Factoring Predicate Argument and Scope Semantics : underspecified Semantics with LTAG

In this paper we propose a compositional semantics for lexicalized tree-adjoining grammar (LTAG). Tree-local multicomponent derivations allow separation of the semantic contribution of a lexical item into one component contributing to the predicate argument structure and a second component contributing to scope semantics. Based on this idea a syntax-semantics interface is presented where the compositional semantics depends only on the derivation structure. It is shown that the derivation structure (and indirectly the locality of derivations) allows an appropriate amount of underspecification. This is illustrated by investigating underspecified representations for quantifier scope ambiguities and related phenomena such as adjunct scope and island constraints

A note on the strong and weak generative powers of formal systems

AbstractThis paper is a note on some relationships between the strong and weak generative powers of formal systems, in particular, from the point of view of squeezing more strong power out of a formal system without increasing its weak generative power. We will comment on some old and new results from this perspective. Our main goal of this note is to comment on the strong generative power of context-free grammars, lexicalized tree-adjoining grammars (and some of their variants) and Lambek grammars, especially in the context of crossing dependencies, in view of the recent work of Tiede (Ph.D. Dissertation, Indiana University, Bloomington, 1999)

Lexicalized non-local MCTAG with dominance links is NP-complete

An NP-hardness proof for non-local Multicomponent Tree Adjoining Grammar (MCTAG) by Rambow and Satta (1st International Workshop on Tree Adjoining Grammers 1992), based on Dahlhaus and Warmuth (in J Comput Syst Sci 33:456–472, 1986), is extended to some linguistically relevant restrictions of that formalism. It is found that there are NP-hard grammars among non-local MCTAGs even if any or all of the following restrictions are imposed: (i) lexicalization: every tree in the grammar contains a terminal; (ii) dominance links: every tree set contains at most two trees, and in every such tree set, there is a link between the foot node of one tree and the root node of the other tree, indicating that the former node must dominate the latter in the derived tree. This is the version of MCTAG proposed in Becker et al. (Proceedings of the 5th conference of the European chapter of the Association for Computational Linguistics 1991) to account for German long-distance scrambling. This result restricts the field of possible candidates for an extension of Tree Adjoining Grammar that would be both mildly context-sensitive and linguistically adequate

Tree-local MCTAG with shared nodes : an analysis of word order variation in German and Korean

Tree Adjoining Grammars (TAG) are known not to be powerful enough to deal with scrambling in free word order languages. The TAG-variants proposed so far in order to account for scrambling are not entirely satisfying. Therefore, an alternative extension of TAG is introduced based on the notion of node sharing. Considering data from German and Korean, it is shown that this TAG-extension can adequately analyse scrambling data, also in combination with extraposition and topicalization.Les Grammaires dArbres Adjoints (TAG) sont connues pour ne pas etre assez puissantes pour traiter le brouillage darguments dans des langues à ordre desmots libre. Les variantes TAG proposées jusqu´à maintenant pour expliquer le brouillage ne sont pas entièrement satisfaisantes. Nous présentons ici une extension alternative de TAG, basée sur la notion du partage de noeuds. En considerant des données de lallemand et du coréen, on montre que cette extension de TAG peut en juste proportion analyser des données de brouillage d’arguments, également en combinaison avec lextraposition et la topicalisation

Mild context-sensitivity and tuple-based generalizations of context-free grammar

This paper classifies a family of grammar formalisms that extend context-free grammar by talking about tuples of terminal strings, rather than independently combining single terminal words into larger single phrases. These include a number of well-known formalisms, such as head grammar and linear context-free rewriting systems, but also a new formalism, (simple) literal movement grammar, which strictly extends the previously known formalisms, while preserving polynomial time recognizability. The descriptive capacity of simple literal movement grammars is illustrated both formally through a weak generative capacity argument and in a more practical sense by the description of conjunctive cross-serial relative clauses in Dutch. After sketching a complexity result and drawing a number of conclusions from the illustrations, it is then suggested that the notion of mild context-sensitivity currently in use, that depends on the rather loosely defined concept of constant growth, needs a modification to apply sensibly to the illustrated facts; an attempt at such a revision is proposed

An Alternative Conception of Tree-Adjoining Derivation

The precise formulation of derivation for tree-adjoining grammars has important ramifications for a wide variety of uses of the formalism, from syntactic analysis to semantic interpretation and statistical language modeling. We argue that the definition of tree-adjoining derivation must be reformulated in order to manifest the proper linguistic dependencies in derivations. The particular proposal is both precisely characterizable through a definition of TAG derivations as equivalence classes of ordered derivation trees, and computationally operational, by virtue of a compilation to linear indexed grammars together with an efficient algorithm for recognition and parsing according to the compiled grammar.Comment: 33 page

Unifying synchronous tree-adjoining grammars and tree transducers via bimorphisms.

We place synchronous tree-adjoining grammars and tree transducers in the single overarching framework of bimorphisms, continuing the unification of synchronous grammars and tree transducers initiated by Shieber (2004). Along the way, we present a new definition of the tree-adjoining grammar derivation relation based on a novel direct inter-reduction of TAG and monadic macro tree transducers.Engineering and Applied Science

Tree-Adjoining Grammars and Lexicalized Grammars

In this paper, we will describe a tree generating system called tree-adjoining grammar(TAG)and state some of the recent results about TAGs. The work on TAGS is motivated by linguistic considerations. However, a number of formal results have been established for TAGs, which we believe, would be of interest to researchers in tree grammars and tree automata. After giving a short introduction to TAG, we briefly state these results concerning both the properties of the string sets and tree sets (Section 2). We will also describe the notion of lexicalization of grammars (Section 3) and investigate the relationship of lexicalization to context-free grammars (CFGs) and TAGS (Section 4)