Model-theoretic grammar
{{distinguish|Constraint grammar}}
{{Linguistics|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.{{cite book |last1=Pullum |first1=Geoffrey Keith |author-link1=Geoffrey K. Pullum |last2=Scholz |first2=Barbara C.
|editor-last1=de Groote |editor-first1=Philippe |editor-last2=Morrill |editor-first2=Glyn |editor-last3=Retor |editor-first3=Christian
|title=Logical Aspects of Computational Linguistics: 4th International Conference |publisher=Springer Verlag |date=2001 |pages=17–43 |chapter=On the distinction between generative-enumerative and model-theoretic syntactic frameworks |chapter-url=http://ling.ed.ac.uk/~gpullum/bcscholz/Distinction.pdf}} 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.{{cite book |last=Pullum |first=Geoffrey Keith |author-link=Geoffrey K. Pullum |editor-last1=Rogers |editor-first1=James |editor-last2=Kepser |editor-first2=Stephan |title=Model-theoretic syntax at 10 – Proceedings of the ESSLLI2007 MTS@10Workshop |publisher=Trinity College Dublin |date=2007 |pages=1–10 |chapter=The evolution of model-theoretic frameworks in linguistics |chapter-url=http://ling.ed.ac.uk/~gpullum/Dublin.pdf}} 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.{{Cite book |last=Johnson |first=David E |url= |title=Arc Pair Grammar |last2=Postal |first2=Paul M |publisher=Princeton University Press |year=1980 |isbn=978-1-4008-5555-1 |oclc= |author-link=David E. Johnson |author-link2=Paul M. Postal}}
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
- 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)
- Lexical functional grammar (LFG) in the formalization of Ronald Kaplan (1995)
- Head-driven phrase structure grammar (HPSG) in the formalization of King (1999){{cite book|last1=Müller|first1=Stefan|title=Grammatical theory: From transformational grammar to constraint-based approaches|date=2016|publisher=Language Science Press|location=Berlin|pages=490–491|url=http://www.oapen.org/download?type=document&docid=611693}}
- Constraint Handling Rules (CHR) grammarsChristiansen, Henning. "[http://dtai.cs.kuleuven.be/projects/CHR/papers/chr2004/christ_grammars_mult_stores_chr04.pdf CHR Grammars with multiple constraint stores]." First Workshop on Constraint Handling Rules: Selected Contributions. Universität Ulm, Fakultät für Informatik, 2004.
- The implicit model underlying The Cambridge Grammar of the English Language{{Cite journal |last1=Pullum |first1=Geoffrey K. |author-link=Geoffrey K. Pullum |last2=Rogers |first2=James |date=2008 |title=Expressive power of the syntactic theory implicit in the Cambridge Grammar of the English Language |url=http://www.lel.ed.ac.uk/~gpullum/EssexLAGB.pdf |journal=Annual Meeting of the Linguistics Association of Great Britain |pages=1–16}}
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."{{Cite journal|last=Pullum|first=Geoffrey K.|date=2013|title=The Central Question in Comparative Syntactic Metatheory|journal=Mind & Language|language=en|volume=28|issue=4|pages=492–521|doi=10.1111/mila.12029}}
References
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{{Mathematical logic}}
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