Model-theoretic grammar

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.

History

David E. Johnson and Paul M. Postal introduced the idea of model-theoretic syntax in their 1980 book Arc Pair Grammar.^[3]

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^[4]
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)^[4]
Lexical functional grammar (LFG) in the formalization of Ronald Kaplan (1995)^[4]
Head-driven phrase structure grammar (HPSG) in the formalization of King (1999)^[4]
Constraint Handling Rules (CHR) grammars^[5]
The implicit model underlying The Cambridge Grammar of the English Language^[6]

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. Generative grammars, in contrast "entail a sharp boundary between the perfect and the nonexistent, and do not even permit gradience in ungrammaticality to be represented."^[7]

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.
^ Johnson, David E; Postal, Paul M (1980). Arc Pair Grammar. Princeton University Press. ISBN 978-1-4008-5555-1.
^ ^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.; Rogers, James (2008). "Expressive power of the syntactic theory implicit in the Cambridge Grammar of the English Language" (PDF). Annual Meeting of the Linguistics Association of Great Britain: 1–16.
^ Pullum, Geoffrey K. (2013). "The Central Question in Comparative Syntactic Metatheory". Mind & Language. 28 (4): 492–521. doi:10.1111/mila.12029.

[=PullumScholz-1] 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-2] 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.

[3] Johnson, David E; Postal, Paul M (1980). Arc Pair Grammar. Princeton University Press. ISBN 978-1-4008-5555-1.

[=Müller-4] Müller, Stefan (2016). Grammatical theory: From transformational grammar to constraint-based approaches. Berlin: Language Science Press. pp. 490–491.

[5] Christiansen, Henning. "CHR Grammars with multiple constraint stores." First Workshop on Constraint Handling Rules: Selected Contributions. Universität Ulm, Fakultät für Informatik, 2004.

[6] Pullum, Geoffrey K.; Rogers, James (2008). "Expressive power of the syntactic theory implicit in the Cambridge Grammar of the English Language" (PDF). Annual Meeting of the Linguistics Association of Great Britain: 1–16.

[7] Pullum, Geoffrey K. (2013). "The Central Question in Comparative Syntactic Metatheory". Mind & Language. 28 (4): 492–521. doi:10.1111/mila.12029.

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