An algorithm is described which extracts primitive regions (i.e., convex, spiral shaped, and biconcave lens) from complex shapes. The interior region bounded by the shape is decomposed by first slicing it into a set of convex subregions and then rotating and dissolving the various boundaries between subregions until a satisfactory decomposition is obtained. The same algorithm also is used to decompose the exterior region between the shape and its convex hull. The algorithm has been implemented as an Algol-W computer program for the UNIVAC 90/80 and results of running the program are presented for a wide variety of complex shapes. These results compare favorably with the experience reported by previous programs.

A deductive system is described which combines aspects of resolution (e.g. unification and the use of Skolem functions) with that of natural deduction and whose performance compares favorably with the best predicate calculus theorem provers.

A computer program is described that serves in the dual capacity of being a modified programming language as well as a general problem-solving program with a heuristic search procedure which efficiently selects the seemingly best avenue to explore next.Among the preliminary experiments conducted with the program was the demonstration of its ability not only to prove all theorems in the propositional calculus found in Russell and Whitehead's Principia Mathematica, but to do so in a manner similar to the proofs found in that work.