Higher order grammar
Higher order grammar is a grammar theory based on higher-order logic. It can be viewed simultaneously as generative-enumerative or model theoretic.Key features
- There is a propositional logic of types, which denote sets of linguistic entities. For example, the type NP denotes the syntactic category of noun phrases.
- HOG maintains Haskell Curry's distinction between tectogrammatical structure and phenogrammatical structure.
- Abstract syntactic entities are identified with structuralist free forms. 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 proof term calculus, whose terms denote linguistic entities.
- The term calculus is embedded in a classical higher-order logic.
- The syntax-phonology and syntax-semantics interfaces are expressed as axiomatic theories in the HOL.
- The HOL admits 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.
