Int. J. Man-Machine Studies (1972) 4, 169-199 Axioms for Adaptive Behaviour B. R. GAINES Department of Electrical Engineering Science, University of Essex, U.K. (Received 28 March 1972) The study of adaptive behaviour, both natural and artificial, has developed without any generally accepted definitions of the terms " adaptive" or "adap- ted ", 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 connota- tion, 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. 1. Introduction The terms "adaptive ", " adapted ", and "learning ", are ones which originally arose in the biological sciences to denote the plasticity of behaviour shown by an organism in its struggle to survive in a novel or changeable environment. In recent years the same terms have come to be applied in the engineering sciences to systems designed to optimize their performance through interaction with their environment, and since these, or similar terms form an essential part of the statement of objectives of major areas of research into adaptive control and artificial intelligence, it is reasonable to expect the terms to be capable of fairly exact definition. This is not so, however, and the terms are used very loosely with tacit switches of connotation, particularly between " structural " and "behavioural" aspects of adaption. In this first section previous attempts at definition are critically analysed to demonstrate the variety of connotations of the term "adaptive " 169