# Model-theoretic grammar

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**Model-theoretic grammars**, also known as constraint-based 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 model-theoretic 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 well-formed structures are the models that satisfy the theory.

## Examples of model-theoretic grammars

The following is a sample of grammars falling under the model-theoretic umbrella:

- the non-procedural 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]} - Head-driven phrase structure grammar (HPSG) in the formalization of King (1999)
^{[3]} - Constraint Handling Rules (CHR) grammars
^{[4]}

## Strengths

One benefit of model-theoretic grammars over generative grammars is that they allow for gradience in grammaticality. A structure may deviate only slightly from a theory or it may be highly deviant. A generative grammar, in contrast "entail a sharp boundary between the perfect and the nonexistent, and do not even permit gradience in ungrammaticality to be represented."^{[5]}

## References

**^**Pullum, Geoffrey Keith; Scholz, Barbara C. (2001). "On the distinction between generative-enumerative and model-theoretic syntactic frameworks" (PDF). In de Groote, Philippe; Morrill, Glyn; Retor, Christian (eds.).*Logical Aspects of Computational Linguistics: 4th International Conference*. Springer Verlag. pp. 17–43.**^**Pullum, Geoffrey Keith (2007). "The evolution of model-theoretic frameworks in linguistics" (PDF). In Rogers, James; Kepser, Stephan (eds.).*Model-theoretic syntax at 10 – Proceedings of the ESSLLI2007 MTS@10Workshop*. Trinity College Dublin. pp. 1–10.- ^
^{a}^{b}^{c}^{d}Müller, Stefan (2016).*Grammatical theory: From transformational grammar to constraint-based 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.**^**Pullum, Geoffrey K. (2013). "The Central Question in Comparative Syntactic Metatheory: The Central Question in Comparative Syntactic Metatheory".*Mind & Language*.**28**(4): 492–521. doi:10.1111/mila.12029.