A number of representational phrase structure theories of grammar never acknowledged phrase structure rules, but have pursued instead an understanding of sentence structure in terms the notion of schema. Here phrase structures are not derived from rules that combine words, but from the specification or instantiation of syntactic schemata or configurations, often expressing some kind of semantic content independently of the specific words that appear in them. This approach is essentially equivalent to a system of phrase structure rules combined with a noncompositional semantic theory, since grammatical formalisms based on rewriting rules are generally equivalent in power to those based on substitution into schemata.
So in this type of approach, instead of being derived from the application of a number of phrase structure rules, the sentence Colorless green ideas sleep furiously would be generated by filling the words into the slots of a schema having the following structure:
- VP AP]
And which would express the following conceptual content:
- X DOES Y IN THE MANNER OF Z
Though they are noncompositional, such models are monotonic. This approach is highly developed within Construction grammar and has had some influence in Head-Driven Phrase Structure Grammar and Lexical Functional Grammar, the latter two clearly qualifying as phrase structure grammars.
Read more about this topic: Phrase Structure Rules, Alternative Approaches
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