Multiple-valued logic as a programming language

Abstract

A method for specifying the computable functions using multiple-valued logics is described. The logics in question provide a uniform environment both for specifying computable functions on the natural numbers and for proving theorems about such specifications. They arise via a generalisation to the countable-valued case of techniques that may be used in specifying multiple-valued switching circuits by finite-valued predicate logics. In this paper a concrete instance of such a language, based on a modification of dual skew Boolean logic, is constructed. The result may be viewed as a a simple functional/logic programming language that is, in principle, executable.