This paper describes a new formalization of Lexical-Functional Grammar called R-LFG (where the "R" stands for "Resource-based"). The formal details of R-LFG are presented in Johnson (1997); the present work concentrates on motivating R-LFG and explaining to linguists how it differs from the "classical" LFG framework presented in Kaplan and Bresnan (1982). This work is largely a reaction to the linear logic semantics for LFG developed by Dalrymple and colleagues (Dalrymple et al., 1995, 1996a,b,c). As explained below, it seems to me that their "glue language" approach bears a partial resemblance to those versions of Categorial Grammar which exploit the Curry-Howard correspondence to obtain semantic intepretation (van Benthem, 1995), such as Lambek Categorial Grammar and its descendants. A primary goal of this work is to develop a version of LFG in which this connection is made explicit, and in which semantic interpretation falls out as a by-product of the Curry-Howard correspondence rather than needing to be stipulated via semantic interpretation rules. Once one has enriched LFG's formal machinery with the linear logic mechanisms needed for semantic interpretation, it is natural to ask whether these make any existing components of LFG redundant. As Dalrymple and her colleagues note, LFG's f-structure completeness and coherence constraints fall out as a by-product of the linear logic machinery they propose for semantic interpretation, thus making those f-structure 2 Chapter 1. Type-driven semantic interpretation and feature dependencies in R-LFG mechanisms redundant. Given that linear logic machinery or something like it is independently needed for semantic interpretation, it seems reasonable to explore the extent to which it is capable of handling feature structure con...

We study path constraints for deterministic graph model [9], a variation of semistructured data model in which data is represented as a rooted edge-labeled directed graph with deterministic edge relations. The path constraint languages considered include the class of word constraints introduced in [4], the language P c investigated in [8], and an extension of P c defined in terms of regular expressions. Complexity results on the implication and finite implication problems for these constraint languages are established. 1 Introduction Semistructured data is characterized as having no type constraints, irregular structure and rapidly evolving or missing schema [1, 6]. Examples of such data can be found on the WorldWide -Web, in biological databases and after data integration. In particular, documents of XML (eXtensible Markup Language [5]) can also be viewed as semistructured data [10]. The unifying idea in modeling semistructured data is the representation of data as an edge-labeled, r...

We present a constraint system OF of feature trees that is appropriate to specify and implement type inference for first-class messages. OF extends traditional systems of feature constraints by a selection constraint xhyiz "by first-class feature tree" y, in contrast to the standard selection constraint x[ f ]y "by fixed feature" f . We investigate the satisfiability problem of OF and show that it can be solved in polynomial time, and even in quadratic time in an important special case. We compare OF with Treinen's constraint system EF of feature constraints with first-class features, which has an NP-complete satisfiability problem. This comparison yields that the satisfiability problem for OF with negation is NP-hard. Based on OF we give a simple account of type inference for first-class messages in the spirit of Nishimura's recent proposal, and we show that it has polynomial time complexity: We also highlight an immediate extension that is desirable but makes type inference NP-hard.

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• Goal: To provide an overview of the historical development of dependency grammar, set within the context of theoretical linguistics. • History in overview

Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper considers, in a light example-based manner, where this elegant logical paradigm stands when confronted with the wear and tear of reality. Starting from a brief history of the Lambek tradition since the 1980s, we discuss three main issues: (a) the fit of the lambda calculus engine to characteristic semantic structures in natural language, (b) the coexistence of the original type-theoretic and more recent modal interpretations of categorial logics, and (c) the place of categorial grammars in the complex total architecture of natural language, which involves - amongst others - mixtures of interpretation and inference.

This paper describes a new formalization of Lexical-Functional Grammar called R-LFG (where the "R " stands for "Resource-based"). The formal details of R-LFG are presented in Johnson (1997); the present work concentrates on motivating R-LFG and explaining to linguists how it differs from

am 23. Juni 2000

this paper. Needless to say, we bear sole responsibility for the arguments presented here. 1 Draft March 19, 1998 Comments welcome

ersion `x such that the father of x is a plumber', using variables as formalized pronouns. Writing `fx j . . . x . . . g' for `x such that . . . x . . . ', it can be rendered into `fx j P (yF yx)g', with `F ' for `fxy j x is father of yg' and `P ' for `plumber'. Elimination of the denite description leads to: fx j 9y(Fyx ^ Py) ^ 8yz(Fyx ^ F zx ! y = z)g . Presupposing `F ' as functional, that is, 8xyz(Fxz ^ Fyz ! x =<F12.24