System Theory

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By B. Goertzel

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178) Bundy proposes that one can program a computer to demonstrate high-level understanding of mathematical proofs, by supplying it with the ability to manipulate entities called proof plans. A proof plan is defined as a common structure that underlies and helps to generate many differentmathematical proofs. Proof plans are not formulated based on mathematical logic alone, they are rather refined to improve their expectancy, generality, prescriptiveness, simplicity, efficiency and parsimony while retaining their correctness.

Com 37 CHAOTIC LOGIC 5 3 ... " Thus, although in a sense transformation systems add no content to their initials, they are capable of producing new patterns. For a list of length 100, as given above, both are clearly patterns. But what if the list were of length 4? Then perhaps "2q + r=1" would not be a pattern: the trouble involved in using it might be judged to exceed the difficulty of using the list itself. But perhaps q = (1+r)/2 would still be a pattern. It all depends on who's doing the judging of complexities -- but for any judge there is likely to be some list length for which one formula is a pattern and the other is not.

Early AI theorists -- in the sixties and early seventies -- brought back logism with a vengeance. The techniques of early AI were little more than applied Boolean logic and tree search, with a pinch or two of predicate calculus, probability theory and other mathematical tricks thrown in for good measure. But every few years someone optimistically predicted that an intelligent computer was just around the corner. At this stage AI theorists basically ignored psychology -- they felt that deductive logic, and deductive logic alone, was sufficient for understanding mental process.

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