Ternary relational semantics and beyond: programs as arguments (data) and programs as functions (programs).

Abstract

The purpose of this paper is to review some ideas from Dunn and Meyer (1997) and Dunn (2001) and "write them large". The first paper showed how to represent combinatory algebras using ternary frames, and the second paper showed how to do the same for relation algebras. It should be pointed out that these representations both fall under the general heading of "gaggle theory", as developed in a series of papers beginning with Dunn (1991), in which an n-ary operator is represented using an л+7-placed relation. These results were presented in a somewhat mathematical fashion, although philosophical motivations were introduced as well. The present paper will focus on these philosophical motivations and clarify and extend them. In addition it will point to some future research directions in connection with Pratt's dynamic logic and Hoare's logic of programming.