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Commonsense Reasoning by Erik T. Mueller

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CHAPTER 7

Continuous Change

Discrete change is change that is limited to a countable, usually finite, set of timepoints. We represent discrete change in the event calculus using effect axioms. In a number of commonsense domains ranging from the physical to the mental, we find continuous change. A function f(t) is continuous at a point t0 if and only if for every ∈ > 0, there is a δ > 0 such that |tt0| < δ implies |f(t) − f(t0)| < ∈. A function is continuous on an interval if and only if it is continuous at all points of the interval. Examples of continuous change include the change in the height of a falling object, the location of a projectile, the water level of a filling bathtub, the volume of a balloon in the process of inflation, the ...

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