Programming languages, logic and cooperative games

Abstract

An application of computers is presented which is not restricted to a single problem area but is perhaps not general purpose enough to be considered a programming language, even a problem-oriented one. The application is a program to eliminate quantifiers and bound variables from logical statements in the theory of addition on the real numbers. These statements differ from work in linear inequalities by formal use of quantifiers. The first, introductory, part of the paper argues that from one point of view, this application does provide a higher level programming language. The second part is a description of the method, due basically to Langford, that has been programmed. The last section describes a subapplication to the problem area of bargaining sets of cooperative games where other interesting non-numerical problems arise.