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

Restricting the Weak-Generative Capacity of Synchronous Tree-Adjoining Grammars

The formalism of synchronous tree-adjoining grammars, a variant of standard tree-adjoining grammars (TAG), was intended to allow the use of TAGs for language transduction in addition to language specification. In previous work, the definition of the transduction relation defined by a synchronous TAG was given by appeal to an iterative rewriting process. The rewriting definition of derivation is problematic in that it greatly extends the expressivity of the formalism and makes the design of parsing algorithms difficult if not impossible. We introduce a simple, natural definition of synchronous tree-adjoining derivation, based on isomorphisms between standard tree-adjoining derivations, that avoids the expressivity and implementability problems of the original rewriting definition. The decrease in expressivity, which would otherwise make the method unusable, is offset by the incorporation of an alternative definition of standard tree-adjoining derivation, previously proposed for completely separate reasons, thereby making it practical to entertain using the natural definition of synchronous derivation. Nonetheless, some remaining problematic cases call for yet more flexibility in the definition; the isomorphism requirement may have to be relaxed. It remains for future research to tune the exact requirements on the allowable mappings.Comment: 21 pages, uses lingmacros.sty, psfig.sty, fullname.sty; minor typographical changes onl

Synchronous tree-adjoining grammars

The unique properties of tree-adjoining grammars (TAG) present a challenge for the application of TAGs beyond the limited confines of syntax, for instance, to the task of semantic interpretation or automatic translation of natural language. We present a variant of TAGs, called synchronous TAGs, which characterize correspondences between languages. The formalism's intended usage is to relate expressions of natural languages to their associated semantics represented in a logical form language, or to their translates in another natural language; in summary, we intend it to allow TAGs to be used beyond their role in syntax proper. We discuss the application of synchronous TAGs to concrete examples, mentioning primarily in passing some computational issues that arise in its interpretationEngineering and Applied Science

Generation and synchronous tree-adjoining grammars

Tree-adjoining grammars (TAG) have been proposed as a formalism for generation based on the intuition that the extended domain of syntactic locality that TAGs provide should aid in localizing semantic dependencies as well, in turn serving as an aid to generation from semantic representations. We demonstrate that this intuition can be made concrete by using the formalism of synchronous tree-adjoining grammars. The use of synchronous TAGs for generation provides solutions to several problems with previous approaches to TAG generation. Furthermore, the semantic monotonicity requirement previously advocated for generation grammars as a computational aid is seen to be an inherent property of synchronous TAGs.Engineering and Applied Science

Multiple Context-Free Tree Grammars: Lexicalization and Characterization

Multiple (simple) context-free tree grammars are investigated, where "simple" means "linear and nondeleting". Every multiple context-free tree grammar that is finitely ambiguous can be lexicalized; i.e., it can be transformed into an equivalent one (generating the same tree language) in which each rule of the grammar contains a lexical symbol. Due to this transformation, the rank of the nonterminals increases at most by 1, and the multiplicity (or fan-out) of the grammar increases at most by the maximal rank of the lexical symbols; in particular, the multiplicity does not increase when all lexical symbols have rank 0. Multiple context-free tree grammars have the same tree generating power as multi-component tree adjoining grammars (provided the latter can use a root-marker). Moreover, every multi-component tree adjoining grammar that is finitely ambiguous can be lexicalized. Multiple context-free tree grammars have the same string generating power as multiple context-free (string) grammars and polynomial time parsing algorithms. A tree language can be generated by a multiple context-free tree grammar if and only if it is the image of a regular tree language under a deterministic finite-copying macro tree transducer. Multiple context-free tree grammars can be used as a synchronous translation device.Comment: 78 pages, 13 figure

Restricting the weak-generative capacity of synchronous tree-adjoining grammars

The formalism of synchronous tree-adjoining grammars, a variant of standard tree-adjoining grammars (TAG), was intended to allow the use of TAGs for language transduction in addition to language specification. In previous work, the definition of the transduction relation defined by a synchronous TAG was given by appeal to an iterative rewriting process. The rewriting definition of derivation is problematic in that it greatly extends the expressivity of the formalism and makes the design of parsing algorithms difficult if not impossible. We introduce a simple, natural definition of synchronous tree-adjoining derivation, based on isomorphisms between standard tree-adjoining derivations, that avoids the expressivity and implementability problems of the original rewriting definition. The decrease in expressivity, which would otherwise make the method unusable, is offset by the incorporation of an alternative definition of standard tree-adjoining derivation, previously proposed for completely separate reasons, thereby making it practical to entertain using the natural definition of synchronous derivation. Nonetheless, some remaining problematic cases call for yel more flexibility in the definition; the isomorphism requirement may have to be relaxed. It remains for future research to rune the exact requirements on the allowable mappings.Engineering and Applied Science

Korean Grammar Using TAGs

This paper addresses various issues related to representing the Korean language using Tree Adjoining Grammars. Topics covered include Korean grammar using TAGs, Machine Translation between Korean and English using Synchronous Tree Adjoining Grammars (STAGs), handling scrambling using Multi Component TAGs (MC-TAGs), and recovering empty arguments. The data for the parsing is from US military communication messages

Bimorphisms and synchronous grammars

We tend to think of the study of language as proceeding by characterizing the strings and structures of a language, and we think of natural language processing as using those structures to build systems of utility in manipulating the language. But many language-related problems are more fruitfully viewed as requiring the specification of a relation between two languages, rather than the specification of a single language. We provide a synthesis and extension of work that unifies two approaches to such language relations: the automata-theoretic approach based on tree transducers that transform trees to their counterparts in the relation, and the grammatical approach based on synchronous grammars that derive pairs of trees in the relation. In particular, we characterize synchronous tree-substitution grammars and synchronous tree-adjoining grammars in terms of bimorphisms, which have previously been used to characterize tree transducers. In the process, we provide new approaches to formalizing the various concepts: a metanotation for describing varieties of tree automata and transducers in equational terms; a rigorous formalization of tree-adjoining and tree-substitution grammars and their synchronous counterparts, using trees over ranked alphabets; and generalizations of tree-adjoining grammar allowing multiple adjunction.Engineering and Applied Science

Synchronous grammars as tree transducers

Tree transducer formalisms were developed in the formal language theory community as generalizations of finite-state transducers from strings to trees. Independently, synchronous tree-substitution and -adjoining grammars arose in the computational linguistics community as a means to augment strictly syntactic formalisms to provide for parallel semantics. We present the first synthesis of these two independently developed approaches to specifying tree relations, unifying their respective literatures for the first time, by using the framework of bimorphisms as the generalizing formalism in which all can be embedded. The central result is that synchronous tree-substitution grammars are equivalent to bimorphisms where the component homomorphisms are linear and complete.Engineering and Applied Science

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