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

generative grammar Generative grammar, or generativism , is a linguistic theory that regards linguistics as the study of a hypothesised innate grammatical structure. It is a biological or biologistic modification of earlier structuralist theories of linguisti ...

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 (math ...

to the task of syntactic description: a grammar is a

theory A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may ...

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 ''modulus'', a measure. Models c ...

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 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 con ...

, 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) * Constraint Handling Rules (CHR) grammars

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."

References

Grammar Grammar frameworks Mathematical logic Model theory {{grammar-stub