We describe a computer proof of the 17-point version of a conjecture originally made by Klein-Szekeres in 1932 (now commonly known as the “Happy End Problem”) that a planar configuration of 17 points, no 3 points collinear, always contains a convex 6-subset. The proof makes use of a combinatorial model of planar configurations, expressed in terms of signature functions satisfying certain simple necessary conditions. The proof is more general than the original conjecture as the signature functions examined represent a larger set of configurations than those which are realisable. Three independent implementations of the computer proof have been developed, establishing that the result is readily reproducible.
Evaluation has remained a major challenge for knowledge acquisition and little data is available on how experts actually use knowledge acquisition technology. A number of companies offer Ripple-Down Rules to enable on-going knowledge acquisition and maintenance while a system is in use. One of these companies, Pacific Knowledge Systems 1 has logged user activity over a number of years. Data from these logs demonstrate that domain experts continue to add knowledge to a knowledge base over years. The logs also demonstrate that new knowledge can be added very rapidly regardless of knowledge base size or age. We assume that the on-going knowledge acquisition observed was driven by the need to make changes and encouraged and allowed by the ease of the knowledge acquisition technology used. The question arises of whether experts in other domains would also chose to continue to add knowledge to their knowledge bases if this was supported.
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