nLab
higher-order logic

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.

Higher-order intuitionistic logic is often identified with the internal logic of a topos.

Related concepts

• propositional logic (0th order)

• predicate logic (1st order)

• higher order logic

  • Isabelle