Semantic Databases An Information Flow (IF) and Formal Concept Analysis (FCA) Reinforced Information Bearing Capability (IBC) Model

Semantic Databases: An Information Flow IF and Formal Concept Analysis FCA Reinforced Information Bearing Capability IBC Model Yang Wang and Junkang Feng Database Research Group Semantic

Semantic Databases: An Information Flow (IF) and Formal Concept Analysis (FCA) Reinforced Information Bearing

Capability (IBC) Model Yang Wang and Junkang Feng Database Research Group

Semantic Database (SDB) seems hitherto somehow

overlooked in the literature compared with its ‘big

brother’, Semantic Web What are the hindrances to

the development of SDB, which hence have to be taken

into account as we observe, include information

representation, knowledge management, meaning

elicitation, constraints/regularity identification and

formulation, and also partiality preservation We

propose an architecture, which is a result of

reinforcing the notion of the Information Bearing

Capability (IBC) that we put forward elsewhere

before by applying the theory of Information Flow

(IF) and that of Formal Concept Analysis (FCA) We

believe that this architecture should enable SDB to

cover a number of these aspects, which build upon

and go beyond the relational database (RDB).

1 INTRODUCTION

Semantic Web (SW) is the supreme elegance of topics,

which covers numerous fields, such as knowledge

organization and management, network technology

and even data modeling Comparing to this prosperous

triumph, the seemingly evident lack of attention to

Semantic Database (SDB) would appear rather

peculiar Whereas it is well known that SDB aims at

capturing, modeling and yielding meanings rather than

raw data, we observe that the short of robust

theoretical modeling foundation and guidance lies as a

gulf before the ‘fortune’ In our opinion, if we want to

achieve a satisfactory SDB, not only primary

pre-requisites such as capturing more semantics and

constraints, but also profound concepts of information,

representations and partiality, need to be addressed

To get across this gulf, the foundation of this research

is a series of theories (we refer to them as ‘SIT’, short

for Semantic Information Theories) concerning

semantic information and information flow including

Dreske (1981), Devlin (1991), and in particular,

Barwise and Seligman’s (1991) information channel

theory (IF for short) We believe that an Information

Flow (hereafter IF for short) and Formal Concept

Analysis (FCA) reinforced Information Bearing

Capability (IBC) model (We will say more about it shortly) provides a new prospective to SDB, which both assures traditional requirements of design and brings up some philosophical and mathematical insights This would, therefore, promote SDB to be compatible with Knowledge base (KB) and hence to

be a strong support for SW

1.1 A Short Review of Semantic Databases (SDB)

A database system is a representation system, which should be able to reflect real objects in the circumstance being modeled The content of a database rests with what actually exists in the modeled domain while any change operates on this content should correspond with what happens to those real world objects Sustaining this tie is not easy as at the first glance Designing a data model that captures as much as meaning as the modeled domain is the solution of many researchers (Hammer and McLeod

1981, Jagannathan et.al, 1988, Tsur and Zamolo 1984) To this end, concepts around SDB came into the scene

Bearing the goal of representing, describing and structuring more semantics and meanings than contemporary database (viz Relational Database) in mind, SDB needs to be closely related to the modeled domain Hammer addresses a number of criteria that should be enforced during SDM design (Hammer and

McLeod 1981):

• The constructs of the database model should provide for the explicit specification of a large portion of the meaning of a database So called semantic expressiveness is not sufficiently achieved by many current data modeling techniques, such as hierarchical, network, and relational models

• A database model must support a relativist view of the meaning of a database, and allow the structure of a database to support alternative ways of looking at the same information Being capable of capturing more meaning requires never rigid definitions and distinctions between ‘entities’, ‘attributes’ and

‘association’

• A database model must support the definition

of schemata that are based on abstract entities

This point, in fact, addresses that a database

should have the mechanism to support

possible semantic constraints

In the related literature, there are mainly two most

interesting streams identified by the authors in SDB

modeling The first one is that some of the researchers

are developing their SDM structure on the root of

available modeling techniques Most related to this

research, some systems are inheriting the basic

modeling constructs of RDM’s apparatus, for

example, Iris Data Model (Lyngback and Vianu 1987),

Generic SDM (Chen and McLeod 1989) and SDB

management System SIM (Boyed 2003) Meanwhile,

Rishe and his group build up a Semantic Wrapper over

RDB which produces set of SDB tools including

Knowledge database tool, Knowledge base and Query

Translator

(http://n1.cs.fiu.edu/SemanticWrapper.ppt) The

second is that some research shows that SDB is more

likely linked to Ontology and Knowledge base

(http://www.fmridc.org/f/fmridc/dmt/sdm.html)

This would seem to orientate SDB to flourishing the

development of SW

Besides this, currently, research around SDB

encounters numerous obstacles The bottleneck, as we

have identified, resides in lack of certain infrastructure

to retrieve semantics and formulate semantic

constraints, not from traditional database point of view

but follow vigorous guidance of Semantic Information

Theory (SIT in short) We believe that by

philosophically separating truly information from raw

data, dually grasping semantic constraints and

partially representing semantic information relation,

an advance model of SDB can be achieved

1.2 IF and FCA Based IBC Prospect of SDB

In 1998, we identified a research problem, namely the

‘information content’ of a formalized information

system (Feng 1998) In that paper numerous works

were cited and it was shown that the main cause of

this problem seemed that information had been treated

as ‘mystical liquid’ We then argued that the lack of

clearly expressed and defined ‘information content’ of

a conceptual data schema was responsible for many

difficulties in data modeling and analysis as a process

of inquiry, which is a basis for the design of an

information system

Then in 1999 we formulated a notion called

‘information bearing capability’ (IBC for short) by

drawing on interdisciplinary views of information

creation and transmission (Feng 1999) A four-facet

principle currently elaborates this notion, which is

concerned with a set of sufficient and necessary

conditions for the IBC of an information system The

conditions are: information content containment, distinguishability, accessibility and derivability (Feng

2005) The principle about IBC and their associated concepts that have been put forward in a series of research papers (such as Xu and Feng 2002, Feng and

Hu 2002, Xu 2005, and Wang and Feng 2005a) may

be seen as forming an innovative perspective for looking at information systems Now, IBC as a cornerstone is applied to a number of research problems that are being looked at by our group such as schema mapping, data exchanging and modeling The ideas around IBC however should be further developed and tested in real world applications To this end, it seems that the most appropriate tool to reason about and verify IBC would be IF combined with FCA We envisage that endeavor along this line will uplift the articulation of what might be called ‘the microscopic infrastructure’ of the IBC principle to an adaptable, adoptable and applicable level in SDB modeling

This paper proceeds as follows In the next section, we highlight some aspects of SDB modeling that seem to have been overlooked in the light of SIT rooted IBC model Our approach of combined use of IF and FCA

in the IBC model, which would, we believe, advance the state of the art of SDB, is introduced in section 3 Following this, a conceptual picture of IF and FCA reinforced IBC model for SDB described and elucidated in section 4

2 WHAT SHOULD A SDB MODEL, REPRESENT AND PROVIDE?

As aforementioned, SDB is proposed in the literature

to address those problems encountered in other forms

of data modeling As summarized by Boyed (2003), there are several essential goals, which need to be sustained, during SDB development The SDB is a high-level semantics-based database description and structural formalism for databases (Hammer, 1981) Although attempting to capture all the semantics of the modeled domain is unattainable, SDB should endeavor to incorporate most of the semantics SDB advances RDB and other database models in terms of its real-world perception of the problems, different perspectives of queries, and most importantly its inheritance-based hierarchical modeling structure In addition to these known characteristics, following the insight of IBC based on SIT, we would propose more significant features for SDB Only when these features are delivered can we say that SDB is satisfiably achieved

2.1 Data, Information and Semantics

Database is the vehicle for storing and providing information Without the guidance of interdisciplinary

philosophical semantic information theory, it is not

surprising that contemporary database modeling dose

not separate data and truly information

Notwithstanding modeling methods like RDB being

many and varied, as far as SDB is concerned, it should

broaden its edge to tackle the truth of data,

information, meaning and semantics in order to

capture semantics and to solve some difficult issues,

for example, query answering, lossless transformation,

etc

In a typical contemporary database, ‘what you see is

what you get’ is the prevailing feature Relation

between data and information remains scrupulously

bypassed For a long decade, data with its meaning is

treated as information in the context of database

(Checkland, 1981) A famous schema transformation

approach, i.e., ‘information capacity’ (IC) (Miller

1993), straightly takes data instances of schemata as

information Fusing Organizational Semiotics (OS)

into database, ‘meaning is created from the

information carried by signs’ (Mingers 1995)

A veritably practical SDB should take the challenges

that lie in several aspects around definitions of

information, information content and meaning Some

of my colleagues have provided an analysis about this

(Wang and Feng 2005) Firstly, instances are not

always faithful to their semantic types Traditionally,

the schema of a database is thought to represent the

type level of information while database instances fill

into these type level classes whereby receive their

semantics or meaning from the classes However, this

view overlooks the facts that instances may not loyal

to their respective semantic infrastructures These

instances do not represent any information that

originated the types (Dretske 1991) Secondly, the

meaning of data in the database is not necessarily to

be part of their information content SDB should be

able to use alternative ways to represent the same

information Therefore, a data construct represents a

piece of information only when the information

content of the data construct includes that piece of

information It is not convincing to use meaning as the

criteria for the information content of a piece of data

Finally, it is not adequate to take the ability of

accommodating instances into the schema as the

information capacity of data constructs in the database

(Wang and Feng 2005) The fewer constraints being

modeled, the less specific the instances are Hence,

less information there is SDB modeling should take

this point into consideration and facilitate it

2.2 Constraints and Representations

No matter what form it is in; a database is after all

need to represent objects and relations in the

represented domain The modes of representation

(Shimojima 1996) obey structural constraints that mirror the regularities that govern things going on in the represented domain Any representation involves certain kind of information flow Information flow results from the regularities in a distributed system (Barwise and Seligman 1997, P.8)

Contemporary database like RDB limit themselves into a particular structure of constraints such as relational objects and associated relations SDB should

go beyond these limits in the way of finding the best fit between the representing system and the represented domain Apart from this aspect, SDB should also ensure that its reasoning be consistent with the represented domain In other words, reasoning over constraints needs great care Wobcke (2000) identifies the differences between schema-based and information flow based reasoning The former is partly subjective and defeatable contrasting to the objectiveness and non-defeatability holding by the latter If given a fixed context by discarding all alternative situations, schema-based reasoning and information flow based reasoning are transferable Shimojima (1996) uses basic mathematical instruments to model constraints in order to perform a rigorous investigation on a wide range representation issues His research provides a sound theoretical foundation for developing our IBC model for SDB in virtue of inferential reasoning intimate to what happens in the domain to be modeled

2.3 Partiality

Talking about semantics, it is evident to many researchers, especially those who are familiar with logics and linguistics, that there are ‘holes in reality’ (Duzi 2003) These holes reside in our abstract way of modeling particular dependency relations among real world objects Many attempts have been made to philosophically address such issues as Possible World Semantics and Situation Semantics As aforementioned, in database, there exit instances that

do not inherit semantics from its corresponding class types Following Duzi (2003), if we take these instances as the logical construction C (not unlike the notion of ‘concept’ of Dretske 1981) for the ‘mode of representation’, which is discussed in previous section, it should link the expression E and its denotation D

Problems arise when we use empty concepts, the construction C will fail to achieve anything, not even any meaning As a result, the denotation D will fail to give any truth-value in an argument

Macroscopically, it is necessary for SDB to be

equipped with partial order to handle overall

informational relationships Based on Dretske’s

information flow (1991) and Barwise and Perry’s

situation semantics (1993), Wobcke (2000) argues that

using conditionals as basic appliance, people could

evaluate the subjectiveness and intentionality of a

collection of schemata The idea is to treat those

conditionals as expressing constraints which are

actually informational relations between facts and

events of the kind that can be modeled using structures

of situations (Wobcke 2000) The order of situations

for the collection of constraints is in the form of

partial order supporting subjective reasoning In

certain circumstances, i.e., providing certain fixed

context (situation), reasoning on this order is identical

to the reasoning of information flow Also, in Duzi’s

thesis (2001), she points out that information content

inclusion relations (in relation to attributes) are of

partial order Most specifically, she formalizes

informational capability in a complete lattice based on

the power set of the attributes in question

Furthermore, it is interesting that this lattice is proved

to be isomorphic to its substituting partial ordered set

of equivalence classes

Therefore, for the sake of manipulating informational

scenarios, the need of supporting partial order of the

IBC model both philosophically and mathematically

should not be ignored Moreover, we believe that such

a work would be aligned with issues in knowledge

representation in the AI field

3 ARCHITECTURE BASED UPON

INFORMATION FLOW (IF) AND FORMAL

CONCEPT ANALYSIS (FCA)

The central idea of IBC is called the IBC principle

This principle, is made up of conditions of information

content containment, distinguishability, accessibility

and derivability and it is put forward by Feng (2005)

and his colleagues through a period of arduous work

in the sense of drawing interdisciplinary views of

information creation and transmission (Feng 1999, Xu

and Feng 2002, Feng and Hu 2002, Xu 2005, and

Wang and Feng 2005a) IF is first introduced into IBC

for reasoning about and for verifying the principle

(Wang and Feng 2005) As being successively

compatible and content with the IBC, IF has become a

headstone for further development and application of

the IBC model For the purpose of elevating

implementation, FCA is probed and found that it is

adaptable, applicable and adoptable both theoretically

and practically with IF

3.1 Channel-Theoretical Information Flow

The Channel-theoretical Information Flow theory (IF)

is a mathematical model of semantic information flow

Information flow is possible due to the regularities among normally disparate components of a distributed system It is known that such a theory succeeds in capturing partial order of classifications (Kalfoglou and Schorlemmer 2005) that underlies the flow of information Sophisticated notions (we do not go into details here) stemming from IF now have been formulated for explorations on semantic information and knowledge mapping and exchanging Kent (2002a, 2002b) exploits semantic integration of ontologies by extending a first order logic based approach (Kent 2000) which is also based on IF 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) From Kent’s work, Kalfoglou and Schorlemmer (2003a) develop an automated ontology mapping method in the field of knowledge sharing and cooperation IF and its surrounding concepts are also relevant to solving problems of semantic interoperability (Kalfoglou and Schorlemmer 2003b) Apart from this main stream of applications, IF supports various research efforts from defensible reasoning (Cavedon 1998); endo-perspective formal model (Gunji et al 2004) to semiconcept and protoconcept graphs (Malik 2004) Besides the effective effort of using IF to represent, capture and model constraints for a given modelled domain, it is also observed that IF ‘was not developed

as a tool to be used in real world reasoning’ (Devlin 1999) and we observe that it is on its own insufficient for describing domain information or knowledge To fill these gaps, Formal Concept Analysis (FCA) was proposed as a silver bullet

3.2 Formal Concept Analysis (FCA)

FCA was developed by Rudolf Wille (Wille 1982) as a method for data analysis, information management, and knowledge representation (Priss 2005a) Presumably due to its applicable nature, it does not take long for FCA to become a common interest in many research communities, for example, social net work analysis (Freean and White 1993), linguistics (Priss 2005b), and software engineering (Fischer

1998, Eisenbarth et al 2001) As aforementioned, FCA provides solid foundations for not only information and knowledge retrieval by its underlying mathematical theory (Godin et al 1989, Kalfoglou et

al 2004) but also for respective representations by concept lattice (Wille 1982, 1992, 1997b) along with concept graphs (Prediger and Wille 1999) We maintain that the use of FCA will supplement with IF

in SDB modeling

By using IF along, it would appear that the construction of an ‘information channel’ in many

cases is difficult when applying IF to real information

system problems To alleviate it, we envisage that

‘Conceptual Scaling’ techniques (Ganter and Wille

1989, Prediger and Stumme 1999)’, which are affinity

with FCA, will be useful Furthermore, reasoning and

inference over difference levels of a channel can be

characterized by ‘Concept Graph’ (Prediger and Wille

1999) in the light of FCA-based ‘Concept Lattice’

(Wille 1982, Wille 1992, Wille 1997b) In other

words, FCA provides the investigation with a basis for

extraction, representation and demonstration of

informational aspect of semantics, and at the same

time IF-based techniques/methods can be charged with

the task of information flow based reasoning As a

result, the combined use of IF and FCA can shed some

light on solving problems around the IBC within the

context of SDB, which is also harmonious with

knowledge discovery and representation

3.3 Prospect of Combined Use of IF and FCA

The essential element of our IBC mode for SDB is the

combined use of IF and FCA They provide vital

insights for our SDB model The compatibility

between them is crucial for any combined use We

give reasons below for using IF theory and the theory

of FCA in combination Firstly, both IF and FCA share

the same origin, i.e., category theory with the means

of Chu space (Gupta 1994, Barr 1996 and Pratt 1995)

As Wolff (2000) observes, ‘it is really astonishing that

these tools (IF and FCA) are not mutually taken into

account in each other’s theory’ Priss (2005a) treats

the ‘classifications’ in IF as a general sense of

‘concept lattices’ in FCA Following this line of

thinking, secondly, nearly all fundamental concepts

invented by both of IF and FCA can find counterparts

in each other For example, the notions of

‘classifications’ in IF matches that of ‘formal context’

in FCA; ‘information channels’ in IF matches ‘scaled

many-valued contexts’ in Conceptual Scaling (Ganter

and Wille 1989, Ganter and Wille 1999) associated

with FCA Other basic notions presented in IF, such as

‘state space’, ‘refinement of channels’, and ways of

handling ‘vagueness’ are also delivered in FCA

mathematically (Wolff 2000) Finally, IF bears

epistemological resemblance to FCA To be explicit,

starting from the same algebraic category, IF together

with FCA aim at formulating and justifying ‘partial

order’ that relies on agreed understanding of the

existence of ‘duality’ between separated situations,

which is exactly why information flow commences

Combined use of IF and FCA is beneficial to

constructing the IBC model of SDB SDB highly

needs to capture more semantics In IF and FCA

reinforced IBC model, FCA would serve as the

linkage between IF reasoning and the modelled

domain Due to the ‘non-directly-applicable’ nature of

IF (Devlin 1999), applying it directly to modeling informational semantics proves to be problematic In contrast, a number of works stemming from FCA around knowledge discovery and information retrieval have been put forward For example, Stumme and his colleagues have encouraged the use of FCA in exploration and representation of implied information and facilitating the conversion of information into knowledge (Hereth et al 2000, Stumme et al 1998)

We would use the ‘Conceptual Scaling’ techniques (Prediger and Stumme 1999, Prediger and Wille 1999)

to combine FCA with IF reasoning because of FCA’s logical equivalence with ‘Information Channel’ The results of reasoning would be presented in Concept Graphs, which has advantages in representing semantics in partial order

Also, a combined use of IF and FCA can satisfactorily model more semantic constraints identified by Hammer (1987) To tackle information flow, IF insists

on analyzing relations between tokens and types According to the second principle of information flow, i.e., ‘information flow crucially involves both types and their particulars’ (Barwise and Seligman 1997, P.27) Originally and largely following Dretske (1981), we thought that semantics are presented on the type level which further provides the meanings to the tokens involved in information flow However, from the paper of Kalfoglou and Schorlemmer on IF-map (2003a), we find the important role of tokens, e.g., the same set of rivers and streams, played in determining semantics or constraints of the whole system in terms

of semantic correspondences between the types We observe that in fact, Kalfoglou and Schorlemmer has employed primary thinking of FCA in exploring

‘intension’ and ‘extension’ of formal concepts within a given formal context That is from either set, i.e., intensions or extensions; we can define its counterpart

in the context, and thus the formal concepts Therefore, using relations in tokens (extensions), we would gain relation of concepts and hence arrive at a set of constrains, which reflect a type of regularities of the whole system in the given context This is exactly how tokens take part in defining the semantics of a system, and in achieving semantic interoperability Further to this point, we envisage that duality held by both IF and FCA enables us to support alternative ways for the user to view even the same information

in SDB Start with the relations that reside in types and we would end up with relation of tokens and vice versa Therefore, depending on what aim we want to achieve, we could selectively take either tokens or types as our starting point in different analysis Explicitly, if we want to solve the semantic interoperability problem, as Kalfoglou and Schorlemmer did, we shall investigate

tokens-determined relations in order to achieve the relations

on types On the other hand, if we want to find out

why and how data constructs represents (or conveys)

the information about a given semantic relation (i.e., a

relation between some real world objects), in most

cases, we will take the semantics on types of this

structure as a foundation

4 OUTLINE OF IF AND FCA REINFORCED

IBC MODEL FOR SDB

Based on previous sections, we can now start

describing the IF and FCA reinforced IBC model

designed for SDB We will begin with data schemata

as we believe that original databases and schemata is

too valuable to be retained (Figure 1)

The original database schema together with a serial of

dependencies held by the schema would be analyzed

by using IF and FCA This analysis needs to be

assisted by obtained initiative business constraints e.g

stake holder views, presented in the format of scales,

so that subjectiveness is preserved at this early stage The construction of ‘information channel’ of IF will benefit from the technique of ‘conceptual scaling’ of FCA The output of investigation is a conceptual space which contains all the constraints (semantics) captured

by every information channel This space is called by

us as the ‘kernel of IBC’ When the user puts a query for a piece of information to this kernel, if there is no direct answer, an inference will be carried out by means of a set of ‘information content inference rules’ (Feng and Hu 2002) Then, final results are added into

a separate conceptual space following the decision of the user Connected with knowledge representation and management, the consequent results could be transformed using XML-extended Information Flow Framework (IFF) (http://www.ontologos.org/IFF/The

%20IFF%20Language.html) language

Figure 1 Overall Picture of IF and FCA Reinforced IBC model

There are two most important parts of this model

which show in two boxes in Figure 1 To clarify what

actually happens inside of them, we will use two more

diagrams

In Figure 2, there is a detailed process for arriving at the kernel of IBC Both primary database schemata and instances are translated into many-valued context

by FCA Then, two scaling processes are performed

The first one called ‘conceptual scaling’ It is based on

the idea that embedded structural constraints are used

as scales to construct corresponding IF channels The

many-valued context will then become single-valued

context as a result Following this, using dependencies

that are determined by business rules as the other

scales, another scaling, i.e., the ‘relational scaling’, will be accomplished by a final lattice layout also with

a crowd of information channels The ultimate results are sets of ‘IF’ theories derived from all of the channels This is what we want to model as the system regularities

Figure 2 How to Achieve Kernel of IBC

In addition, another significant part in our model is

inference on information content (Figure 3) The

information content based inference rules are put

forward by Feng and Hu (Feng and Hu 2002)

Furthermore, through two MSc projects (Wang 2005

and Xu 2005), we found that these inference rules can be justified by theory of IF In the future, we will generalize these verifications by not only IF but also FCA

Figure 3 Information Inference Rules (IIR)

5 CONLUSIONS

This paper represents our first step towards

satisfactorily modeling a SDB by means of an IF and

FCA reinforced IBC Three more criteria, i.e.,

extracting information, modeling semantic

constraints and also partially representing

information flow, have been proposed in addition to

traditional SDB requirements The overall idea of the

IBC model for SDB is shown with diagrams that

heavily draw on concepts from both IF and FCA

This attempt seems worthwhile for the development

of SDB, and it is also compatible with most modern

knowledge management systems, and therefore

relevant to the area of semantic web

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