=Paper=
{{Paper
|id=Vol-298/paper-7
|storemode=property
|title=Modeling Adaptive behavior with conceptual spaces
|pdfUrl=https://ceur-ws.org/Vol-298/paper7.pdf
|volume=Vol-298
|dblpUrl=https://dblp.org/rec/conf/context/Cebulla07
}}
==Modeling Adaptive behavior with conceptual spaces==
https://ceur-ws.org/Vol-298/paper7.pdf
Modeling Adaptive Behavior
with Conceptual Spaces
Michael Cebulla
Technische Universität Berlin, Fakultät für Elektrotechnik und Informatik,
Institut für Softwaretechnik und Theoretische Informatik,
Franklinstr. 28/29, 10587 Berlin
mce@cs.tu-berlin.de
Abstract. We discuss a membrane-based calculus for the combination of con-
ceptual spaces during runtime. Since our goal is to support emergent properties
of behavior (and due to the fact that it is not possible to define a complete cal-
culus for all situations) we introduce the notion of self-modification. Terms from
situational description can evolve according to simple rules thus providing various
possibilities for reactions.
1 Introduction
In this paper some of the problems which are connected with context-dependent behav-
ior are developed as a general problem of combining conceptual spaces. Examples from
the field of medical workflows are given. The approach which is discussed in this paper
relies on the notion of conceptual integration which was developed in the field of cog-
nitive semantics [2]. This integration can be simulated by the rule-based integration of
ontologies.
The framework described in this paper partly follows previous proposals for the for-
malization of contextual reasoning. While classifications [1] heavily rely on universal
algebra or category theory [3] we focus on an operational treatment using membrane
computing [4].
In this paper we make an attempt to bridge the gap between highly reactive behavior
during runtime and the need for highly abstract and meaningful concepts for context-
awareness. Especially we propose to integrate highly abstract forms of common sense
reasoning (as proposed by [1]) with membrane computing (as proposed by [4]) in order
to support a way of runtime reasoning whose robustness is comparable to human reason-
ing. By this proposal we extend previous suggestions concerning high-level and intuitive
specifications (cf. [5]). Especially we propose to exploit common sense reasoning for the
robustness of context-aware behavior in distributed systems.
2 Context and Behavior
Simplified models of medical workflows are employed in this paper as examples for the
treatment of adaptive behavior.
Example 1 (Intubation: A Medical Workflow) The activity of intubation is con-
sidered with represents a specific part of a medical operation. Although there is certainly
a definition of the process (i.e. a pattern) the exact shape of the final activity highly
depends on the context in which this pattern is activated. In this paper we propose to rep-
resent the definition of the process (the pattern) as well as the situation as input spaces
(in the sense of [2]). We develop an emergent calculus which establishes links between
these spaces. ♦
The Intubation Space. The conceptual space containing the process of intubation contains
a constraint-based description of this process (cf. Figure 2). The important actions are
described with their causal relationships as well as constraints which have to hold in
certain states. Especially three subtasks can be identified (Preparation, Laryngoscopy
and Introduction) which have different relevance values for the overall process. Since
the intubation space contains a pattern which is described in this space there are many
variables which have to be bound to actual values from a specific situation. For instance,
agents are represented by roles which have to be bound to real agents taken from another
conceptual space. In a similar way constraints which are specified over objects or states
are applied to elements from other spaces.
The Situation Space. While the intubation space contains roles for the agents which are
responsible for certain actions the situation space is populated by (entities representing)
real agents and resources. In addition in this conceptual space specific relations and
circumstances can be described which are of informal nature but which heavily influence
the shape of the resulting process. As an example a relation of informal hierarchy is given
which may hold between an experienced nurse and a less experienced anesthesist.
Fig. 1. Conceptual Spaces
Cross-Space Mapping. The combination of conceptual spaces is triggered by cross-space
mappings. Cross-space mappings are enabled by morphisms between ontologies. Mor-
phisms represent background knowledge for combining conceptual spaces. In our example
relevant morphisms are:
mapping intsit from Intubation to Situation
sort Intubation-Task Intubation-Capability
As we will see the background knowledge is used to establish infomorphisms between
the conceptual spaces. As we will see there are multiple possibilities to establish these
infomorphisms. One of our main points consist in the claim that the adaptive or self-
configuring capabilities of complex systems (like human teams in the operation theatre)
can be simulated by an adequate selection of the best possibility.
Generally the process of blending results in the creation of a blended space. Due to
space restrictions we concentrate on the establishment of vital relations in this paper.
3 Operational Treatment of Vital Relations
Under operational aspects we represent conceptual spaces as P-systems PCS . Basically
a conceptual space is enclosed by a membrane. These entities which are contained in the
space are mapped to components of P-systems (cf. [4]). While concepts are mapped to
molecules, individuals and relations are mapped to labeled membranes.
Definition 1 (P-System PCS ) The P-System for the representation of conceptual spaces
PCS is defined by the tuple hV, L, µ, wi , Rni i where V is the terminology of the classifi-
cations (containing concept names) and the label algebra L (containing individuals, sit-
uations and the concatenation operator “,”). µ is the structure of membranes containing
the multi-fuzzy sets wi . The rules contained in Rni are discussed below. 2
One of our central goals is to support self-organizational capabilities in the dynamic
composition of conceptual spaces. This is especially due to the fact that it is impossible
to foresee every possible combination of situations. Since we do not want to define a
uniform rigid calculus which is restricted to a certain set of known combinations we take
the opposite approach which promises a more flexible solution. This means that we allow
the terms to evolve in a solution and to look for possible combinations by themselves.
This decentralized approach is robust against local evolutions and to unforeseen changes.
We proceed in two steps. Firstly we have to map context descriptions to membrane
structures. This can be easily done by mapping individuals and situations to labeled
membranes and concepts to molecules floating in a solution. In the same way we have
to represent ontology morphisms by membrane structures. In a second step we give the
rules for the evolution of these structures and for the establishment of valid combinations
of contexts.
Airlock Rules. In our membrane-based approach molecules are enclosed by membranes.
In order to make reactions possible however they have be able to leave their membranes.
This is defined by the airlock rule. We introduce an extended version (EAL) which enables
molecules to cross multiple membranes.
(AL) [a C1 ]a ⇌ C1 hai [a ]a
(EAL) [b C1 hL,ai [a ]a ]b ⇌ C1 hL,a,bi [b [a ]a ]b
Intuitively we enable the molecules to travel through the membrane structure keeping
track of the membranes they crossed in a list which is an annotation of the airlock-
operator.
Interaction. The main goal is to find and encourage possible interactions. Especially
molecules from situations should react with molecules from morphisms. Such reactions
are only possible because both situations and morphisms evolve according to the airlock
rules. The rule for interaction can be given as follows.
(INT) C1+ hsrc,mori [mor [src ]src ]mor , C1− ha,s1i [s1 [a ]a ]s1 →
[hmor,s1i [hsrc,s1,ai C1 ]hsrc,s1,ai ]hmor,s1i [hs1,mori [ha,mori C1 ]ha,mori ]hs1,mori
Intuitively the reaction between the molecules is recorded by the labels. Thus the
labels of the morphism are added to the labels of the situation. In the same way the
labels of the morphism are extended. Note that we only treat the matching of the source
ontology of the morphism. We presume that the molecules of the morphism are charged
negatively while the molecules of the situation are charged positively. Note that there
can be many different reactions between situations and morphisms because many copies
of the structures are floating in the solution.
Completing the Infomorphism. An ontology morphism is completely bound when two
molecules from two context description have been bound to its source and target ports.
Since the knowledge about the creation of the bindings is contained in the labels the
information is present which which completes an infomorphism (i.e. the relation between
the individuals which is contravariant to the original ontology morphism).
Compression. Elements from the input spaces which are connected by a vital relation
(i.e. infomorphisms) are projected into the blend. The resulting individuals which are
created in the blend can be considered a tuple-valued individuals which establish a con-
nection between the original tokens (or es equivalence classes). We cannot deepen these
issues due to space restrictions.
4 Outlook
We discussed a membrane-based calculus for the creation of infomorphisms between con-
ceptual spaces during runtime. We consider this line of research as a contribution to the
exploration of adaptive and context-aware behavior in distributed systems. The treat-
ment of infomorphisms is the strategic foundation for the integration of more advanced
formal constructs from common sense reasoning.
References
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Univ. Press, 1997.
2. G. Fauconnier and M. Turner. The Way we Think. Basic Books, 2002.
3. J. Goguen. Information integration in institutions. In Memorial Volume for Jon Barwise.
Indiana University Press, Indiana, 2005.
4. G. Păun. Membrane Computing. An Introduction. Springer, Berlin, 2002.
5. P. Pepper, M. Cebulla, K. Didrich, and W. Grieskamp. From program languages to software
languages. The Journal of Systems and Software, 60, 2002.