ABSTRACT
Response times (in a very general meaning of the term, including physiological latencies and durations of theoretically assumed mental actions) can be subjected to two basic forms of analysis: (a) the representation of response times by durations of unobservable processes identified by their final outcomes and developing until they meet certain termination conditions; and (b) the decomposition of response times into component durations identified by observable external factors that influence them selectively. This chapter overviews and elaborates theoretical concepts and mathematical results related to these two analyses. It begins with a general theory of process representations for arbitrary response arrangements (i.e., the rules determining which responses may co-occur within a trial). This theory extends the Grice-representability and McGill-representability analysis proposed previously for mutually exclusive responses. Then the notion of selectively influenced but (generally) interacting processes is introduced and related to that of selectively influenced but (generally) stochastically interdependent component durations: the two notions turn out to be related in an indirect and complex way. Finally, an overview is given of the available mathematical facts related to (a) the recovery of the algebraic operation connecting the response time components that are identified by the factors selectively influencing them and by the form of stochastic relationship among them (independence or perfect positive interdependence); and (b) the choice between the independence and perfect positive interdependence of signal-dependent and signal-independent components identified by the algebraic operation connecting them.
