Interval Timing Theories

Scalar timing theory is designed to account for the behavior of human beings and other animals in temporal perception and timed performance procedures (Allan, 1998; Gibbon, 1991). Many alternative timing theories have been designed to account for the same facts. These include the behavioral theory of timing (Killeen and Fetterman, 1988), the learning-to-time model (Machado, 1997), the multiple-oscillator model (Church and Broadbent, 1990), the spectral timing theory (Grossberg and Schmajuk, 1989), and the multiple-timescale model (Staddon and Higa, 1999). Although this chapter is restricted to a description of scalar timing theory, the approach that is described can be applied to any timing theory that is completely and precisely described (Church and Kirkpatrick, 2001).

Conditioning theories were also designed to account for the behavior produced by procedures that involve the specification of the times of onset and termination of stimuli and reinforcers, and of responses. The goal of standard conditioning theories (such as Rescorla and Wagner, 1972) was to describe the relative response rates or probabilities averaged over a stimulus, and not the time of responses. But real-time theories of conditioning were developed by Sutton, Barto, and others that were designed to account for the time of responses (Barto and Sutton, 1982; Sutton and Barto, 1981, 1990). Although this chapter will not describe these real-time conditioning theories, the same approach used in this chapter for the analysis of scalar timing theory can be applied to the real-time conditioning theories (Church and Kirkpatrick, 2001). Until recently, theories of timing and conditioning were developed quite separately, but it is no longer clear that separate theories for timing and conditioning are necessary (see Gibbon and Balsam, 1981; Gallistel and Gibbon, 2000, 2002; Hopson, this volume; Kirkpatrick and Church, 1998).

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