In linguistics, Arc Pair grammar is a syntactic theory developed by David E. Johnson and Paul Postal which is a formalized continuation of relational 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 structure focus of other generative theories like versions of Chomskyan transformational grammar). 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.