Higher-order grammar
Encyclopedia
Higher Order grammar 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
).
Higher-order logic
In mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and a stronger semantics...
. It can be viewed simultaneously as generative-enumerative (like Categorial Grammar
Categorial grammar
Categorial grammar is a term used for a family of formalisms in natural language syntax motivated by the principle of compositionality and organized according to the view that syntactic constituents should generally combine as functions or according to a function-argument relationship...
and Principles & Parameters
Principles and parameters
Principles and parameters is a framework within generative linguistics in which the syntax of a natural language is described in accordance with general principles and specific parameters that for particular languages are either turned on or off...
) or model theoretic (like Head-Driven Phrase Structure Grammar
Head-driven phrase structure grammar
Head-driven phrase structure grammar is a highly lexicalized, non-derivational generative grammar theory developed by Carl Pollard and Ivan Sag. It is the immediate successor to generalized phrase structure grammar. HPSG draws from other fields such as computer science and uses Ferdinand de...
or Lexical Functional Grammar
Lexical functional grammar
Lexical functional grammar is a grammar framework in theoretical linguistics, a variety of generative grammar. It is a type of phrase structure grammar, as opposed to a dependency grammar. The development of the theory was initiated by Joan Bresnan and Ronald Kaplan in the 1970s, in reaction to...
).
Key features
- There is a propositional logicPropositional calculusIn mathematical logic, a propositional calculus or logic is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules and axioms allows certain formulas to be derived, called theorems; which may be interpreted as true...
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 phrasesNoun phraseIn grammar, a noun phrase, nominal phrase, or nominal group is a phrase based on a noun, pronoun, or other noun-like word optionally accompanied by modifiers such as adjectives....
. - HOG maintains Haskell CurryHaskell CurryHaskell Brooks Curry was an American mathematician and logician. Curry is best known for his work in combinatory logic; while the initial concept of combinatory logic was based on a single paper by Moses Schönfinkel, much of the development was done by Curry. Curry is also known for Curry's...
's distinction between tectogrammatical structure (abstract syntaxSyntaxIn linguistics, syntax is the study of the principles and rules for constructing phrases and sentences in natural languages....
) and phenogrammatical structure (concrete syntax). - Abstract syntactic entities are identified with structuralist (BloomfieldLeonard BloomfieldLeonard Bloomfield was an American linguist who led the development of structural linguistics in the United States during the 1930s and the 1940s. His influential textbook Language, published in 1933, presented a comprehensive description of American structural linguistics...
-Hockett) free forms (words and phrases). For example, the NP your cat is distinct from its phonologyPhonologyPhonology is, broadly speaking, the subdiscipline of linguistics concerned with the sounds of language. That is, it is the systematic use of sound to encode meaning in any spoken human language, or the field of linguistics studying this use...
or its semanticsSemanticsSemantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
. - Concrete syntax is identified with phonologyPhonologyPhonology is, broadly speaking, the subdiscipline of linguistics concerned with the sounds of language. That is, it is the systematic use of sound to encode meaning in any spoken human language, or the field of linguistics studying this use...
, broadly construed to include word order. - The modelling of Fregean sensesSense and referenceSinn and bedeutung are usually translated, respectively, as sense and reference. Two different aspects of some terms' meanings, a term's reference is the object that the term refers to, while the term's sense is the way that the term refers to that object.Sinn and bedeutung were introduced by...
is broadly similar to MontagueMontague grammarMontague grammar is an approach to natural language semantics, named after American logician Richard Montague. The Montague grammar is based on formal logic, especially higher order predicate logic and lambda calculus, and makes use of the notions of intensional logic, via Kripke models...
'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 logicHigher-order logicIn mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and a stronger semantics...
(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 accusativeAccusative caseThe accusative case of a noun is the grammatical case used to mark the direct object of a transitive verb. The same case is used in many languages for the objects of prepositions...
noun phrases, is a subtype of NP, and denotes a subset of the category denoted by NP.