Predicates and Functions Together

Assuming father is a unary function and Hungry is a unary predicate, the following are well-formed terms

father(Mike)
father(father(Mike))
father(father(father(Mike)))

And the following are well formed atomic sentences

Hungry(Mike)
Hungry(father(Mike))
Hungry(father(father(Mike)))

However, the following are ill formed:

Hungry(Hungry(Mike))
father(Hungry(Mike))

 
• The First Order Language of Arithmetic