Model-theoretic grammars, also known as constraint-based grammars, contrast with

generative grammar Generative grammar is a research tradition in linguistics that aims to explain the cognitive basis of language by formulating and testing explicit models of humans' subconscious grammatical knowledge. Generative linguists, or generativists (), ...

s in the way they define sets of sentences: they state constraints on syntactic structure rather than providing operations for generating syntactic objects. 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. The approach applies the mathematical techniques of

model theory In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mat ...

to the task of syntactic description: a grammar is a

theory A theory is a systematic and rational form of abstract thinking about a phenomenon, or the conclusions derived from such thinking. It involves contemplative and logical reasoning, often supported by processes such as observation, experimentation, ...

in the logician's sense (a consistent set of statements) and the well-formed structures are the

models A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin , . Models can be divided int ...

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''.

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 George Philip Lakoff ( ; born May 24, 1941) is an American cognitive linguist and philosopher, best known for his thesis that people's lives are significantly influenced by the conceptual metaphors they use to explain complex phenomena. The ...

, 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 Ronald M. Kaplan (born 1946) has served as a vice president at Amazon.com and chief scientist for Amazon Search ( A9.com). He was previously vice president and distinguished scientist at Nuance Communications and director of Nuance' Natural La ...

(1995) * Head-driven phrase structure grammar (HPSG) in the formalization of King (1999) * Constraint Handling Rules (CHR) grammars * The implicit model underlying ''

The Cambridge Grammar of the English Language ''The Cambridge Grammar of the English Language'' (''CamGEL''The abbreviation ''CamGEL'' is less commonly used for the work than is ''CGEL'' (and the authors themselves use ''CGEL'' in their other works), but ''CGEL'' is ambiguous because it has ...

Strengths

One benefit of model-theoretic grammars over generative grammars is that they allow for gradience in

grammaticality In linguistics, grammaticality is determined by the conformity to language usage as derived by the grammar of a particular speech variety. The notion of grammaticality rose alongside the theory of generative grammar, the goal of which is to formu ...

. 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."

References

{{Authority control Grammar Grammar frameworks Mathematical logic Model theory