Qualitative Superposition

Results are presented generalising superposition to non-linear systems by using qualitative differential equations. These are applied to allow the composition and decomposition of qualitative histories. Histories record the qualitative changes in a system over time, and they can be automatically generated by qualitative simulation. The qualitative superposition of such histories is shown to be identical to the qualitative simulation of interactions within linear systems, and many non-linear systems. The result of adding two histories is a partial envisionment for the system, and the recreation of the interaction history is a path traversal of the envisionment space. The technique is useful when a reasoning system needs to decompose an interaction history to identify the state of each contributing history, and when examples of a systems's behaviours exist as histories but no model is available. Formalising the limits to qualitative superposition also has implications for other forms of inference, such as the resolution of multiple causal inferences through a single parameter.