The introduction of process descriptions in GIS is a long-standing desire. A partial answer is given by models of geographic, continuous processes with Partial Differential Equations. Other spatial processes can be modeled with cellular automatons and multi-agent simulation.
If a GIS maintains data with relation to observation time (e.g., snapshots) and includes in its ontology the description of the processes then the datasets in the GIS become linked by the processes. The GIS can simulate the development and compare it with the observed changes in the real world, deriving values for (local) constants for the process models, etc.
Integrating time related observations with process models in a GIS give a substantially different information system than current GIS, which are well organized, useful repositories for data. The new GIS is a spatial simulation systems.
It may be interesting to speculate on the timeframe in which such a transformation could occur; consider that from a gleam of GIS in researcher's eyes to the current reality of GIS workhorses took some 20 years; consider further that the integration of snapshot time into GIS is past the research but not yet fully integrated in practice. One may conclude that the "GIS as a geographic simulation system" may take another 25 years.