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International Conference on Complex Systems (ICCS2006)

On the complexity monotonicity thesis for environment, behaviour and cognition

Tibor Bosse
Vrije Universiteit Amsterdam, Dept of AI

Alexei Sharpanskykh
Vrije Universiteit Amsterdam, Dept of AI

Jan Treur
Vrije Universiteit Amsterdam, Dept of AI

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     Last modified: May 23, 2006

Behaviour of organisms can occur in different types and complexities, varying from very simple behaviour to more sophisticated forms. Depending on the complexity of the externally observable behaviour, the internal mental representations and capabilities required to generate the behaviour also show a large variety in complexity. From an evolutionary viewpoint, for example, Wilson (1992)1 and Darwin (1871)2 point out how the development of behaviour relates to the development of more complex cognitive capabilities. Godfrey-Smith (1996, p. 3) assumes a relationship between the complexity of the environment and the development of mental representations and capabilities. He formulates the main theme of his book in condensed form as follows: ‘The function of cognition is to enable the agent to deal with environmental complexity’ (the Environmental Complexity Thesis). In this paper, this thesis is refined as follows:
• the more complex the environment, the more sophisticated is the behaviour required to deal with this environment,
• the more sophisticated the behaviour, the more complex are the mental representations and capabilities needed

This refined thesis will be called the Complexity Monotonicity Thesis. The idea is that to deal with the physical environment, the evolution process has generated and still generates a variety of organisms that show new forms of behaviour. These new forms of behaviour are the result of new architectures of organisms, including cognitive systems with mental representations and capabilities of various degrees of complexity. The occurrence of such more complex architectures for organisms and the induced more complex behaviour itself increases the complexity of the environment during the evolution process. New organisms that have to deal with the behaviour of such already occurring organisms live in a more complex environment, and therefore need more complex behaviour to deal with this environment, (to be) realised by an architecture with again more complex mental capabilities. In particular, more complex environments often ask for taking into account more complex histories, which requires more complex internal cognitive representations and dynamics, by which more complex behaviour is generated.

This perspective generates a number of questions. First, how can the Complexity Monotonicity Thesis be formalised, and in particular how can the ‘more complex’ relation be formalised for (1) the environment, (2) externally observable agent behaviour and (3) internal cognitive dynamics? Second, connecting the three items, how to formalise (a) when does a behaviour fit an environment: which types of externally observable behaviours are sufficient to cope with which types of environments, and (b) when does a cognitive system generate a certain behaviour: which types of internal cognitive dynamics are sufficient to generate which types of externally observable agent behaviour?

In this paper these questions are addressed from a dynamics perspective, and formalised by a temporal logical approach. Complexity of the dynamics of environment, externally observable agent behaviour and internal cognitive system are formalised in terms of structure of the formalised temporal specifications describing them, thus answering (1) to (3). Moreover, (a) and (b) are addressed by establishing formalised logical (entailment) relations between the respective temporal specifications. Furthermore, four cases of an environment, suitable behaviour and realising cognitive system are analysed and compared with respect to complexity, thus testing the Complexity Monotonicity Thesis.

1 ‘The overall average across the history of life has moved from the simple and few to the more complex and numerous. During the past billion years, animals as a whole evolved upward in body size, feeding and defensive techniques, brain and behavioural complexity, social organisation, and precision of environmental control - in each case farther from the nonliving state than their simpler antecedents did’ (Wilson, 1992, p. 187).
2 ‘As the reasoning powers and foresight of the members became improved, each man would soon learn that if he aided his fellow-men, he would commonly receive aid in return’ (Darwin, 1871, p. 163).

Darwin, C. (1871). The Descent of Man. John Murray, London.
Godfrey-Smith, P. (1996). Complexity and the Function of Mind in Nature. Cambridge University Press.
Wilson, O. (1992). The Diversity of Life. Harvard University Press, Cambridge, Massachusetts.


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