Arc pair grammar
Encyclopedia
In linguistics, Arc Pair grammar is a syntactic theory developed by David E. Johnson
David E. Johnson
David E. Johnson is an American linguist. He is the co-inventor of arc pair grammar.- Work :...

 and Paul Postal
Paul Postal
Paul Martin Postal is an American linguist and member of the faculty of New York University.Postal received his PhD from Yale University in 1963 and taught at MIT until 1965. That year, he moved to the City University of New York...

 which is a formalized continuation of relational grammar
Relational grammar
In linguistics, Relational Grammar is a syntactic theory which argues that primitive grammatical relations provide the ideal means to state syntactic rules in universal terms. Relational grammar began as an alternative to transformational grammar....

 developed by David M. Perlmutter and Paul M. Postal.

Like relational grammar, arc pair grammar is greatly concerned with grammatical relations (as opposed to the constituent
Constituent (linguistics)
In syntactic analysis, a constituent is a word or a group of words that functions as a single unit within a hierarchical structure. The analysis of constituent structure is associated mainly with phrase structure grammars, although dependency grammars also allow sentence structure to be broken down...

 structure focus of other generative
Generative grammar
In theoretical linguistics, generative grammar refers to a particular approach to the study of syntax. A generative grammar of a language attempts to give a set of rules that will correctly predict which combinations of words will form grammatical sentences...

 theories like versions of Chomskyan transformational grammar
Transformational grammar
In linguistics, a transformational grammar or transformational-generative grammar is a generative grammar, especially of a natural language, that has been developed in the Chomskyan tradition of phrase structure grammars...

). In contrast to the generative-enumerative (proof-theoretic) approach to syntax assumed by transformational grammar, arc pair grammar takes a model-theoretic approach. In arc pair grammar, linguistic laws and language-specific rules of grammar are formalized in the same manner, namely, as logical statements in an axiomatic theory. Further, sentences of a language, understood as structures of a certain type, are the models of the set of linguistic laws and language-specific statements, thereby reducing the notion of grammaticality to the logical notion of model-theoretic satisfaction.

For a brief history of early work on relational grammar and arc pair grammar, see Newmeyer, 1980. For a more detailed history of model-theoretic approaches in linguistics, see Pullum and Scholz, 2005 and Pullum, 2007.
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