Higher order grammar
Higher Order grammar (HOG) is a
grammar theorybased on higher-order logic. It can be viewed simultaneously as generative-enumerative (like Categorial Grammar and Principles & Parameters) or model theoretic (like Head-Driven Phrase Structure Grammaror Lexical Functional Grammar).
* 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 phonologyor 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
* 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.
* [http://www.ling.ohio-state.edu/~hana/hog/ Higher Order Grammar] , Ohio State
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