Noun is a noun (terminology)

Solution 1:

There is some terminology in logic for these kinds of statements.

Karl is a teacher.

This is a singular membership proposition: a proposition asserting that an individual (in this case Karl) is member of a category (teachers).

Pigeons are birds.

meaning

All pigeons are birds.

This is an A-form categorical proposition: a proposition asserting that all of the members of one category, the subject term (pigeons), are included in another category, the predicate term (birds).

In logic, the predicate in this example is the function “is a bird”, which takes an individual as an argument (the subject), and outputs “true” or “false”.

There are 4 standard forms of categorical propositions:

• A-form: All S are P.
• E-form: No S are P.
• I-form: Some S are P.
• O-form: Some S are not P.

Quantity: A-form and E-form categorical propositions are universal, I-form and O-form categorical propositions are particular (or existential).

Quality: A-form and I-form categorical propositions are affirmative, E-form and O-form categorical propositions are negative.

Karl is a teacher.

Pigeons are birds.

In grammar, both sentences consist of a subject (“Karl”, “Pigeons”), a copula (“is”, “are”) and a predicative complement (“a teacher”, “birds”).

Both a subject and a predicative complement can be much longer than just a noun. A predicative complement can also consist of just an adjective, or an adjective phrase.