Modeltheoretic grammars
Modeltheoretic grammars, also known as constraintbased grammars, contrast with generative grammars in the way they define sets of sentences: they state constraints on syntactic structure rather than providing operations for generating syntactic objects.[1] A generative grammar provides a set of operations such as rewriting, insertion, deletion, movement, or combination, and is interpreted as a definition of the set of all and only the objects that these operations are capable of producing through iterative application. A modeltheoretic grammar simply states a set of conditions that an object must meet, and can be regarded as defining the set of all and only the structures of a certain sort that satisfy all of the constraints.[2] The approach applies the mathematical techniques of model theory to the task of syntactic description: a grammar is a theory in the logician's sense (a consistent set of statements) and the wellformed structures are the models that satisfy the theory.
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Examples of such grammars include
 the nonprocedural variant of Transformational grammar (TG) of George Lakoff, that formulates constraints on potential tree sequences[3]
 Johnson and Postal's formalization of Relational grammar (RG) (1980), Generalized phrase structure grammar (GPSG) in the variants developed by Gazdar et al. (1988), Blackburn et al. (1993) and Rogers (1997)[3]
 Lexical functional grammar (LFG) in the formalization of Ronald Kaplan (1995)[3]
 Headdriven phrase structure grammar (HPSG) in the formalization of King (1999)[3]
 Constraint Handling Rules (CHR) grammars[4]
References
 Pullum, Geoffrey Keith; Scholz, Barbara C. (2001). "On the distinction between generativeenumerative and modeltheoretic syntactic frameworks". In de Groote, Philippe; Morrill, Glyn; Retor, Christian (eds.). Logical Aspects of Computational Linguistics: 4th International Conference (PDF). Springer Verlag. pp. 17–43.
 Pullum, Geoffrey Keith (2007). "The evolution of modeltheoretic frameworks in linguistics". In Rogers, James; Kepser, Stephan (eds.). Modeltheoretic syntax at 10 – Proceedings of the ESSLLI2007 MTS@10Workshop (PDF). Trinity College Dublin. pp. 1–10.
 Müller, Stefan (2016). Grammatical theory: From transformational grammar to constraintbased approaches. Berlin: Language Science Press. pp. 490–491.
 Christiansen, Henning. "CHR Grammars with multiple constraint stores." First Workshop on Constraint Handling Rules: Selected Contributions. Universität Ulm, Fakultät für Informatik, 2004.