Higher order grammar (HOG) is a grammar theory based on

higher-order logic In mathematics and logic, a higher-order logic (abbreviated HOL) is a form of logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are m ...

.Hana, Jiri
Czech Clitics in Higher Order Grammar
Diss. The Ohio State University, 2007. It can be viewed simultaneously as generative-enumerative (like categorial grammar 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, sw ...

) or model theoretic (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 t ...

lexical functional grammar Lexical functional grammar (LFG) is a constraint-based grammar framework in theoretical linguistics. It posits several parallel levels of syntactic structure, including a phrase structure grammar representation of word order and constituency, an ...

Key features

* There is a

propositional logic The propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. Sometimes, it is called ''first-order'' propositional logic to contra ...

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 A noun phrase – or NP or nominal (phrase) – is a phrase that usually has a noun or pronoun as its head, and has the same grammatical functions as a noun. Noun phrases are very common cross-linguistically, and they may be the most frequently ...

s. * HOG maintains

Haskell Curry Haskell Brooks Curry ( ; September 12, 1900 – September 1, 1982) was an American mathematician, logician and computer scientist. Curry is best known for his work in combinatory logic, whose initial concept is based on a paper by Moses Schönfin ...

's distinction between tectogrammatical structure (abstract

syntax 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 (constituenc ...

) and phenogrammatical structure (concrete syntax). * Abstract syntactic entities are identified with

structuralist Structuralism is an intellectual current and methodological approach, primarily in the social sciences, that interprets elements of human culture by way of their relationship to a broader system. It works to uncover the structural patterns tha ...

( Bloomfield- Hockett) free forms (words and phrases). For example, the NP ''your cat'' is distinct from its

phonology Phonology (formerly also phonemics or phonematics: "phonemics ''n.'' 'obsolescent''1. Any procedure for identifying the phonemes of a language from a corpus of data. 2. (formerly also phonematics) A former synonym for phonology, often pre ...

or its

semantics Semantics is the study of linguistic Meaning (philosophy), meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction betwee ...

. * 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 called subtype polymorphism or inclusion polymorphism) is a form of type polymorphism. A ''subtype'' is a datatype that is related to another datatype (the ''supertype'') by some notion of substi ...

, e.g. NPacc, the type of

accusative In grammar, the accusative case (abbreviated ) of a noun is the grammatical case used to receive 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", " ...

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