A hierarchy of local TDGs

Many recent variants of Tree Adoining Grammars (TAG) allow an underspecifiaction of the parent relation between nodes in a tree, i.e. they do not deal with fully specified trees as it is the case with TAGs.Such TAG variants are for example Description Tree Grammars (DTG), Unordered Vector Grammars with Dominance Links (UVG-DL), a definition of TAGs via so-called quasi trees and Tree Description Grammars (TDG. The last TAg variant, local TDG, is an extension of TAG generating Tree Descriptions. Local TDGs even allow an underspecification of the dominance relation between node names and thereby provide the possibility to generate underspecified representations for structural ambiguities such as quantifier scope ambiguities. This abstract deals with formal properties of local TDGs. A hierarchiy of local TDGs is established together with a pumping lemma for local TDGs of a certain rank

Tree Description Grammars and Underspecified Representations

In this thesis, a new grammar formalism called (local) Tree Description Grammar (TDG) is presented that generates tree descriptions. This grammar formalism brings together some of the central ideas in the context of Tree Adjoining Grammars (TAG) on the one hand, and approaches to underspecified semantics for scope ambiguities on the other hand. First a general definition of TDGs is presented, and afterwards a restricted variant called local TDGs is proposed. Since the elements of a local TDG are tree descriptions, an extended domain of locality as in TAGs is provided by this formalism. Consequently, local TDGs can be lexicalized, and local dependencies such as filler gap dependencies can be expressed in the descriptions occurring in the grammar. The tree descriptions generated by local TDGs are such that the dominance relation (i.e. the reflexive and transitive closure of the parent relation) need not be fully specified. Therefore the generation of suitable underspecified representations for scope ambiguities is possible. The generative capacity of local TDGs is greater than the one of TAGs. Local TDGs are even more powerful than set-local multicomponent TAGs (MC-TAG). However, the generative capacity of local TDGs is restricted in such a way that only semilinear languages are generated. Therefore these languages are of constant growth, a property generally ascribed to natural languages. Local TDGs of different rank can be distinguished depending on the form of derivation steps that are possible in these grammars. This leads to a hierarchy of local TDGs. For the string languages generated by local TDGs of a certain rank, a pumping lemma is proven that allows to show that local TDGs of rank n can generate a language Li := {a1k···a1k|k ≥ 0} iff i ≤ 2n holds. In order to describe the relation between two languages, synchronous local TDGs are introduced. The synchronization with a second local TDG does not increase the generative power of the grammar in the sense that each language generated by a local TDG that is part of a synchronous pair of local TDGs, also can be generated by a single local TDG. This formalism of synchronous local TDGs is used to describe a syntax-semantics interface for a fragment of French which illustrates the derivation of underspecified representations for scope ambiguities with local TDGs

Tree description grammars and underspecified representations

In dieser Dissertation wird ein neuer Grammatikformalismus zur Erzeugung von Baumbeschreibungen entwickelt, sogenannte (lokale) Tree Description Grammars (TDG). TDGs verbinden einige der zentrale Ideen im Zusammenhang mit Tree Adjoining Grammars (TAG) mit Ansätzen zur unterspezifizierten Semantik, speziell der Behandlung von Skopusambiguitäten. Zunächst werden allgemeine TDGs definiert, und dann wird eine eingeschränkte Variante, lokale TDGs eingeführt. Da die Elemente der Grammatik Baumbeschreibungen sind, erlaubt der Formalismus, genau wie TAG, größere lokale Bereiche. In den von (lokalen) TDGs generierten Baumbeschreibungen muss die Dominanz zwischen den Knoten (reflexive transitive Hülle der Mutter-Tochter Beziehung) nicht vollständig beschrieben sein. Dies ermöglicht die Ableitung geeigneter unterspezifizierte Repräsentationen für Skopusambiguitäten. Lokale TDGs sind mächtiger als TAGs, sogar mächtiger als mengen-lokale Multicomponent TAGs. Allerdings erzeugen lokale TDGs nur semilineare Sprachen, also Sprachen mit konstantem Kettenwachstum, eine Eigenschaft, die für natürliche Sprachen i.a. angenommen wird. Abhängig von der Form der möglichen Ableitungsschritte werden lokale TDGs verschiedenen Rangs unterschieden. Es ergibt sich eine Hierarchie, für deren einzelne Klassen ein Iterationslemma gezeigt wird. Um die Beziehung zwischen zwei Sprachen zu beschreiben, werden synchrone lokale TDGs eingeführt. Die Synchronisation mit einer zweiten lokalen TDG beeinflusst nicht die Ausdrucksstärke der Grammatik. Als Anwendungsbeispiel werden synchrone lokale TDGs zur Beschreibung einer Syntax-Semantik Schnittstelle für ein Fragment des Französischen eingesetzt. An diesem Beispiel wird die Ableitung von unterspezifizierten Repräsentationen für Skopusambiguitäten illustriert. Es zeigt sich, dass sich in dieser Architektur Inselbeschränkungen für Quantorenskopus als natürliche Folge der Lokalität der Grammatiken ergebenIn this thesis, a new grammar formalism called (local) Tree Description Grammar (TDG) is presented that generates tree descriptions. This formalism brings together some of the central ideas in the context of Tree Adjoining Grammars (TAG) on the one hand, and approaches to underspecified semantics for scope ambiguities on the other hand. First a general definition of TDGs is presented, and then a restricted variant called local TDGs is proposed. Since the elements of local TDGs are tree descriptions, an extended domain of locality as in TAGs is provided by this formalism. The tree descriptions generated by local TDGs are such that the dominance relation between nodes (reflexive transitive closure of the parent relation) need not be fully specified. This allows the generation of suitable underspecified representations for scope ambiguities. Local TDGs are more powerful than TAGs and even more powerful than set-local multicomponent TAGs. However, local TDGs generate only semilinear languages, i.e. languages of constant growth, a property generally ascribed to natural languages. Local TDGs of different rank can be distinguished depending on the derivation steps possible in these grammars. This leads to a hierarchy of local TDGs. For the classes of this hierarchy, a pumping lemma is proven. In order to describe the relation between two languages, synchronous local TDGs are introduced. The synchronization with a second local TDG does not increase the generative power of the grammar, i.e. a language generated by a local TDG that is part of a synchronous pair of local TDGs, also can be generated by a single local TDG. This formalism of synchronous local TDGs is used to describe a syntax-semantics interface for a fragment of French which illustrates the derivation of underspecified representations for scope ambiguities. In this framework, island constraints for quantifier scope ambiguities arise as a natural consequence of the localit