Contents 1 Introduction: grammatical reasoning 1 2 Linguistic inference: the Lambek systems 5 2.1 Modelinggrammaticalcomposition ............................ 5 2.2 Gentzen calculus, cut elimination and decidability . . . . . . . . . . . . . . . . . . . . 9 2.3 Discussion: options for resource management . . . . . . . . . . . . . . . . . . . . . . 13 3 The syntax-semantics interface: proofs and readings 16 3.1 Term assignment for categorial deductions . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Natural language interpretation: the deductive view . . . . . . . . . . . . . . . . . . . 21 4 Grammatical composition: multimodal systems 26 4.1 Mixedinference:themodesofcomposition........................ 26 4.2 Grammaticalcomposition:unaryoperations ....................... 30 4.2.1 Unary connectives: logic and structure . . . . . . . . . . . . . . . . . . . . . . . 31 4.2.2 Applications: imposing constraints, structural relaxation

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...

Copyright by Roger Levy 2005 ii

Abstract not found

Gottlob Frege (1892) is credited with the so-called “principle of compositionality”, also called “Frege’s Principle”, which one often hears expressed this way: Frege’s Principle (so-called) “The meaning of a sentence is a function of the meanings of the words in it and the way they are combined syntactically.” (Exactly how Frege himself understood “Frege’s Principle ” is not our concern here; 1 rather, it is the understanding that this slogan has acquired in contemporary linguistics that we want to pursue, and this has little further to do with Frege.) But why should linguists care what compositionality is or whether natural languages “are compositional ” or not? 2.1.1 An “Empirical Issue”? Often we hear that “compositionality is an empirical issue ” (meaning the question whether natural language is compositional or not)—usually asserted as a preface to expressing skepticism about a “yes ” answer. In the most general sense of Frege’s Principle, however, the fact that natural languages are compositional is beyond any serious doubt. Consider that:

This paper takes as its starting point the work of Moortgat (1991) and aims to provide a linguisticallymotivated extension to the basic Lambek calculus that will allow, among other things, for an elegant treatment of various `discontinuous constituency' phenomena, including `tough'-constructions in English, cross-serial agreement in Swiss German and quantifier scoping. The proposal is contrasted favorably with related proposals by Moortgat, Morrill and Solias (1993) and Hepple (1994). Keywords: categorial grammar, Lambek calculus, discontinuous constituents, labelled deductive systems 1 Preliminaries This paper takes as its starting point the work of Moortgat (1991) and proposes an alternative extension to the basic Lambek Calculus that will allow, among other things, for the treatment of discontinuous constituents (exemplified herein by toughclass adjective phrases in English and cross-serial dependencies in Swiss German) in terms of operations on headed strings (along the lines of...

types in this paper are built up from ground types s, np and n with the help of implication, and thus have forms such as np s, n((np s)s), etc. A restriction on signs is that a sign of abstract type A should have a term of type A in its i-th dimension. The values of the function : for ground types can be chosen on a per grammar basis and in this paper are as in Table 2. For complex types, the rule is that (AB) = A B . This means, for example, that np(np s) = np(np s) = (t)((t)t) and that np(np s) = e(e(st)). As a consequence, (2c) should be of type np(np s). Similarly, (2a) and (2b) can be taken to be of type np, (3a) and (3b) are of types np s and s respectively, etc. In general, if M has abstract type AB and N abstract type A, then the pointwise application M(N) is de ned and has type B.

The GF Resource Grammar Library is a set of natural language grammars implemented in GF (Grammatical Framework). These grammars are in a strong sense parallel: they are built upon a common abstract syntax, i.e. a common tree structure. Individual languages are obtained via compositional mappings from abstract syntax trees to feature structures specific to each language. The grammar defines, for each language, a complete set of morphological paradigms and a syntax fragment comparable to CLE (Core Language Engine). It is available as open-source software under the GNU LGPL License.

We present a new grammar formalism for parsing with lYeer word-order languages, motivated by recent linguistic research in German and the Slavic lan- guages. Unlike CFGs, these grammars contain two primitive notions of constituency that are used to preserve the semantic or interpretational aspects of phrase structure, while at the same time providing a more efficient backbone for parsing based on word-order and contiguity constraints. A simple parsing algorithm is presented, and compilation of grammars into Constraint Handling Rules is also discussed.

This paper suggests an analysis of Modern Hebrew noun phrases in the framework of HPSG. It focuses on the peculiar properties of the definite article, including the requirement for definiteness agreement among various elements in the noun phrase, definiteness inheritance in construct-state nominals, the fact that the article does not combine with constructs and the similarities between construct-state nouns and adjectives. Central to our analysis is the assumption that the Hebrew definite article is an affix, rather than a clitic or a stand-alone word. Several arguments, from all levels of linguistic representation, are provided to justify this claim. Adopting the lexical hypothesis, we conclude that the article combines with nominals in the lexicon, and is no longer available for syntactic processes. This leads to an analysis of noun phrases as NPs, rather than as DPs; we show that such a view is compatible with accepted criteria for headedness. We provide an HPSG analysis that covers...