Position Statement
Thomas Karbe
Berlin Institute of Technology, Berlin, Germany
Subject-dependency, Context, Conception, Knowledge representation, Modeling.
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.
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
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.
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
Karbe T..
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
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
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-
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-
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-
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
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.
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
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-
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-
There are several approaches to create a mathemati-
cal realization of the Model of Conception. In (Eilers,
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-
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
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.
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.
Position Statement
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-
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
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.
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 Conceptions
could provide the means to reason about competi-
tors and to devolop dynamically adapting winning
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.
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-
Dey, A. K. (2001). Understanding and using context. Per-
sonal and Ubiquitous Computing, 5:4–7.
Dourish, P. (2004). What we talk about when we talk about
context. Personal and Ubiquitous Computing, 8.
Eilers, F. (2009). ε-semantische Modellierung eines Mod-
ells der Auffassung. volume 155 of KIT-Report. Tech-
nische Universit¨at Berlin.
Guha, R. V. (1992). Contexts: a formalization and some
applications. PhD thesis, Stanford, CA, USA.
KEOD 2011 - International Conference on Knowledge Engineering and Ontology Development
Karbe, T. (2011). Conceptions and Context as a Fundament
for the Representation of Knowledge Artifacts. sub-
Karbe, T. and Mahr, B. (2011). On the Modelling of Con-
text. In Proceedings of CECS 2010 : International
Workshop on Systems Communication and Engineer-
ing in Computer Science. Springer (to appear).
Kokinov, B. (1995). A dynamic approach to context mod-
eling. In Brezillon, P. and Abu-Hakima, S., editors,
Proceedings of the IJCAI-95 Workshop on Modeling
Context in Knowledge Representation and Reasoning.
LAFORIA 95/11.
Lenat, D. B. and Guha, R. V. (1990). Building Large
Knowledge-Based Systems: Representation and Infer-
ence in the CYC Project. Addison-Wesley, Reading,
Mahr, B. On the Epistemology of Models. In Rethinking
Mahr, B. (2010). Intentionality and Modelling of Concep-
tion. In Bab, S. and Robering, K., editors, Judgements
and Propositions — Logical, Linguistic and Cognitive
Issues. Logos.
McCarthy, J. (1987). Generality in artificial intelligence.
Communications of the ACM, 30:1030–1035.
McCarthy, J. (1993). Notes on formalizing context. In Pro-
ceedings of the 13th international joint conference on
Artifical intelligence - Volume 1, pages 555–560, San
Francisco, CA, USA. Morgan Kaufmann Publishers
McCarthy, J., Buvac, S., Costello, T., Fikes, R., Genesereth,
M., and Giunchiglia, F. (1995). Formalizing context
(expanded notes).
Wieczorek, T. (2008). On Foundational Frames for Formal
Modelling: Sets, ε-Sets and a Model of Conception.
PhD thesis, Technische Universit¨at Berlin.
Position Statement