Higher order grammar (HOG) is a

grammar theory In linguistics, syntax () is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure ( constituency ...

based on

higher-order logic mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more expres ...

.Hana, Jiri
Czech Clitics in Higher Order Grammar
Diss. The Ohio State University, 2007. It can be viewed simultaneously as

generative Generative may refer to: * Generative actor, a person who instigates social change * Generative art, art that has been created using an autonomous system that is frequently, but not necessarily, implemented using a computer * Generative music, ...

-enumerative (like

categorial grammar Categorial grammar is a family of formalisms in natural language syntax that share the central assumption that syntactic constituents combine as functions and arguments. Categorial grammar posits a close relationship between the syntax and sema ...

and

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'' (i.e. abstract rules or grammars) and specific ''parameters'' (i.e. markers, ...

) or

model theoretic In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the st ...

(like

head-driven phrase structure grammar Head-driven phrase structure grammar (HPSG) is a highly lexicalized, constraint-based grammar developed by Carl Pollard and Ivan Sag. It is a type of phrase structure grammar, as opposed to a dependency grammar, and it is the immediate successor ...

or lexical functional grammar).

Key features

* There is a

propositional logic Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations ...

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 phrase In linguistics, a noun phrase, or nominal (phrase), is a phrase that has a noun or pronoun as its head or performs the same grammatical function as a noun. Noun phrases are very common cross-linguistically, and they may be the most frequently o ...

s. * HOG maintains

Haskell Curry Haskell Brooks Curry (; September 12, 1900 – September 1, 1982) 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 ...

'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 Phonology is the branch of linguistics that studies how languages or dialects systematically organize their sounds or, for sign languages, their constituent parts of signs. The term can also refer specifically to the sound or sign system of a ...

or its

semantics Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and compu ...

. * Concrete syntax is identified with

, 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

(HOL). * The syntax-phonology and syntax-semantics interfaces are expressed as axiomatic theories in the HOL. * The HOL admits (separation-style)

subtyping In programming language theory, subtyping (also subtype polymorphism or inclusion polymorphism) is a form of type polymorphism in which a subtype is a datatype that is related to another datatype (the supertype) by some notion of substitutability, ...

, e.g. NPacc, the type of

accusative The accusative case ( abbreviated ) of a noun is the grammatical case used to mark the direct object of a transitive verb. In the English language, the only words that occur in the accusative case are pronouns: 'me,' 'him,' 'her,' 'us,' and ‘th ...

noun phrases, is a subtype of NP, and denotes a subset of the category denoted by NP.

References

{{Reflist

External links

Higher Order Grammar
Ohio State Grammar frameworks