 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 & 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. ==external links== *higher order grammar, ohio state
Grammar_frameworks