The Relation Between Derivations and Syntactical Structures in Phrase-Structure Grammars

It is well known that, for context-free grammars, a leftmost derivation of a sentence univocally defines its syntactical tree; the construction of this tree consists of an iterative procedure during which two successive strings in the leftmost derivation are compared (see, e.g., [1, 2]). These -o r similar--properties do not hold for leftmost derivations in general phrase-structure grammars [3-5] nor for (not necessarily leftmost) derivations in context-free grammars (see, e.g., [6, 7]). In this paper conditions for a general phrase-structure grammar are established under which each of its derivations univocally defines a syntactical structure (Sections 2-5). The simplifications for context-sensitive and context-free grammars are indicated in Sections 6 and 7. The case of leftmost derivations is discussed briefly in Section 8.