Higher order grammar

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title: "Higher order grammar" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["grammar-frameworks"] topic_path: "general/grammar-frameworks" source: "https://en.wikipedia.org/wiki/Higher_order_grammar" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

Higher order grammar (HOG) is a grammar theory based on higher-order logic. It can be viewed simultaneously as generative-enumerative (like categorial grammar and principles and parameters) or model theoretic (like head-driven phrase structure grammar or lexical functional grammar).

Key features

  • 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 term calculus is embedded in a classical higher-order logic (HOL).
  • 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.

References

References

  1. [[Carl Pollard. Pollard, Carl]]. "[https://www.researchgate.net/profile/Carl_Pollard/publication/249797500_Higher-Order_Categorical_Grammar/links/02e7e53424af4912df000000.pdf Higher-order categorial grammar]." International Conference on Categorial Grammars, Montpellier, France. 2004.
  2. (January 2026)

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