Abstract: This is a history of relevant and substructural logics, written for the Handbook of the History and Philosophy of Logic, edited by Dov Gabbay and John Woods. 1 1

This paper describes a number of log-linear parsing models for an automatically extracted lexicalized grammar. The models are "full" parsing models in the sense that probabilities are defined for complete parses, rather than for independent events derived by decomposing the parse tree. Discriminative training is used to estimate the models, which requires incorrect parses for each sentence in the training data as well as the correct parse. The lexicalized grammar formalism used is Combinatory Categorial Grammar (CCG), and the grammar is automatically extracted from CCGbank, a CCG version of the Penn Treebank. The combination of discriminative training and an automatically extracted grammar leads to a significant memory requirement (over 20 GB), which is satisfied using a parallel implementation of the BFGS optimisation algorithm running on a Beowulf cluster. Dynamic programming over a packed chart, in combination with the parallel implementation, allows us to solve one of the largest-scale estimation problems in the statistical parsing literature in under three hours. A key component of the parsing system, for both training and testing, is a Maximum Entropy supertagger which assigns CCG lexical categories to words in a sentence. The supertagger makes the discriminative training feasible, and also leads to a highly efficient parser. Surprisingly,

Abstract not found

tem of rewrite rules or "productions" like (2), which have their origin in early work in recursion theory by Post, among others. (1) Dexter likes Warren. (2) S ! NP VP VP ! TV NP TV ! flikes;sees; : : :g Categorial Grammar (CG), together with its close cousin Dependency Grammar (which also originated in the 1950s, in work by Tesniere) stems from an alternative approach to context-free grammar pioneered by Bar-Hillel 1953 and Lambek 1958, with earlier antecedents in Ajdukiewicz 1935 and still earlier work by Husserl and Russell in category theory and the theory of types. Categorial Grammars capture the same information by associating a functional type or category with all grammatical entities. For example, all transitive verbs are associated via the lexicon with a category that can be written as follows: (3) likes := (SnNP)=NP The no

Several recent stochastic parsers use bilexical grammars, where each word type idiosyncratically prefers particular complements with particular head words. We present O(n^4) parsing algorithms for two bilexical formalisms, improving the prior upper bounds of O(n^5). For a common special case that was known to allow O(n³) parsing (Eisner, 1997), we present an O(n³) algorithm with an improved grammar constant.

Abstract not found

This thesis presents accounts of a range of linguistic phenomena in an extended categorial framework, and develops proposals for processing grammars set within this framework. Linguistic phenomena whose treatment we address include word order, grammatical relations and obliqueness, extraction and island constraints, and binding. The work is set within a flexible categorial framework which is a version of the Lambek calculus (Lambek, 1958) extended by the inclusion of additional type-forming operators whose logical behaviour allows for the characterization of some aspect of linguistic phenomena. We begin with the treatment of extraction phenomena and island constraints. An account is developed in which there are many interrelated notions of boundary, and where the sensitivity of any syntactic process to a particular class of boundaries can be addressed within the grammar. We next present a new categorial treatment of word order which factors apart the specification of the order of a h...

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

Abstract not found

Grammatical Framework (GF) is a special-purpose functional language for defining grammars. It uses a Logical Framework (LF) for a description of abstract syntax, and adds to this a notation for defining concrete syntax. GF grammars themselves are purely declarative, but can be used both for linearizing syntax trees and parsing strings. GF can describe both formal and natural languages. The key notion of this description is a grammatical object, which is not just a string, but a record that contains all information on inflection and inherent grammatical features such as number and gender in natural languages, or precedence in formal languages. Grammatical objects have a type system, which helps to eliminate run-time errors in language processing. In the same way as an LF, GF uses...