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

17

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 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].

2 Related works

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 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.

3 The theory of information flow

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’.

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].

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:

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 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 Î Γ) [ a ╞ α ] ⇒ (∃α Î 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 Ù, f Ú) of functions that satisfies the following Fundamental Property of Infomorphism:

f Ú (c) ╞ A α iff c ╞ C f Ù (α)

for all tokens c of C and all types α of A. We refer to f Ù as “f-up” and f Ú as “f-down”. We take account of the fact that the functions f Ù and f Ú act in opposite directions by writing

f : A⇄C

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 } iI 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.

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 Í 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.

4 Semantic interoperability via 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.