On additivity of duration reproduction functions

In the present paper properties of theoretical response functions in the duration reproduction task (drt) are studied. If the drt response is to be interpreted as the measure of a temporal duration elapsed in the past, the reproduction function (rf) must be additively measuring. The additivity property is defined for bivariate rfs, taking into account the delay between retention and reproduction. The requirement that an rf be additively measuring leads to a system of two functional equations, which are solved by (i) linear functions of time, or (ii) functions of the form yielded by the ‘dual klepsydra model’ of duration reproduction Wackermann, J., & Ehm, W. (2006). The klepsydra model of internal time representation and time reproduction. Journal of Theoretical Biology, 239, 482-493]. This result supports the outstanding rôle of the ‘klepsydraic reproduction function’ (krf) in models of internal representation and reproduction of temporal durations.