# nLab higher-order logic

foundations

## Foundational axioms

foundational axiom

# Contents

## Idea

A higher-order logic is any logic which features higher-order predicates, which are predicates of predicates or of operations. If we think of a predicate as a function to truth values, then a higher-order predicate is a function on a power set or a function set.

Typed higher-order logic may be called higher-order type theory. Typed higher-order intuitionistic logic is often identified with the internal logic of a topos.

Revised on October 12, 2013 21:10:29 by Toby Bartels (98.19.41.253)