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# Approximate Concepts and Approximate Theories

Other kinds of imprecision are more fundamental for intelligence than numerical imprecision. Many phenomena in the world are appropriately described in terms of approximate concepts. Although the concepts are imprecise, many statements using them have precise truth values. We offer two examples: the concept of Mount Everest and the concept of the welfare of a chicken. The exact pieces of rock and ice that constitute Mount Everest are unclear. For many rocks, there is no truth of the matter as to whether it is part of Mount Everest. Nevertheless, it is true without qualification that Edmund Hillary and Tenzing Norgay climbed Mount Everest in 1953 and that John McCarthy never set foot on it.

The point of this example is that it is possible and even common to have a solid knowledge structure from which solid conclusions can be inferred based on a foundation built on the quicksand of approximate concepts without definite extensions.

As for the chicken, it is clear that feeding it helps it and wringing its neck harms it, but it is unclear what its welfare consists of over the course of the decade from the time of its hatching. Is it better off leading a life of poultry luxury and eventually being slaughtered or would it be better off escaping the chicken yard and taking its chances on starvation and foxes? There is no truth of the matter to be determined by careful investigation of chickens. When a concept is inherently approximate, it is a waste of time to try to give it a precise definition. Indeed different efforts to define such a concept precisely will lead to different results--if any.

Most human common sense knowledge involves approximate concepts, and reaching human-level AI requires a satisfactory way of representing information involving approximate concepts.

Next: Nonmonotonic Reasoning Up: FROM HERE TO Previous: The Use of Mathematical

John McCarthy
Sun Apr 19 15:21:34 PDT 1998