A Formal Deductive Problem-Solving System

Abstract

A formalism is defined in which solutions to theorem-proving and similar problems take the form of a sequence of transformations of states into other states. The data used to solve a problem then consists of a set of rewriting rules which defines the allowable transformations. A method for selecting “useful” transformations, i.e. those which will most probably lead to a solution, is developed. Two problem-solving processes based on the above are defined; one, called the FORTRAN Deductive System (FDS) is shown to be more powerful than the other. A class of problems to which FDS will always find solutions is constructed. Examples of solutions found by a computer implementation of FDS are given and, in some cases, are compared with human performance. Finally, FDS is compared with some of the better-known problem-solving systems.