There is a
propositional logic of types, which denote sets of linguistic (phonological, syntactic, or semantic) entities. For example, the type NP denotes the syntactic category (or form class) of
noun phrases.
HOG maintains
Haskell Curry's distinction between tectogrammatical structure (abstract
syntax) and phenogrammatical structure (concrete syntax).
Abstract syntactic entities are identified with
structuralist (
Bloomfield-
Hockett) free forms (words and phrases). For example, the NP your cat is distinct from its
phonology or its
semantics.
Concrete syntax is identified with
phonology, broadly construed to include word order.
The modelling of
Fregean senses is broadly similar to
Montague's, but with intensions replaced by finer-grained hyperintensions.
There is a (
Curry-Howard) proof term calculus, whose terms denote linguistic (phonological, syntactic, or semantic) entities.
The HOL admits (separation-style)
subtyping, e.g. NPacc, the type of
accusative noun phrases, is a subtype of NP, and denotes a subset of the category denoted by NP.