The plain record of a variable's numerical values over time does not invoke appreciable levels of cognitive activity to a human.  Although it can cause a fervor of numerical computations by a computer, the levels of cognitive appreciation of the variable's temporal behavior remain low.  On the other hand, if one presents the human with a graphical depiction of the variable's temporal behavior, the level of cognition increases and a wave of reasoning activities is unleashed.  Nevertheless, when the human is presented with scores of graphs, depicting the temporal behavior of interacting variables, his/her reasoning abilities are severely tested.  In such case, the computer will happily continue crunching numbers without ever raising above the fray and thus developing a "mental" model, interpreting correctly the temporal interactions among the many variables.
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	Reasoning in time is very demanding, because time introduces a new dimension with significant levels of additional freedom and complexity.  While the real-valued representation of variables in time is completely satisfactory for many engineering tasks (e.g. control, dynamic simulation, planning and scheduling of operations), it is very unsatisfactory for all those tasks, which require decision-making via logical reasoning (e.g. diagnosis of process faults, recovery of operations from large unsolicited deviations, "supervised" execution of start-up for shut-down operating procedures).
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	To improve the computer's ability to reason efficiently in time, we must first establish new forms for the representation of temporal behaviors.  It is the purpose of this chapter to examine the engineering needs for temporal decision-making and to propose specific models which encapsulate the requisite temporal characteristics of individual variables and composite processes.  Through a combination of analytical techniques, such as scale-space filtering and wavelet-based, multiresolution decomposition of functions, and modeling paradigms from artificial intelligence, we have developed a concise framework that can be used to model, analyze, and synthesize the temporal trends of process operations.  Within this framework, the modeling needs for logical reasoning in time can be fully satisfied, while maintaining consistency with the numerical tasks carried out at the same time.  Thus, through the modeling paradigms of this chapter one may put together intelligent systems which use consistent representations for their logical-reasoning and numerical tasks.