose
the IF-Map methodology. Kalfoglou and Schorlemmer
provided precise definitions for ontology and ontology
3 The theory of information flow
Barwise and Seligman’s theory of information flow is a
sophisticated mathematical model of information flow
within a collection of sets of objects that are linked to one
another in some particular way; and the linkages manifest
certain regularities among these sets of objects. Such a
collection of sets of objected are modelled as a
distributed system, which leads to the term of
‘information flow within a distributed system’. That is to
say, a ‘distributed system’ in this context is not
necessarily a hard system as such, and it can be a
notional one [2].
2
3.1 The Four Principles of Information Flow
In developing the theory, Barwise and Seligman
formulated four guiding principles concerning
information flow without giving philosophical
justification:
• Information flow results from regularities in a
distributed system ([1], p.8).
• Information flow crucially involves both types and
tokens ([1], p.27).
• It is by virtue of regularities among connections that
information about some components of a distributed
system carries information about other components ([1],
p.35).
• The regularities of a given distributed system are
relative to its analysis in terms of information channels
([1], p.43).
3.2 Basic notions in information flow
classifications
A classification is a structure A = < tok (A ), typ
(A ), ╞ A >, where tok (A ) is a set of objects to be
classified, called the tokens of A, typ (A ) is a set of
objects used to classify the tokens, called the types of A,
and ╞ A is a binary relation between tok(A) and typ(A)
that determines which tokens are classified by which
types. If a ╞ A α, then we say that a is of type α in
classification A. We sometimes illustrate a classification
by virtue of a diagram as follows:
notion of ‘the theory of a classification’ is used. A theory
is made up of constraints.
Given a classification A, a sequent is a pair ( Γ, Δ ) of
sets of types of A.
A token a of A is said to satisfy the sequent ( Γ, Δ ) if,
(∀α  Γ) [ a ╞ α ] ⇒ (∃α  Δ ) [ a ╞
α]
We say that Γ entails Δ in A, written Γ ├ A Δ, if every
token of A satisfies (Γ, Δ).
If Γ ├ A Δ, then the pair (Γ, Δ) is said to be a constraint
supported by the classification A.
The set of all constraints supported by A is called the
complete theory of A, denoted by Th (A). The complete
theory of A represents all the regularities supported by
the system being modelled by A.
Infomorphisms
Let A = < tok(A), typ(A), ╞ A >, and C = < tok(C),
typ(C), ╞ C >, be two classifications. An infomorphism
between A and C is a contravariant pair of function f =
(f , f ) of functions that satisfies the following
Fundamental Property of Infomorphism:
f  (c) ╞ A α iff c ╞ C f  (α)
for all tokens c of C and all types α of A. We refer to f 
as “f-up” and f  as “f-down”. We take account of the fact
that the functions f  and f  act in opposite directions by
writing
f : A⇄C
∑A
╞A
U
Figure 1. Classification Relation
For example, when looking at a conceptual data schema
as a classification, the types could be the entity types,
relationship types, participation constraint types and etc,
and the tokens could be individual entities, individual
relationships and so on.
To model what it is (i.e., information) that flows; the
Infomorphisms allow us to show how a component links
to the whole of the system; therefore we can model a
distributed system as an ‘information channel’.
Information channel
An information channel consists of an indexed family C
= { f i: Ai ⇄C } i
I
of infomorphisms with a common
codomain C, called the core of the channel. The intuition
is that the Ai are individual components of the larger
system C, and it is by virtue of being parts of the system
C that the constituents Ai can carry information about one
another.
3
4 Semantic interoperability via information flow
Local logics
A local logic L = <A, ├ L , NL> consists of a
classification A, a set ├ L of sequents (satisfying certain
structural rules) involving the types of A, called the
constraints of L, and a subset NL  A, called the normal
tokens of L, which satisfy all the constraints of ├ L .
Given an infomorphism f: A ⇄B and a logic L on one of
these classifications, we obtain a natural logic on the
other. If L is a logic on A, then f [L] denotes the logic on
B obtained from L by f -Intro. If L is a logic on B, then f
−1
[L] denotes the logic on A obtained from L by f -Elim.
A local logic L is sound if every token is normal; it is
complete if every sequent that holds of all normal tokens
is in the consequence relation ├ L. Using infomorphisms,
we can move local logics around from one classification
to another. If L is a local logic on classification A, if L is
sound, then f [L] is sound; if f is token subjective and L is
complete, then f [L] is complete. If L is a local logic on
classification B, if L is complete, then f −1[L] is complete;
if f is token subjective and L is sound, then f −1[L] is
sound.
3.3 How information really flows
Barwise and Seligman proposed the following definition
([1], p.43):
Suppose A and B are constituent
classifications in an information channel with
core C. A token a being of type α in A carries
the information that a token b is of type β in B
relative to the channel C if a and b are
connected in C and the translation of α entails
the translation of β in Th (C).
Notice that the types in C provide the logical structure —
the regularities — that gives rise to information flow, but
information only flows in the context of a particular
token c of C (i.e., a particular flashlight), for this is what
provides the specific connections required to facilitate
information flow.
Suppose two communities A and B need to inter-operate,
but are using different ontologies in different contexts.
To have communities A and B semantically
inter-operating will mean to know the semantic
relationship in which they stand to each other. What is
meant by ‘semantics’ in this context will be explained
shortly. To establish such a semantic interoperability, we
suggest proceeding as follows.
We use a classification as a mathematical structure that
effectively captures the local syntax and semantics of a
community. The syntactic expressions that a community
uses will constitute the types of the classification.
Depending on the kind of semantic interoperation we
want to achieve, types can be concepts or class symbols,
relation names, complex queries or logical expressions,
or even sets of expressions. The meaning that these
expressions take within the context of the community
will be represented by the way tokens are classified to
types. Hence, the semantics is characterized by what we
choose to be the tokens of the classification for a
particular community; therefore, these will vary
depending on the particularities of a semantic
interoperability scenario. Tokens may, for example, be
particular instances of classes or abstract first-order
structures. The crucial point is that the semantics of the
interoperability scenario crucially depends on our choice
of types, tokens and their classification for each
community.
In the channel-theoretic context, to have communities A
and B semantically inter-operating means to know a
theory that describes how the different types from A and
B are logically related to each other, i.e., a theory on the
union of types typ (A) and typ (B) that respects the local
classification systems of each community, and a sequent
like α ├ β with α  typ (A) and β  typ ( B )
would represent an implication of types among
communities that is in accordance to how the tokens of
different communities are connected between each other.
This theory is the theory of the distributed logic of a
4
channel that represents the information flow between A
and B.
C
f1
A
f2
B
This channel can either be stated directly or indirectly by
some sort of token alignment of A and B. The logic we
are after is the one we get from moving a logic on the
core of the channel to the sum of components A + B,
which is in turn a classification with the following
features:
1. Its set of types is the disjoint union of all the types
of the component classifications A and B. To think
of A + B as such a classification is necessary for our
approach to semantic interoperability, because we
want to know when type α of one component
corresponds to a type β of another component.
2. Its theory will be over this set of types, hence a
constraint α ├ β will represent that every α is a β,
that is, every token of the former is one of the latter.
If there is also a constraint β ├ α, we obtain type
equivalence.
3. The theory will be induced at the core of the channel;
the distributed logic is the inverse image of the logic
at the core; therefore the type and tokens system at
the core and the classification of tokens to types will
determine the logic at this core. We usually take the
natural logic as the logic of the core.
4. It should be noted that since the distributed logic is
an inverse image, soundness is not guaranteed,
which means that the semantic interoperability is not
reliable in general. Even if α ├ β and β ├ α in the
logic, there might be tokens (instances, situations,
models, possible worlds) of the respective
components for which this is not the case. Reliable
information flow is only achieved for tokens that are
connected through the core. The way in which
infomorphisms from components to the core are
defined in an interoperability scenario is crucial. If
these infomorphisms are token-surjective, then the
distributed logic will preserve the soundness of the
logic of the core. Proving the token-surjectiveness is
hence a necessary task in order to guarantee reliable
semantic interoperability.
Our approach to semantic interoperability consists of the
following four steps:
1. We define the various contexts of each community by
means of a distributed IF system of classifications.
2. We construct a channel—its core and
infomorphisms—connecting the classifications of the
various communities.
3. We identify a logic on the core classification of the
channel that enables (in the sense of revealing a
mechanism for) the information flow between
communities.
4. We distribute the logic to the sum of community
classifications to obtain the theory that embodies the
desired semantic interoperability.
These steps illustrate a theoretical framework. In the
remainder of this section we apply the above four steps to
our interoperability scenario.
4.1 IF based semantic interoperability scenario
between top levels of antique classifications
Classification
Provided that local museums 1 and 2 use different
ontologies to represent their antique classifications C1
and C2 (see Figure 1 and Figure 2). To model the
ontologies by means of ‘IF classification’ in order to
arrive at semantic interoperability, we need to tackle
categories of all levels and instances:
a) The top-level antique classifications of C1 and C2 and
instances, and their respective types are:
typ (C1) = {BGV, BWV}
typ (C2) = {FCV, AV, WV, MPV}
b) The second level antique classifications of C1 and C2
and instances, and their respective types are:
typ (C1) = {CV,DV,WV,MV,B}
typ (C2) = {ADV,ACV,S}
5
c) The third level antique classifications of C1 and
instances, and its types are:
typ (C1) = {J,Z}.
食器(CV)
Cooking Vessel
作册大方鼎
Bronze Fading
Vessel
酒器(DV)
Drinking Vessel
青铜兵器(BWV)
Brone Weapon Vessel
水器(WV)
Water Vessel
爵(J)
Jue
尊(Z)
Zun
子父辛爵
Bronze Zifuxin
Vessel
子母象尊
Bronze Zimuxiang
Vessel
乐器(MV)
Music Vessel
匕(B)
Bi
大编钟
Big Bianzhong
Vessel
Figure 1 Antique classification 1 of Bronze Vessels
青铜器(BV)
Brone Vessel
饪食器(FCV)
Food Cooking Vessel
酒器(AV)
Alcohol Vessel
兵器(WV)
Weapon Vessel
奏乐器(MPV)
Music Play Vessel
饮酒器(ADV)
容酒器(ACV)
首(S)
Alcohol Drinking Vessel Alcohol Containing Vessel Shou
作册大方鼎
Bronze Fading
Vessel
子父辛爵
Bronze Zifuxin
Vessel
子母象尊
Bronze Zimuxiang
Vessel
is a
category
instance
青铜器(BV)
Brone Vessel
青铜礼器(BGV)
Brone Gift Vessel
is part of
宗周钟
Zongzhou Bell
Figure 2 Antique classification 2 of Bronze Vessels
We decide to find out first how types of the top level
correspond to each other, that is, the connections between
typ (C1) = {BGV, BWV} and typ (C2) = {FCV,
AV, WV, MPV}. We should be able to discover
connections between types on other levels with the same
approach.
We model the interoperability scenario using a separate
classification for each antique classification. The types of
a classification are the subcategories of the Bronze
Vessel, and tokens are the particular antique(s) belonging
to one of these categories. To have these two different
antique classifications semantically inter-operable will
mean to know the semantic relationship in which they
stand to each other.
It is sensible to assume that there will be no obvious
one-to-one correspondence between categories of two
antique classifications because antiques of one category
in one antique classification may spread across many
categories of the other, and vice versa. But we can
attempt to derive a theory that describes how the different
category types are logically related to each other — a
theory on the union of antique types typ (C1) and typ (C2)
in which a constraint like FCV ├ BGV would represent
the fact that an antique that belongs to the Food Cooking
Vessel in antique classification 2 also belongs to category
Bronze Gift Vessel in antique classification 1.
We shall construct the channel that will allow us to
derive the desired theory using the hierarchical structures
of antique classifications shown in Figure 1 and Figure 2.
From the hierarchical structures we can extract a theory,
which is made up of ‘consequence’ relations between the
types of a classification.
The following are the two theories of classification
6
1 and classification 2, respectively:
Th (C1) :
Here tokens b1 to b9 represent antiques. Token b2 stands
for the antique Bronze Fading Vessel belonging to
Cooking Vessel and hence also to the Bronze Gift Vessel
in antique classification 1. Token b1 stands for an antique
belonging to the Bronze Gift Vessel only. The tokens b1
to b9 denote the antiques involved in classification 1
shown Figure 1, of which those that are explicitly
illustrated in Figure 1 are shown below. Note that for
each category shown in the Figures there exists at least
one token even though they are not explicitly illustrated
such as b1 and b9.
BGV, BWV ├
CV ├ BGV
DV ├ BGV
WV ├ BGV
MV ├ BGV
CV, DV, WV, MV ├
J ├ DV
Z ├ DV
J ,Z ├
B ├ BWV
Th (C2) :
bn
Names in figure 1
b2
Bronze Fading Vessel
b4
Bronze Zifuxin Vessel
b5 Bronze Zimuxiang Vessel
FCV,AV,WV,MPV ├
ADV ├ AV
ACV ├ AV
ADV,ACA ├
S ├ WV
b7 Bronze Bianzhong Vessel
For antique classification 2 we proceed in the same way:
FCV AV ADV ACV WV S MPV
Note that the classification for each antique classification
has antiques as tokens and categories (and subcategories)
as types; and we then classify antiques to their respective
categories. These classifications will have to be in
accordance to the hierarchy as represented in the theories.
That is, if an antique is classified to a category, it shall
also be classified to all its super-category. This process
can be automated. For antique classification 1, we have
classification A1 below:
BGV
CV
DV
J
Z
WV
MV
BWV
B
b1
1
0
0
0
0
0
0
0
0
b2
1
1
0
0
0
0
0
0
0
b3
1
0
1
0
0
0
0
0
0
b4
1
0
1
1
0
0
0
0
0
b5
1
0
1
0
1
0
0
0
0
b6
1
0
0
0
0
1
0
0
0
b7
1
0
0
0
0
0
1
0
0
b8
0
0
0
0
0
0
0
1
0
b9
0
0
0
0
0
0
0
1
1
v1 1
0
0
0
0
0
0
v2 0
1
0
0
0
0
0
v3 0
1
1
0
0
0
0
v4 0
1
0
1
0
0
0
v5 0
0
0
0
1
0
0
v6 0
0
0
0
1
1
0
v7 0
0
0
0
0
0
1
The tokens v1 to v9 represent the antiques in Figure 2 as
follows:
vn
Names in figure 2
v1
Bronze Fading Vessel
v3 Bronze Zifuxin Vessel
v4 Bronze Zimuxiang Vessel
v7
Zongzhou Bell
Following the aforementioned idea about the
correspondences
between
types
of
different
classifications, we want to find pairs of types (one from
each classification) to the both of which the same token
(i.e., a particular antique) belongs. Thus we need to find
7
the type set of each token. That is to say, we want to see
how types would be classified according to tokens. This
leads to the idea of using the flip classifications of the
original classifications. Furthermore, in order to identify
how a category may relate to a set of antiques, we will
use the disjunctive power of the flip classifications. For
our example then, to find out how category types (like
BGV，BWV) from the classification A1 relates to the
category types (like FCV,AV,WV,MPV) of classification
A2, we will use the flip of the classification table and its
⊥
disjunctive power ∨A 1 . The flip classifies categories to
antiques, and for the antique classification 1 case it is:
CV
1
0
DV
1
0
J
1
0
Z
1
0
WV
1
0
MV
1
0
BWV
0
1
B
0
1
⊥
A fragment of classification ∨A 2 is:
{v1}
{v2,v3,v4}
{v5,v6}
{v7}
FCV
1
0
0
0
b1
b2
b3
b4
b5
b6
b7
b8
b9
AV
0
1
0
0
BGV
1
1
1
1
1
1
1
0
0
ADV
0
1
0
0
CV
0
1
0
0
0
0
0
0
0
ACV
0
1
0
0
DV
0
0
1
1
1
0
0
0
0
WV
0
0
1
0
J
0
0
0
1
0
0
0
0
0
S
0
0
1
0
Z
0
0
0
0
1
0
0
0
0
MPV
0
0
0
1
WV
0
0
0
0
0
1
0
0
0
MV
0
0
0
0
0
0
1
0
0
BWV
0
0
0
0
0
0
0
1
1
B
0
0
0
0
0
0
0
0
1
The way categories relate to these sets of antiques can
then be represented with an infomorphism: h 1:A1 ⇄∨A
⊥
1
:
For the antique classification 2 case it is:
v1
v2
v3
v4
v5
v6
v7
FCV
1
0
0
0
0
0
0
AV
0
1
1
1
0
0
0
ADV
0
0
1
0
0
0
0
ACV
0
0
0
1
0
0
0
WV
0
0
0
0
1
1
0
S
0
0
0
0
0
1
0
MPV
0
0
0
0
0
0
1
The disjunctive power of this flip classifies category
units to sets of antiques, whenever some of the antiques
belonging to this category are among those in the set.
⊥
Here is a fragment of this classification ∨A 1 :
BGV
{b1,b2,b3,b4,b5,b6,b7}
{b8,b9}
1
0
h 1 (BGV) = {b1, b2, b3, b4, b5, b6, b7}
h 1 (BWV) = {b8, b9}
And another infomorphism: h 2:A2⇄∨A 2 :
⊥
h 2 (FCV) = {v1}
h 2 (AV) = {v2, v3, v4}
h 2 (WV) = {v5, v6}
h 2 (MPV) = {v7}
Each context for a antique classification, with its
categories, their respective units subcategories ， and
hierarchy captured by a theory, is then represented as a
distributed IF system of classifications. For the antique
classification 1 this distributed system is the following:
8




∨A 1⊥
h1
ηA1
A1
A 1⊥
And for antique classification 2:
∨A 2⊥
h2
A2
ηA2
A 2⊥
⊥
⊥
In the next step we use the flips A 1 and A 2 to align
antiques in order to achieve the desired semantic
interoperability.
The channel
We construct a channel based on a token alignment of
some of the antiques extracted from the antique
classification web sites. This is the crucial aspect of the
semantic interoperability, since it is the point where
relations in meaning between antique categories of
different classifications of antiques are established. We
assume a token alignment, that is, one where not all
antiques b1,…, b9 that belong to antique classification 1
are related to antiques v1,…,v5 of antique classification 2.
In particular, because of the uniqueness of the antique
objects, we know for certain that the antique object
Bronze Fading Vessel in antique classification 1 is the
same antique object Bronze Fading Vessel in antique
classification 2; and the antique object Bronze Zifuxin
Vessel in antique classification 1 is the same antique
object Bronze Zifuxin Vessel in antique classification 2.
The antique object Big Bianzhong Vessel in antique
classification 1 is not the same antique object Zongzhou
Bell in antique classification 2, but they are
indistinguishable tokens ([1], p.71). The antique object
Bronze Zimuxiang Vessel in antique classification 1 is the
same antique object Zimuxiang Vessel in antique
classification 2. Therefore we have token alignment
between b2, b4, b7, b5 of antique classification 1 and v1, v3,
v7, v4 of antique classification 2 as follows:
b2←→v1
b4←→v3:
b7←→v7
b5←→v4
Token alignment is necessary for the approach we
present here. To establish a token alignment heuristic
mechanism may be used, which may involve domain
experts’ opinion and some machine matching techniques.
It would appear that the more tokens that are covered in
an alignment, the more constraints we can infer. In this
paper we provide a framework that shows how a token
alignment of a few antiques fits into the larger picture of
an alignment scenario for semantic interoperability
concerning different antique classifications, which is
described here, and represented as a distributed IF system,
and how a global theory of semantic interoperability on
the top level of categories can be derived from this token
alignment.
The above token alignment is a binary relation between
⊥
⊥
typ(A 1 ) and typ(A 2 ). In order to represent this
alignment as a distributed IF system in channel theory,
which would require infomorphisms between
classifications, we decompose the binary relation into a
couple of total functions g ^1, g ^2 from a common
domain typ(A) = {α, β, γ, δ} as follows:
g ^1(α)
g ^2(α)
g ^1(β)
g ^2(β)
g ^1(γ)
g ^2(γ)
g ^1( δ )
g ^2( δ )
=
=
=
=
=
=
=
=
b2
v1
b4
v3
b7
v7
b5
v4
This will constitute the type-level of a couple of
infomorphisms. We then have a system of classifications
for the alignment:
1
2

A 1⊥ 
A 
A 2⊥
g
g
by generating the classification on typ (A) with all
9
possible tokens, which we generate formally, and their
classification:
α
β
γ
δ
n0
0
0
0
0
n1
0
0
0
1
n2
0
0
1
0
n3
0
0
1
1
n4
0
1
0
0
n5
0
1
0
1
n6
0
1
1
0
n7
0
1
1
1
n8
1
0
0
0
n9
1
0
0
1
n10
1
0
1
0
n11
1
0
1
1
n12
1
1
0
0
n13
1
1
0
1
n14
1
1
1
0
n15
1
1
1
1
To satisfy the fundamental property of infomorphisms,
the token-level of g 1, g 2 must be as follows:
g ˇ1 (CV)
g ˇ1 (J)
g ˇ1 (MV)
g ˇ1 (Z)
g ˇ1 (DV)
g ˇ1 (BG V)
=
=
=
=
=
=
g ˇ2(AV)
g ˇ2 (FCV)
g ˇ2 (ADV)
g ˇ2 (MPV)
g ˇ2 (ACV)
= n5
= n8
= n4
= n2
= n1
n8
n4
n2
n1
n5
n15
This alignment allows us to generate the desired channel
between classification 1 and 2 that captures the
information flow according to the aligned sub categories.
This is done by constructing a classification C and a
couple of infomorphisms f1: ∨ A 1⊥ ⇄C and f2: ∨ A 2⊥ ⇄C
that correspond to a colimit in terms of the category
theory [15] of the following distributed IF system, which
includes the alignment and the contexts of each
classification:
C
fz
f1
h1
∨ A2
h2
ηA2
ηA1
A1⊥
⊥
⊥
∨ A1 ⊥ + ∨ A2
∨ A1⊥
A1
A2
A1 + A 2
g1
A 2⊥
g2
A
This is a cover of the distributed IF system.
The logic on the core
This is how colimit C is constructed: Its set of types
typ(C) is the disjoint union of types of
∨ A 1⊥ and
∨ A 2⊥ ; its tokens are connections — pairs of tokens —
that connect a token of a of ∨ A 1⊥ and a token b of ∨ A
⊥ only when a and b are sent by the alignment
2
infomorphisms g 1 and g 2 to tokens of the alignment
classification A that are classified as of the same type.
For example, the core C will have a token <FCV, BGV>
connecting ∨ A 1⊥ with token FCV and ∨ A 2⊥ with token
BGV, because: g ˇ1 (BGV) = n15 and g ˇ2 (FCV) =
n8, and both n15 and n8 are of type α in A.
The following is a fragment of the classification on the
core (not all types are listed, but all tokens are):
{v1}
{v2,v3,v4}
{v5,v6}
{v7}
{b1,b2,b3,b4,b5,b6,b7}
{b8,b9}
<CV,FCV>
1
0
0
0
1
0
<J,ADV>
0
1
0
0
1
0
<MV,MPV>
0
0
0
1
1
0
<Z,ACV>
0
1
0
0
1
0
<DV,AV>
0
1
0
0
1
0
<BGV,FCV>
1
0
0
0
1
0
<BGV,ADV>
0
1
0
0
1
0
10
<BGV,MPV>
0
0
0
1
1
0
<BGV,ACV>
0
1
0
0
1
0
It shows the classification of all connections to those
types of the core that are in the image of f1 ° h 1 and f2 ° h 2,
which are the infomorphisms we will use in the next step
to distribute the logic on the core to the classifications 1
and 2. As the logic on the core we will take the natural
logic of the classification C, whose constraints are:
{v1} ├ {b1, b2, b3, b4, b5, b6, b7}
{v2, v3, v4} ├ {b1, b2, b3, b4, b5, b6, b7}
{v7} ├ {b1, b2, b3, b4, b5, b6, b7}
{b1, b2, b3, b4, b5, b6, b7}, {v5, v6}├
The natural logic is the one that captures in its constraints
a complete knowledge of the classification. Since we
have constructed the classification from those in the
distributed system—which captured the contexts of
classifications together with the alignment of certain sub
categories—the natural logic will have as its theory all
those sequents that conform to the classification’s
contexts as well as to the alignment, which is what we
desire for semantic interoperability.
The distributed logic
The natural logic has a theory whose types are sets of
antiques, but we want to know how this theory translates
to the top level categories of the antique classifications
by virtue of what known antiques each category has. For
that reason we take the theory of the distributed logic of
the channel:
FCV ├ BGV
AV ├ BGV
MPV ├ BGV
BGV, WV ├
These constraints capture the semantic interoperability
between top level classification of antique classifications
1 and 2.
4.2 Top level of C1 and second level of C2
interoperability (typ (C1) = {BGV, BWV} and typ
(C2) = {ADV, ACV, S})
To find the Semantic interoperability between top level
classification from C1 and second level classification
from C2, The disjunctive power of this flip classifies
category units to sets of antiques, whenever some of the
antiques belong to this category is among those in the set.
Here is a fragment of this classification for ∨ A 1⊥ :
{b1,b2,b3,b4,b5,b6,b7}
{b8,b9}
BGV
1
0
CV
1
0
DV
1
0
J
1
0
Z
1
0
WV
1
0
MV
1
0
BWV
0
1
B
0
1
Here is a fragment of this classification for ∨ A 2⊥
C
A1
{v3}
{ v4}
{ v6}
ADV
1
0
0
ACV
0
1
0
S
0
0
1
f2 ° h2
f1 ° h1
f1 ° h1+f2 ° h2
A1 + A 2
A2
which is the inverse image along (f 1 ° h 1) + (f 2 ° h 2) of
the natural logic(C) generated from the core classification.
Its theory has the following constraints:
The way categories relate to these sets of antiques
represent with an infomorphism:
h 1:A1⇄∨ A 1⊥ :
h 1 (BGV) = {b1, b2, b3, b4, b5, b6, b7}
11
h 1 (BWV) = {b8, b9}
this flip classifies category units to sets of antiques,
whenever some of the antiques belong to this category is
among those in the set. Here is a fragment of this
classification for ∨ A 1⊥ :
so another infomorphism: h 2:A2⇄∨ A 2⊥ :
h 2 (ADV) = {v3}
h 2 (ACV) = {v4}
h 2 (S) = {v6}
And the token-level connection of g1, g2 is as the
following:
g ˇ1 (BGV) =
n15
g ˇ2 (ADV) = n4
g ˇ2 (ACV) = n1
{b2}
{b3,b4,b5}
{b6}
{b7}
{b9}
CV
1
0
0
0
0
DV
0
1
0
0
0
J
0
1
0
0
0
Z
0
1
0
0
0
WV
0
0
1
0
0
MV
0
0
0
1
0
B
0
0
0
0
1
The fragment of classification of ∨ A 2⊥ :
The construction of colimit C: Its set of types typ(C) is
the disjoint union of types of ∨ A 1⊥ and ∨ A 2⊥ ; Its
tokens are connections. The following is a fragment of
the classification on the core (not all types are listed, but
all tokens are):
{v3}
{ v4}
{ v6}
{b1,b2,b3,b4,b5,b6,b7}
{b8,b9}
<BGV,ADV>
1
0
0
1
0
<BGV,ACV>
0
1
0
1
0
The logic on the core - the natural logic of the
classification C, whose constraints are:
{v1}
{v2,v3,v4}
{v5,v6}
{v7}
FCV
1
0
0
0
AV
0
1
0
0
ADV
0
1
0
0
ACV
0
1
0
0
WV
0
0
1
0
S
0
0
1
0
MPV
0
0
0
1
The way categories relate to these sets of antiques can
then be represented with an infomorphism: h 1:A1⇄∨ A
{v3} ├ {b1, b2, b3, b4, b5, b6, b7}
{v4} ├ {b1, b2, b3, b4, b5, b6, b7}
Semantic interoperability between Top level of C1 and
second level of C2:
ADV ├ BGV
ACV ├ BGV
⊥:
1
h 1 (CV)
h 1 (DV)
h 1 (WV)
h 1 (MV)
h 1 (B)
=
=
=
=
=
{b2}
{b3,b4,b5}
{b6}
{b7}
{b9}
And another infomorphism: h 2:A2⇄∨ A 2⊥ :
4.3 Second level of C1 and top level of C2
interoperability (typ (C1) = {CV, DV, WV, MV, B}
and typ (C2) = {FCV, AV, WV, MPV})
To find the Semantic interoperability between second
level of C1 and top level of C2, The disjunctive power of
h 2 (FCV) = {v1}
h 2 (AV) = {v2, v3, v4}
h 2 (WV) = {v5, v6}
h 2 (MPV) = {v7}
And the token-level connection of g1, g2 is as the
12
following:
antiques belong to this category is among those in the set.
Here is a fragment of this classification for ∨ A 1⊥ :
g ˇ1 (CV) = n8
g ˇ1 (MV) = n2
g ˇ1 (DV) = n5
g ˇ2 (FCV) = n8
g ˇ2 (MPV) = n2
g ˇ2(AV) = n5
The construction of colimit C: Its set of types typ(C) is
the disjoint union of types of ∨ A 1⊥ and ∨ A 2⊥ ; Its
tokens are connections. The following is a fragment of
the classification on the core (not all types are listed, but
all tokens are):
{v2,v3,v4}
{v5,v6}
{v7}
{b2}
{b3,b4,b5}
{b6}
CV>
1
0
0
0
1
0
0
0
0
MPV>
0
0
0
1
0
0
0
1
0
AV>
0
1
0
0
0
1
0
0
0
{v1} ├ {b2}
{b2} ├ {v1}
{v7} ├ {b7}
{b7} ├ {v7}
{v2, v3, v4} ├ {b3, b4, b5}
{b3, b4, b5} ├ {v2, v3, v4}
Semantic interoperability between second level of C1 and
top level of C2:
CV ├ FCV and FCV ├ CV, so CV = FCV
MV ├ MPV and MPV ├ MV, so MPV = MV
AV ├ DV and DV ├ AV, so AV = DV
4.4 Second level of C1 and second level of C2
interoperability (typ (C1) = {CV, DV, WV, MV, B}
and typ (C2) = {ADV, ACV, S})
To find the Semantic interoperability between second
level classification of C1 and second level classification
of C2, The disjunctive power of this flip classifies
category units to sets of antiques, whenever some of the
{b3,b4,b5}
{b6}
{b7}
{b9}
CV
1
0
0
0
0
DV
0
1
0
0
0
J
0
1
0
0
0
Z
0
1
0
0
0
WV
0
0
1
0
0
MV
0
0
0
1
0
B
0
0
0
0
1
Here is a fragment of this classification for ∨ A 2⊥
{b7} {b9}
{v1}
The logic on the core - the natural logic of the
classification C, whose constraints are:
{b2}
{v3}
{ v4}
{ v6}
ADV
1
0
0
ACV
0
1
0
S
0
0
1
The way categories relate to these sets of antiques
represent with an infomorphism:
h 1:A1⇄∨ A 1⊥ :
h 1 (CV)
h 1 (DV)
h 1 (WV)
h 1 (MV)
h 1 (B)
=
=
=
=
=
{b2}
{b3, b4, b5}
{b6}
{b7}
{b9}
So another infomorphism: h 2:A2⇄∨ A 2⊥ :
h 2 (ADV) = {v3}
h 2 (ACV) = {v4}
h 2 (S) = {v6}
And the token-level connection of g1, g2 is as the
following:
g ˇ1 (CV) = n8
g ˇ1 (MV) = n2
13
g ˇ1 (DV) = n5
g ˇ2 (ADV) = n4
g ˇ2 (ACV) = n1
The construction of colimit C: Its set of types typ(C) is
the disjoint union of types of ∨ A 1⊥ and ∨ A 2⊥ ; Its
tokens are connections. The following is a fragment of
the classification on the core (not all types are listed, but
all tokens are):
{v1}
{v2,v3,v4}
{v5,v6}
{v7}
FCV
1
0
0
0
AV
0
1
0
0
ADV
0
1
0
0
ACV
0
1
0
0
WV
0
0
1
0
S
0
0
1
0
MPV
0
0
0
1
The way categories relate to these sets of antiques
{ v6}represent with an infomorphism:
{b2}
{b3,b4,b5}
{b6}
{b7}
{b9}
{v3}
{ v4}
<DV,ADV>
0
1
0
0
0
1
0
0
<DV,ACV>
0
1
0
0
0
0
1
0
h 1:A1⇄∨ A 1⊥ :
The logic on the core - the natural logic of the
classification C, whose constraints are:
{V3} ├ {B3, B4, B5}
{V4} ├ {B3, B4, B5}
So another infomorphism: h 2:A2⇄∨ A 2⊥ :
Semantic interoperability between second level of C1 and
second level of C2:
ADV ├ DV
ACV ├ DV
4.5 Third level of C1 and top level of C2
interoperability (typ (C1) = {J, Z} and typ (C2) =
{FCV, AV, WV, MPV})
To find the Semantic interoperability between third level
classification of C1 and top level classification of C2, The
disjunctive power of this flip classifies category units to
sets of antiques, whenever some of the antiques belong to
this category is among those in the set. Here is a
fragment of this classification for ∨ A 1⊥ :
{b4}
{b5}
J
1
0
Z
0
1
h 1 (J) = {b4}
h 1 (Z) = {b5}
Here is a fragment of this classification for ∨ A 2
⊥
h 2 (FCV) = {v1}
h 2 (AV) = {v2, v3, v4}
h 2 (WV) = {v5, v6}
h 2 (MPV) = {v7}
And the token-level connection of g1, g2 is as the
following:
g ˇ1 (J) = n4
g ˇ1 (Z) = n1
g ˇ2(AV) = n5
g ˇ2 (FCV) = n8
g ˇ2 (MPV) = n2
The construction of colimit C: Its set of types typ(C) is
the disjoint union of types of ∨ A 1⊥ and ∨ A 2⊥ ; Its
tokens are connections. The following is a fragment of
the classification on the core (not all types are listed, but
all tokens are):
<J,AV>
{b4}
{b5}
{v1}
{v2,v3,v4}
{v5,v6}
{v7}
1
0
0
1
0
0
14
<Z,AV>
0
1
0
1
0
0
So another infomorphism: h 2:A2⇄∨ A 2⊥ :
The logic on the core - the natural logic of the
classification C, whose constraints are:
h 2 (ADV) = {v3}
h 2 (ACV) = {v4}
h 2 (S) = {v6}
{b4} ├ {v2, v3, v4}
{b5} ├ {v2, v3, v4}
Semantic interoperability between third level of C1 and
top level of C2:
And the token-level connection of g1, g2 is as the
following:
g ˇ1 (J) = n4
g ˇ1 (Z) = n1
g ˇ2 (ADV) = n4
g ˇ2 (ACV) = n1
J ├ AV
Z ├ AV
4.6 Third level of C1 and second level of C2
interoperability (typ (C1) = {J, Z} and typ (C2) =
{ADV, ACV, S})
To find the Semantic interoperability between third level
classification of C1 and second level classification of C2,
The disjunctive power of this flip classifies category
units to sets of antiques, whenever some of the antiques
belong to this category is among those in the set. Here is
a fragment of this classification for ∨ A 1⊥ :
The construction of colimit C: Its set of types typ(C) is
the disjoint union of types of ∨ A 1⊥ and ∨ A 2⊥ ; Its
tokens are connections. The following is a fragment of
the classification on the core (not all types are listed, but
all tokens are):
{v3}
{ v4}
{ v6}
{b4}
{b5}
<J,ADV>
1
0
0
1
0
<Z,ACV>
0
1
0
0
1
The logic on the core - the natural logic of the
classification C, whose constraints are:
{b4}
{b5}
J
1
0
Z
0
1
Here is a fragment of this classification for ∨ A 2⊥
{v3}
{ v4}
{ v6}
ADV
1
0
0
ACV
0
1
0
0
0
1
S
The way categories relate to these sets of antiques
represent with an infomorphism:
{v3} ├ {b4}
{b4} ├ {v3}
{v4} ├ {b5}
{b5} ├ {v4}
Semantic interoperability between third level of C1 and
second level of C2:
J├ ADV and ADV ├ J, so J = ADV
Z ├ ACV and ACV ├ Z, so Z = ACV
h 1:A1⇄∨ A
h 1 (J) = {b4}
h 1 (Z) = {b5}
Up to this point, we have arrived at constraints between
15
any pairs of categories, if they exist, from the above two
classifications, which are:
FCV ├ BGV
AV ├ BGV
MPV ├ BGV
BGV, WV ├
ADV ├ BGV
ACV ├ BGV
CV ├ FCV and FCV ├ CV, so CV = FCV
MV ├ MPV and MPV ├ MV, so MPV = MV
AV ├ DV and DV ├ AV, so AV = DV
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of Distributed Systems, Cambridge University Press,
Cambridge.
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[5] Devlin K (2001) Introduction to Channel Theory, ESSLLI
2001, Helsinki, Finland.
[6] Dretske, (1981) Knowledge and the Flow of Information,
ADV ├ DV
ACV ├ DV
J ├ AV
Z ├ AV
Basil Blackwell, Oxford.
[7] Floridi L (2002) What is the Philosophy of Information?
Mataphilosophy, 33(1-2), 123-45.
[8] Heiner Stuckenschmidt,Holger Wache (2000) Context
modelling and transformation for semantic interoperability. In
J ├ ADV and ADV ├ J, so J = ADV
Z ├ ACV and ACV ├ Z, so Z = ACV
Knowledge Representation Meets Databases (KRDB 2000).
[9] Kalfoglou, Y. and Schorlemmer (2003) Using Information
Flow Theory to Enable Semantic Interoperability, In
Note that any constraint above should be interpreted the
same way. That is, for example, FCV ├ BGV means that
if an antique is in category FCV in classification 2, it
must be also in category BGV in classification 1.
Proceedings of the 6th Catalan Conference on Artificial
Intelligence (CCIA '03), Palma de Mallorca, Spain, October
2003
[10] Kalfoglou, Y. and Schorlemmer, M (2003) IFMap: an
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5 Conclusions
In this paper we have presented a practical application of
channel theory to achieve semantic interoperability in
terms of information flow between different systems in
the domain of distributed digital museums that need to be
integrated. The strong mathematical foundations of
channel theory and their potential transformation to logic
programs has enabled us to work out a real world
integration scenario with semantic-preserving exchange
of information. These could provide a better
understanding of the foundations for building and
deploying semantically integrated systems in distributed
environments.
[11] Kent, R. E (2001) The information Flow Framework. Starter
document for IEEE P1600.1, the IEEE Standard Upper
Ontology working Group, http://suo.ieee.org/IFF/.
[12] Kent, R. E (2002) The IFF Approach to Semantic Integration.
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