Computing and Information Systems
© University of Paisley 2006
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
1
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
2
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
REPRESENT AND PROVIDE?
MODEL,
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
3
(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.
4
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); endoperspective 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
5
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%20Langu
age.html) language.
Figure 1. Overall Picture of IF and FCA Reinforced IBC model
actually happens inside of them, we will use two more
There are two most important parts of this model
diagrams.
which show in two boxes in Figure 1. To clarify what
6
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
and Xu 2005), we found that these inference rules
In addition, another significant part in our model is
can be justified by theory of IF. In the future, we will
inference on information content (Figure 3). The
generalize these verifications by not only IF but also
information content based inference rules are put
FCA.
forward by Feng and Hu (Feng and Hu 2002).
Furthermore, through two MSc projects (Wang 2005
7
Figure 3. Information Inference Rules (IIR)
Cavedon, L. (1998). Default Reasoning as Situated
5. CONLUSIONS
Monotonic Inference, Minds and Machines 8.
This paper represents our first step towards
Checkland, P. (1981). Systems Thinking, Systems
satisfactorily modeling a SDB by means of an IF and
Practice. Chichester, UK: Wiley.
FCA reinforced IBC. Three more criteria, i.e.,
Chen, I. A. and McLeod, D. (1989). Derived Data
extracting
information,
modeling
semantic
Update in Semantic Databases, Proceedings of
constraints and also partially representing
the fifteenth international conference on Very
information flow, have been proposed in addition to
large data bases, p.225-235, July, Amsterdam,
traditional SDB requirements. The overall idea of the
The Netherlands.
IBC model for SDB is shown with diagrams that
Devlin, K. (1991). Logic and Information,
heavily draw on concepts from both IF and FCA.
Cambridge.
This attempt seems worthwhile for the development
Devlin, K. (2001). Introduction to Channel Theory,
of SDB, and it is also compatible with most modern
ESSLLI 2001, Helsinki, Finland.
knowledge management systems, and therefore
Dretske, F. (1981). Knowledge and the Flow of
relevant to the area of semantic web.
Information, Basil Blackwell, Oxford.
Duží, M. (2001). Logical Foundations of Conceptual
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