Axioms for adaptive behaviour
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The study of adaptive behaviour, both natural and artificial, has developed without any generally accepted definitions of the terms “adaptive” or “adapted”, and it has been argued that a formal definition of these terms is not possible. However, if only for purposes of meaningful communication, some form of accepted definition would be useful, and it is possible that an investigation of the “impossibility” of definition might throw some light on fundamental problems concerning adaption and learning processes. This paper commences with a critical discussion of previous attempts to define terms concerned with adaption and learning. It is concluded that these terms cannot meaningfully be defined absolutely, and do not have a single connotation, but that rigorous definitions of a variety of phenomena with connotations of adaption may be given relative to (arbitrarily) defined rules for describing behaviour. An extensive set of definitions of behavioural phenomena in these terms is given. Finally a machine, the adaption automaton, is defined whose behaviour is equivalent to that of the adaptive system and the various definitions are re-phrased in terms of the structure of the adaption automaton.
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