Higher Order Logic
Daniel M. Leivant · 1994
Abstract Higher order logics, long considered by many to be an esoteric subject, are increasingly recognized for their foundational importance and practical usefulness, notably in Theoretical Computer Science. In this chapter we try to present a survey of some issues and results, without any pretense of completeness. Our choice of topics is driven by an attempt to cover the foundational aspects of higher order logic, and also to briefly point to some areas of current and potential applications. The chapter falls into two parts. The first part, consisting of sections 1 through 4, is designed to bring forth the essential issues and facts of the topic. Section 1 is intended to motivate our interest in higher order logic, by presenting selected examples of the expressive power of second order logic, and contrasting them with the limitations of first order logic.