Tree-adjoining grammar

About: Tree-adjoining grammar is a research topic. Over the lifetime, 2491 publications have been published within this topic receiving 57813 citations.

On the Generative Power of Multiple Context-Free Grammars and Macro Grammars

Abstract: Several grammars of which generative power is between context-free grammar and context-sensitive grammar were proposed. Among them are macro grammar and tree adjoining grammar. Multiple context-free grammar is also a natural extension of context-free grammars, and is known to be stronger in its generative power than tree adjoining grammar and yet to be recognizable in polynomial time. In this paper, the generative power of several subclasses of variable-linear macro grammars and that of multiple context-free grammars are compared in details.

A Cubic Time Extension of Context-Free Grammars

Abstract: Context-free grammars and cubic parse time are so related in people's minds that they often think that parsing any extension of context-free grammars must need some extra time. Of course, this is not necessarily true and this paper presents a generalization of context-free grammars which nonetheless still has a cubic parse time complexity. This extension, which defines a subclass of context-sensitive languages, has both a theoretical and a practical interest. The class of languages defined by these grammars is closed under both intersection and complement (in fact this class contains both the intersection and the complement of context-free languages). Moreover, these languages belong to an extension of mildly context-sensitive languages in which the constant growth property is relaxed and which can thus potentially be used in natural language processing.

Deductive systems and grammars: proofs as grammatical structures

Abstract: During the last fifteen years, much of the research of proof theoretical grammars has been focused on their weak generative capacity. This research culminated in Pentus’ theorem, which showed that Lambek grammars generate precisely the context-free languages. However, during the same period of time, research on other grammar formalisms has stressed the importance of “strong generative capacity,” i.e. the derivation or phrase structure trees that grammars assign to strings. The first topic of this thesis is the strong generative capacity of Lambek grammars. The proof theoretic perspective on grammars allows us to consider different notions of what “structure assigned by a Lambek grammar to a string” is taken to mean. For example, we can take any proof tree that establishes that a grammar generates a certain string or only those that are in some normal form. It can be shown that the formal properties of these notions of structure differ. The main result of this part of the thesis is that, although Lambek grammars generate context-free string languages, their derivation trees are more complex than those of context-free grammars. The latter were characterized by Thatcher as coinciding with the local tree languages, while the derivation trees of Lambek grammars include tree languages which are not regular. Even non-associative Lambek grammars, which recently have become more popular variants of categorial grammar, can be used to generate non-local tree languages. However, their normal form tree languages are always regular. Finally, categorial grammars lacking introduction rules have local derivation trees. Thus, there is a genuine hierarchy of proof theoretical grammars with respect to strong generative capacity. Additionally, we consider the semantic aspect of the proof theoretic approach to language, which is given by the correspondence between proof theory and type