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...

. Collective entities and collective relations play an important role in natural language. In order to capture the full meaning of sentences like "The Beatles sing `Yesterday' ", a knowledge representation language should be able to express and reason about plural entities -- like "the Beatles" -- and their relationships -- like "sing" -- with any possible reading (cumulative, distributive or collective). In this paper a way of including collections and collective relations within a concept language, chosen as the formalism for representing the semantics of sentences, is presented. A twofold extension of the ALC concept language is investigated : (1) special relations introduce collective entities either out of their components or out of other collective entities, (2) plural quantifiers on collective relations specify their possible reading. The formal syntax and semantics of the concept language is given, together with a sound and complete algorithm to compute satisfiability and subs...

This paper presents the first use of a computational model of natural logic—a system of logical inference which operates over natural language—for textual inference. Most current approaches to the PAS-CAL RTE textual inference task achieve robustness by sacrificing semantic precision; while broadly effective, they are easily confounded by ubiquitous inferences involving monotonicity. At the other extreme, systems which rely on first-order logic and theorem proving are precise, but excessively brittle. This work aims at a middle way. Our system finds a low-cost edit sequence which transforms the premise into the hypothesis; learns to classify entailment relations across atomic edits; and composes atomic entailments into a top-level entailment judgment. We provide the first reported results for any system on the FraCaS test suite. We also evaluate on RTE3 data, and show that hybridizing an existing RTE system with our natural logic system yields significant performance gains. 1

The study of generalized quantifiers over the past 15 years has enriched enormously our understanding of natural language determiners (Dets). It has yielded answers to questions raised independently within generative grammar and it has provided us with new semantic generalizations, ones that were basically unformulable without the conceptual and technica apparatus of generalized quantifier theory. Here we overview results of both these types. historical note It was Montague (1969) who first interpreted natural language NPs as generalized quantifiers (though this term was not used by him). But it was only in the early 1980's with the publication of B&C (Barwise and Cooper, 1981) that the study of natural language Dets took on a life of its own. Also from this period are early versions of K&S (Keenan and Stavi, 1986) and Higginbotham and May (1981). The former fed into subsequent formal studies such as van Benthem (1984, 1986) and Westerstähl (1985). The latter focussed on specific linguistic applications of binary quantifiers, a topic initiated in Altham and Tennant (1974), drawing on the mathematical work of Mostowski (1957), and pursued later in a more general linguistic setting in van Benthem (1989) and Keenan (1987b, 1992). Another precursor to the mathematical study o generalized quantifiers is Lindstr_m (1969) who provides the type notation used to classif

We propose an approach to natural language inference based on a model of natural logic, which identifies valid inferences by their lexical and syntactic features, without full semantic interpretation. We greatly extend past work in natural logic, which has focused solely on semantic containment and monotonicity, to incorporate both semantic exclusion and implicativity. Our system decomposes an inference problem into a sequence of atomic edits linking premise to hypothesis; predicts a lexical entailment relation for each edit using a statistical classifier; propagates these relations upward through a syntax tree according to semantic properties of intermediate nodes; and composes the resulting entailment relations across the edit sequence. We evaluate our system on the FraCaS test suite, and achieve a 27% reduction in error from previous work. We also show that hybridizing an existing RTE system with our natural logic system yields significant gains on the RTE3 test suite. 1

The Lambek calculus, an intuitionistic fragment of Linear Logic, has recently been rediscovered by linguists. Due to its built-in hypothetical reasoning mechanism, it allows for describing a certain range of those phenomena in natural language syntax which involve incomplete subphrases or moved constituents. Previously, it seemed unclear how to extent traditional parsing techniques in order to incorporate reasoning about incomplete phrases, without causing the undesired effect of derivational equivalences. It turned out that the Lambek calculus offers a framework to formulate equivalent but more implementation-oriented calculi where this problem does not occur. In this paper, such a theorem prover for the Lambek calculus, i.e. a parser for Lambek categorial grammars, is defined. Permutations of proof steps which would cause derivational equivalence in a purely sequential formulation do not play a role in a (pseudo-)parallel approach which is based on a lemma table or a "chart". At the...

We prove a theorem stating that any semantics can be encoded as a compositional semantics, which means that, essentially, the standard definition of compositionality is formally vacuous. We then show that when compositional semantics is required to be ”systematic ” (that is, the meaning function cannot be arbitrary, but must belong to some class), it is possible to distinguish between compositional and non-compositional semantics. As a result, we believe that the paper clarifies the concept of compositionality and opens a possibility of making systematic formal comparisons of different systems of grammars. 1

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.

An important part of textual inference is making deductions involving monotonicity, that is, determining whether a given assertion entails restrictions or relaxations of that assertion. For instance, the statement ‘We know the epidemic spread quickly ’ does not entail ‘We know the epidemic spread quickly via fleas’, but ‘We doubt the epidemic spread quickly’ entails ‘We doubt the epidemic spread quickly via fleas’. Here, we present the first algorithm for the challenging lexical-semantics problem of learning linguistic constructions that, like ‘doubt’, are downward entailing (DE). Our algorithm is unsupervised, resource-lean, and effective, accurately recovering many DE operators that are missing from the handconstructed lists that textual-inference systems currently use. 1

In this article we present data from two sets of experiments designed to investigate how children and adult speakers of English and Kannada (Dravidian) interpret scopally ambiguous sentences containing numerally quantified noun phrases and negation (e.g., The detective didn't find two guys). We use this kind of sentence as a way to find evidence in children's linguistic representations for the hierarchical structure and the abstract relations defined over these structures (i.e., the relation of c-command) that linguists take to be at the core of grammatical knowledge. Specifically, we uncover the existence of systematic differences in the way that children and adult speakers resolve these ambiguities, regardless of language. That is, while adults can easily access either scope interpretation, 4-year-old children display a strong preference for the scopal interpretation of the quantified elements which corresponds to their surface syntactic position. Crucially, however, we show that children's interpretations are constrained by the surface hierarchical relations (i.e. the c-command relations) between these elements and not by their linear order. Children's non-adult interpretations are therefore informative about the nature of the syntactic representations they entertain and the rules they use to determine the meaning of a sentence from its structure.