FORMALIZING AND IMPLEMENTING KNOWLEDGE

REPRESENTATION ON THE BASIS OF CONCEPTIONS

Position Statement

Thomas Karbe

Berlin Institute of Technology, Berlin, Germany

Keywords:

Subject-dependency, Context, Conception, Knowledge representation, Modeling.

Abstract:

Bernd Mahr’s Model of Conception is already studied in view of its philosophical background, its mathemati-

cal formalization in regard to consistency and its set theoretic implications. The ongoing work on which this

paper states its position, concerns its mathematical formalization in regard to knowledge representation as well

as its implementation in this respect.

1 INTRODUCTION

To know something involvesa knowing subject which

may be a person, a machine, a civilisation, or a com-

munity that knows. However, the knowing subject is

often abstracted out of knowledge representation.

Another factor to knowledge is its dependency on

context. John McCarthy emphasizes this dependency

in his statement in (McCarthy, 1987): “Whenever we

write an axiom, a critic can say that the axiom is true

only in a certain context.”

A model which takes both, the subject and context

into account is Bernd Mahr’s Model of Conception

(Mahr, 2010). The aim of the model is, to realize the

propositional content of knowledge in an appropriate

way. In this paper we will argue for the following

position:

The Model of Conception can be mathemati-

cally appropriately realized and implemented.

We will ﬁrst introduce Bernd Mahr’s Model of Con-

ception and take a look into the literature that deals

with conceptions and context. Then we explain,

which properties of a good formalization and imple-

mentation of the model we would expect.

2 BERND MAHR’S MODEL OF

CONCEPTION

According to (Mahr, 2010) knowledge is an inten-

tional mental state, which in turn is based on a con-

ception. The term conception is used in a wide va-

riety of senses: We say that something is conceived

of by somebody and mean situations where some-

body perceives something with his senses in a certain

way; where somebody thinks of something somehow;

where somebody wishes something to be; or where

somebody understands that certain things are related

to each other in a certain way.

In the Model of Conception the term conception

is modeled by relating it to the three other terms sub-

ject, object, and context and by deriving from these

the notion of the content of a conception.

It is the idea of the model to see none of these

four terms in isonlation or as the basic one, but that

they are explained only by being related to each other.

Thus, the Model of Conception can also be seen as a

model of “object”, of “context”, or of “content”.

2.1 Clauses of the Model of Conception

Bernd Mahr’s Model of Conception is a conceptual

model given by thirteen clauses in natural language.

The clauses are taken from (Mahr, 2010) and we

added some remarks oriented towards knowledge:

1. An entity is something that is. Anything that is, is

an entity.

2. An entity is the content of some conception.

3. Any two entities are different.

Both, the concepts of conception and content are ex-

plained in later clauses. However, they are entities

317

Karbe T..

FORMALIZING AND IMPLEMENTING KNOWLEDGE REPRESENTATION ON THE BASIS OF CONCEPTIONS - Position Statement.

DOI: 10.5220/0003691603170321

In Proceedings of the International Conference on Knowledge Engineering and Ontology Development (KEOD-2011), pages 317-321

ISBN: 978-989-8425-80-5

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

themselves and so this clause results in a circular rela-

tion, which states that both, conceptions and contents

are themselves a content of some conception.

4. A relationship is an entity by which entities are

related.

5. An entity belongs to a relationship, if it is one of

the entities which are related by this relationship.

Relationships are the basic building blocks of mean-

ing and knowledge. They connect entities and the

meaning of an entity is derived only from its connec-

tion to the others.

6. A complex is an entity by which entities belong to

relationships.

7. A relationship belongs to a complex, if the entities

which belong to this relationship belong to this

relationship by this complex.

8. An entity belongs to a complex, if it belongs to a

relationship which belongs to this complex.

Complexes allow to speak about groups of relation-

ships.

9. A conception is a relationship by which an entity,

identiﬁable as the subject of this conception, an

entity, identiﬁable as the object (or subject matter)

of this conception, and a complex, identiﬁable as

the context of this conception, are related.

10. The content of a conception is a complex, to

which exactly those relationships belong, which

belong to the context of this conception, and to

which the subject matter of this conception be-

longs.

As the name states, conceptions are central in the

model of conception. They relate the subject of a con-

ception to the object and the context and from a con-

ception one can derive its content which can be seen

as its meaning.

11. A situation is a complex in which all entities

which belong to this complex are conceptions.

One can use situations to model the interplay between

different conceptions. Especially communication be-

tween different subjects could be represented as a

chain of situations.

12. A universe is a complex to which with every en-

tity which belongs to it, also belongs a conception,

whose content is this entity.

13. A universe is called reﬂexive, if it belongs to it-

self.

Universes are used to describe knowledge about the

world with all its entities and the rules which hold in

the described world implicitly.

2.2 Conceptions and Context in

Literature

One of the ideas underlying the Model of Conception

is the conditio humana expressed in the phrase “There

is nothing for us, which is not through us.

”. It ex-

plains the idea that we cannot have a conception about

something that was not conceived by us. Clauses 1

and 2 reﬂect this principle.

Another source of inﬂuence was the philosopher

Edmund Husserl, who was probably one of the ﬁrst to

use the term conception. More information about the

connections between Husserl and the Model of Con-

ception can be found in (Mahr, ) and (Mahr, 2010).

The term context has become modern in the last

few years and is extensively used in context-aware

computing. However there is only a small segment of

this work, which particularly focuses on the concept

of context itself.

The need for representing context was probably

ﬁrst stated by John McCarthy in (McCarthy, 1987).

Then, in (McCarthy, 1993) and (McCarthy et al.,

1995) he made a ﬁrst approach, by adding abstract

contexts to logical formulas. Following McCarthy,

Doug Lenat and Ramanathan V. Guha built their com-

mon sense knowledge base CYC (see (Lenat and

Guha, 1990), (Guha, 1992)), which makes explicit

use of contexts, which the call microtheories.

Further important articles concerning context

where written by Dourish (Dourish, 2004), Kokinov

(Kokinov, 1995), Dey (Dey, 2001), Mahr and Karbe

((Karbe and Mahr, 2011) and (Karbe, 2011). One

common property, which was seen in all these papers

is that context is any information that is considered

relevant. It is therefore a challenge for all models of

context to properly capture the idea of relevance.

3 REQUIREMENTS ON A

FORMALIZATION

REGARDING KNOWLEDGE

REPRESENTATION

It is the intention of the Model of Conception, to al-

low for a representation of knowledge, which imposes

little restrictions on the modeler. Therefore, a for-

malization, as well as a subsequent implementation,

should have speciﬁc properties. We’ll explain these

properties in comparison to the basic and well known

formalism of ZFC-sets (Zermelo-Fr¨ankel set theory

including the axiom of choice):

Stated by the German philosopher G¨unther Figal.

KEOD 2011 - International Conference on Knowledge Engineering and Ontology Development

318

Intensionality. In ZFC set-theory sets are exten-

sional, which means, that two sets are the same if

they contain exactly the same elements. However,

we want to be able to differentiate between two

relationships which relate the same entities with

different meaning. An example would be a situa-

tion, where two co-workers are in the same room.

They are related by being in the same room and

by being co-workers, but these two relations are

not the same.

Self-reference. ZFC-sets have to be well-founded,

which means that the elements of a set must

be constructed before the set itself can be con-

structed. This property also forbids self-reference.

In a formalization of the Model of Conception

it should be possible to represent relationships,

which relate themselves to other entities. A spe-

cial relationship, which would beneﬁt from this

possibility is the conception. One could represent

a subject that has a conception about his concep-

tion.

Different Levels of Abstraction. It is most natural

for us to switch to a more abstract, or more spe-

ciﬁc level, when we talk about something. In

terms of the Model of Conception, we can have

a conception about an entity in a given context as

well as having a conception about a conception

that was mentioned before.

Such concepts should be available to the formal-

ization and implementation of knowledge representa-

tion.

4 FORMALIZATION OF THE

MODEL OF CONCEPTION

There are several approaches to create a mathemati-

cal realization of the Model of Conception. In (Eilers,

2009)

Eilers provides a ﬁrst “pre-model” based on

ZFC. However, the axiom of foundation and the ex-

tensionality of ZFC-sets limit this ﬁrst model.

To build a more appropriate realization, Eilers de-

cided to use ε-structures. These structures are mod-

eled in ZFC and can be seen as sets, which impose

no restrictions on the element-relation. It is possible

to have non-founded ε-structures and also to have two

different ε-structures which contain exactly the same

elements. In (Wieczorek, 2008) there is a good intro-

duction to ε-structures.

The second model of Eilers which was based on

Translated into English the title would be ε-semantic

Modeling of a Model of Conception

ε-structures showed the consistency of the clauses of

Bernd Mahr’s Model of Conception, but still it was a

rather trivial model, because it used only empty con-

texts in conceptions and it did not model reﬂexive uni-

verses.

In (Wieczorek, 2008) Tina Wieczorek formalized

the model by writing the logical reading of its clauses

in ﬁrst order logic notation, using appropriate func-

tion and predicate symbols. She gave two axiom sys-

tems for universes, and constructed for each of these

systems a Tarski-style model using ε-sets, a special-

ization of ε-structures.

The models of Tina Wieczorek could represent

different contexts and one of them even provided re-

ﬂexive universes. However, the aim of her models

was not, to use them for modeling knowledge, but to

show useful properties in regard to set-theory.

The aim of the author is it, to provide a new real-

ization of Bernd Mahr’s Model of Conception, which

allows for an easy modeling of conceptions with all

the intended properties. This is actually work in

progress.

The idea of the newrealization is, to use ε-families

to represent relationships. This approach allows for

relationships which are intensional, as well as for

different layers of abstraction and for self-reference.

Further,by using families, we can model relationships

in a very intuitive way: We use the index of each

family-member to indicate the role of the member-

entity in the relationship.

5 IMPLEMENTATION OF THE

MODEL OF CONCEPTION

To implement the Model of Conception, we want to

develop a datastructure which is as close as possible

to the new realization above. Accordingly, we have to

develop solutions for the following questions to im-

plement the model:

• How do we handle Inﬁnite Structures?

This can be done a “lazy” approach, where ele-

ments of relationships are only calculated on de-

mand and not before they are needed.

• How are Conceptions related to their Subjects?

The model of conception does not explain, how a

subject is related to its conceptions. One possi-

ble solution would be the intoduction of the world

model of a subject, which represents the subject’s

view of the world, represented by relationships in

a complex. This world model would then be the

source of all the contexts which the subject uses

in its conceptions.

FORMALIZING AND IMPLEMENTING KNOWLEDGE REPRESENTATION ON THE BASIS OF CONCEPTIONS -

Position Statement

319

• Are the Subjects of a Conception considered to

be Perfect Reasoners?

To model subjects as perfect reasoners, their

world model would have to include all the con-

sequences of the knowledge represented in the

world model. This property seems to be a too big

restriction. It should be possible, to have subjects

with small ﬁnite world models, as well as perfect

reasoners should be possible.

• Is the Knowledge of a Subject always Consis-

tent?

As long as subjects are not considered to be per-

fect reasoners, it is not always possible to analyze

if some pieces of information are contradictory.

Consequently a world model is not nessecarily

consistent.

• What Actions can be performed on Concep-

tions, Situations and Universes?

It should be possible, to add and remove relation-

ships to and from complexesand to calculate con-

sequences of these changes. Changes in the world

model would lead to new possible conceptions.

These questions and their answers provide a ﬁrst

insight into the desired design and implementation of

the datastructure, which we want to develop.

6 ENHANCING SYSTEMS BY

USING CONCEPTIONS

There are many systems that could beneﬁt from the

use of conceptions and a proper handling of contexts.

I will list a few examples and give a short remark on

how they could use the model of conception:

Intelligent Agent Systems. Intelligent agents can be

seen as subjects which have conceptions. Such

agents could create conceptions about their envi-

ronment, as well as about the other agents which

work with or against them. They also could cre-

ate conceptions about conceptions of other agents

and draw conclusions out of this knowledge.

An example where conceptions could be of great

use is the Robocup 2D Simulation competi-

tion (see http://www.robocup.org/). Conceptions

could provide the means to reason about competi-

tors and to devolop dynamically adapting winning

strategies.

Ambient Assisted Living Systems. In the ﬁeld of

ambient intelligence there are many approaches

towards making a house aware of its context. This

means, that the house assists the people who are

living in it, by reacting under certain conditions.

It should close the doors when its inhabitants are

gone and it should start the coffee machine after

waking somebody, if this person likes coffee.

By using conceptions, the system that controls the

house could represent its inhabitants. Based on

this information it could detect changes and learn

new desired behaviours.

Natural Language Processing. It is well known that

the meaning of natural language usually depends

on context information. By placing a word in dif-

ferent contexts one derives different meanings of

it. The surrounding groups of words, sentences

and paragraphs (the cotext) are part of that con-

text, but often other information has inﬂuence on

the meaning of a word, too. The Model of Con-

ception could provide the means to represent such

diverse contexts.

Of course there are more than these three systems,

which could beneﬁt from conceptions, because of the

generality of the idea. Still, all these possibilities need

further investigation to understand the real value of

this approach.

7 CONCLUSIONS

In this paper, Bernd Mahr’s Model of Conception was

presented as a basis for appropriate knowledge repre-

sentation. We argued that the model can be mathemat-

ically realized and we provided a ﬁrst set of ideas re-

garding the implementation of a datastructure for con-

ceptions and contexts. After completing the mathe-

matical realization of the Model of Conception, which

is ongoing work, a ﬁrst very basic version of a datas-

tructure should be constructed and analyzed.

Later research would include the test of the datas-

tructure in Robocup 2D simulation agents. This will

probably result in a better understanding of the power

and usability of conceptions in intelligent agent sys-

tems and lead to further extensions of the basic datas-

tructure.

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Position Statement

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