Talking about trees

1997

In this paper we introduce a modal language L T for imposing constraints on trees, and an extension LT(L r) for imposing constraints on trees decorated with feature structures. The motivation for introducing these languages is to provide tools for formalising grammatical frameworks perspicuously, and the paper illustrates this by showing how the leading ideas of GPS6 can be captured in LT(LF). In addition, the role of modal languages (and in particular, what we have called layered modal languages) as constraint formalisms for linguistic theorising is discussed in some detail.

1994

Abstract A modal logic is developed to deal with finite ordered binary trees a they are used in (computational) linguistics. A modal language is introduced with operators for the 'mother of','first daughter of'and 'second daughter of'relations together with their transitive reflexive closures. The relevant class of tree models is defined and three linguistic applications of this language are discussed: context free grammars, command relations, and trees decorated with feature structures.

Journal of Logic, Language and Information, 2008

While monadic second-order logic (MSO) has played a prominent role in model theoretic syntax, modal logics have been used in this context since its inception. When comparing propositional dynamic logic (PDL) to MSO over trees, Kracht (1997) noted that there are tree languages that can be defined in MSO that can only be defined in PDL by adding new features whose distribution is predictable. He named such features "inessential features". We show that Kracht's observation can be extended to other modal logics of trees in two ways. First, we demonstrate that for each stronger modal logic, there exists a tree language that can only be defined in a weaker modal logic with inessential features. Second, we show that any tree language that can be defined in a stronger modal logic, but not in some weaker modal logic, can be defined with inessential features. Additionally, we consider Kracht's definition of inessential features more closely. It turns out that there are features whose distribution can be predicted, but who fail to be inessential in Kracht's sense. We will look at ways to modify his definition.

Lecture Notes in Computer Science, 2005

This paper presents the basis of Property Grammars, a fully constraintbased theory. In this approach, all kinds of linguistic information is represented by means of constraints. The constraint system constitutes then the core of the theory: it is the grammar, but it also constitutes, after evaluation for a given input, its description. Property Grammars is then a non-generative theory in the sense that no structure has to be build, only constraints are used both to represent linguistic information and to describe inputs. This paper describes the basic notions used in PG and proposes an account of long-distance dependencies, illustrating the expressive power of the formalism.

1985

Lechner (2006) presents an analysis of the scopal interaction of English epistemic modal verbs with negated strong quantifiers in the framework of Transparent Logical Form, which constructs semantic representations as extensions of syntax trees. Noting conceptual and empirical shortcomings of this approach, we propose an analysis in Lexical Resource Semantics, a constraint-based semantics framework embedded in Head-driven Phrase Structure Grammar. Our analysis treats the original English data as well as semantically parallel constructions in German, although the syntax of the German constructions is substantively different from English. The LRS framework views syntax and semantics as independent modules connected by a complex interface employing modern underspecification techniques. It permits a surfaceoriented syntactic analysis without a multitude of additional empty categories, which has clear advantages for the application of efficient parsing algorithms. At the same time, the LRS analysis elegantly captures crosslinguistic generalizations about the semantic phenomenon under investigation.

2008

2001

1997

Natasha Kurtonina and Michael Moortgat abstract. In this paper we study Lambek systems as grammar logics: logics for reasoning about structured linguistic resources. The structural parameters of precedence, dominance and dependency generate a cube of resource-sensitive categorial type logics. From the pure logic of residuation NL, one obtains L, NLP and LP in terms of Associativity, Commutativity, and their combination.