Model-theoretic grammar

Part of a series on
Linguistics
Outline History Index
General linguistics Diachronic Lexicography Morphology Phonology Pragmatics Semantics Syntax Syntax–semantics interface Typology
Applied linguistics Acquisition Anthropological Applied Mathematical Computational Conversation analysis Corpus linguistics Discourse analysis Determinism Distance Documentation Ethnography of communication Ethnomethodology Forensic History of linguistics Interlinguistics Neurolinguistics Philology Philosophy of language Phonetics Psycholinguistics Sociolinguistics Text Translating and interpreting Writing systems
Theoretical frameworks Formalist Constituency Dependency Distributionalism Generative Glossematics Functional Cognitive Construction grammar Functional discourse grammar Grammaticalization Interactional linguistics Prague circle Systemic functional Usage-based Structuralism
Topics Autonomy of syntax Compositionality Conservative and innovative language Descriptivism Etymology Iconicity Internationalism Internet linguistics LGBTQ linguistics Origin of language Orismology Orthography Philosophy of linguistics Prescriptivism Second-language acquisition Theory of language Terminology
Portal
v t e

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. 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 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.

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

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)
• Constraint Handling Rules (CHR) grammars
• The implicit model underlying The Cambridge Grammar of the English Language

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."