Higher order grammar
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Higher Order grammar (HOG) is a grammar
theory based on higher-order
logic. It can be viewed simultaneously as generative-enumerative
Grammar and Principles
& Parameters) or model theoretic (like Head-Driven
Phrase Structure Grammar or Lexical
- 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
- HOG maintains Haskell
Curry's distinction between tectogrammatical
structure (abstract syntax)
and phenogrammatical structure (concrete syntax).
- Abstract syntactic entities are identified with structuralist
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 term calculus is embedded in a classical higher-order
- The syntax-phonology and syntax-semantics interfaces
are expressed as axiomatic theories in the HOL.
- 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.
Published - December 2008