Higher order grammar

Higher order grammar (HOG) is a grammar theory based on higher-order logic.[1][2] 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
  1. Pollard, Carl. "Higher-order categorial grammar." International Conference on Categorial Grammars, Montpellier, France. 2004.
  2. Hana, Jiri. Czech Clitics in Higher Order Grammar. Diss. The Ohio State University, 2007.
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