Linear Grammars with Labels (original) (raw)

Journal of Language Modelling

In this article we make remarks on overt and covert movement inlogical grammar. With respect to the latter (e.g. quantification) weobserve how a treatment in terms of displacement calculus interactswith normal modalities for intensionality to allow a coding in logicalgrammar of the distinction between weak and strong quantifiers(i.e. those that may or may not not scope nonlocally such as'a' and 'every' respectively). With respect to overt movement (e.g.relativisation) we observe how displacement calculus supportsa coding of a filler-gap dependency similar to that employed in lambdagrammars, but we argue that this general approach does not extend toparasitic gaps, for which we propose exponentials.

Categorial Minimalist Grammar: From Generative Syntax To Logical Form

2010

From the early days of the minimalist program of Chomsky (1993), a convergence with categorial grammars was noticed by Epstein and Berwick (1995). The striking similarity lies in the merge operation, which looks like the application rule of the AB grammars. In both cases, word order is a consequence of the consumption rules but in categorial grammars being the head of a compound expression also derives from the categories while in a minimalist setting it can be defined independently from the resource consumption. The ...

Linear logic-based semantics construction for LTAG

2001

In this paper we review existing appoaches to semantics construction in LTAG (Lexicalised Tree Adjoining Grammar) which are all based on the notion of derivation (tree)s. We argue that derivation structures in LTAG are not appropriate to guide semantic composition, due to a non-isomorphism, in LTAG, between the syntactic operation of adjunction on the one hand, and the semantic operations of complementation and modification, on the other. Linear Logic based "glue" semantics, by now the classical approach to semantics construction within the LFG framework (cf. Dalrymple (1999)) allows for flexible coupling of syntactic and semantic structure. We investigate application of "glue semantics" to LTAG syntax, using as underlying structure the derived tree, which is more appropriate for principle-based semantics construction. We show how linear logic semantics construction helps to bridge the nonisomorphism between syntactic and semantic operations in LTAG. The glue approach allows to capture non-tree local dependencies in control and modification structures, and extends to the treatment of scope ambiguity with quantified NPs and VP adverbials. Finally, glue semantics applies successfully to the adjunction-based analysis of long-distance dependencies in LTAG, which differs significantly from the f-structure based analysis in LFG. * We are grateful for valuable comments from the audiences of the LFG'01 conference and the University of Konstanz, in particular Ron Kaplan, Josef Bayer and Ellen Brandner. Thanks go also to Dick Crouch and Mary Dalrymple for comments on earlier versions of this paper. Some interesting observations could not be given full justice in this paper, but gave important feedback for the overall conception of this work, which we hope to extend in future research. This research was partially funded by a BMBF grant to the DFKI project whiteboard (FKZ: 01 IW 002). 1 Hepple (1999) sketches LL-based semantics for D-Trees, to overcome problems faced by categorial semantics in the analysis of quantification. Muskens (2001) develops a description-based syntax-semantics interface for LTAG, yet with extension to tree descriptions as used in D-Trees. We briefly discuss these related approaches in Section 4.7.

The logic of categorial grammars: a deductive account of natural language syntax and semantics

This book is a contemporary and comprehensive introduction to categorial grammars in the logical tradition initiated by the work of Lambek. It guides students and researchers through the fundamental results in the field, providing modern proofs of many classic theorems, as well as original recent advances. Numerous examples and exercises illustrate the motivations and applications of these results from a linguistic, computational and logical point of view. The Lambek calculus and its variants, and the corresponding grammars, are at the heart of these lecture notes. A chapter is devoted to a key feature of these categorial grammars: their very elegant syntax-semantic interface. In addition, we adapt linear logic proof nets to these calculi since they provide efficient parsing algorithms as exemplified in the Grail parser. This book shows how categorial grammars weave together converging ideas from formal linguistics, typed lambda calculus, Montague semantics, proof theory and linear logic, thus yielding a coherent and formally elegant framework for natural language syntax and semantics.

GlueTag-Linear Logic based Semantics Construction for LTAG-and what it teaches us about the relation between LFG and LTAG

2001

Minimalist Grammars and Minimalist Categorial Grammars, definitions toward inclusion of generated languages

2011

Stabler proposes an implementation of the Chomskyan Minimalist Program, [1] with Minimalist Grammars-MG, [2]. This framework inherits a long linguistic tradition. But the semantic calculus is more easily added if one uses the Curry-Howard isomorphism. Minimalist Categorial Grammars-MCG, based on an extension of the Lambek calculus, the mixed logic, were introduced to provide a theoreticallymotivated syntax-semantics interface, [3]. In this article, we give full definitions of MG with algebraic tree descriptions and of MCG, and take the first steps towards giving a proof of inclusion of their generated languages. The Minimalist Program-MP, introduced by Chomsky, [1], unified more than fifty years of linguistic research in a theoretical way. MP postulates that a logical form and a sound could be derived from syntactic relations. Stabler, [2], proposes a framework for this program in a computational perspective with Minimalist Grammars-MG. These grammars inherit a long tradition of generative linguistics. The most interesting contribution of these grammars is certainly that the derivation system is defined with only two rules: merge and move. The word Minimalist is introduced in this perspective of simplicity of the definitions of the framework. If the merge rule seems to be classic for this kind of treatment, the second rule, move, accounts for the main concepts of this theory and makes it possible to modify relations between elements in the derived structure. Even if the phonological calculus is already defined, the logical one is more complex to express. Recently, solutions were explored that exploited Curry's distinction between tectogrammatical and phenogrammatical levels; for example, Lambda Grammars, [4], Abstract Categorial Grammars, [5], and Convergent Grammars [6]. First steps for a convergence between the Generative Theory and Categorial Grammars are due to S. Epstein, [7]. A full volume of Language and Computation proposes several articles in this perspective, [8], in particular [9], and Cornell's works on links between Lambek calculus and Transformational Grammars, [10]. Formulations of Minimalist Grammars in a Type-Theoretic way have also been proposed in [11], [12], [13]. These frameworks were evolved in [14], [3], [15] for the syntax-semantics interface. Defining a syntax-semantics interface is complex. In his works, Stabler proposes to include this treatment directly in MG. But interactions between syntax

Linear Grammars with Labels (original) (raw)

Related papers