On the D-structure position of negative sentence adverbials in French

The author evaluates aspects of recent work by Pollock (1989), Belletti (1990) and Zanuttini (1991), in particular one fundamental assumption made there about the syntax of negative clauses in French. While accepting Pollock's claim that the clitic ne is generated as the X0 head of its own phrasal projection, the author rejects the claim (first made by Pollock (1989: 418) and subsequently endorsed by Belletti (1990: 30) and Zanuttini (1991: 35)) that pas is an Xmax phrasal category base-generated as the specifier of ne, i.e., in the specifier position within NegP. The author offers a three-sided argument against such an analysis, invoking: (a) a significant generalisation regarding the specifier position within functional projections; (b) the relationship between elements like pas and indefinite direct objects in clauses containing a transitive verb; and (c) the syntax of adverbials in general. The author goes on to consider Obenauer's (1983; 1984) work on `quantification at a distance' and Battye's (1989; 1991) work on `nominal quantification'. He argues for a unified account of negative sentence adverbials in French and posits accordingly that pas is generated in a lower position in clause structure, either adjoined to VP or as the head N of a determiner-less direct object indefinite DP

Multi-dimensional Type Theory: Rules, Categories, and Combinators for Syntax and Semantics

We investigate the possibility of modelling the syntax and semantics of natural language by constraints, or rules, imposed by the multi-dimensional type theory Nabla. The only multiplicity we explicitly consider is two, namely one dimension for the syntax and one dimension for the semantics, but the general perspective is important. For example, issues of pragmatics could be handled as additional dimensions. One of the main problems addressed is the rather complicated repertoire of operations that exists besides the notion of categories in traditional Montague grammar. For the syntax we use a categorial grammar along the lines of Lambek. For the semantics we use so-called lexical and logical combinators inspired by work in natural logic. Nabla provides a concise interpretation and a sequent calculus as the basis for implementations.Comment: 20 page

Incremental Interpretation: Applications, Theory, and Relationship to Dynamic Semantics

Why should computers interpret language incrementally? In recent years psycholinguistic evidence for incremental interpretation has become more and more compelling, suggesting that humans perform semantic interpretation before constituent boundaries, possibly word by word. However, possible computational applications have received less attention. In this paper we consider various potential applications, in particular graphical interaction and dialogue. We then review the theoretical and computational tools available for mapping from fragments of sentences to fully scoped semantic representations. Finally, we tease apart the relationship between dynamic semantics and incremental interpretation.Comment: Procs. of COLING 94, LaTeX (2.09 preferred), 8 page

On the syntactic derivation of negative sentence adverbials

We consider recent Government-Binding work on sentential negation, e.g. by Pollock, and evaluate a fundamental assumption made about the syntax of negative clauses. While accepting that ne is generated as the head of NegP, we reject the dual claim that pas is characteristically: (a) a maximal projection, and (b) base-generated as the specifier of ne. We offer a three-sided argument against such an analysis, invoking: (a) the incompatibility of the proposal with the status of pas as a nominal; (b) the interaction between pas, etc, and indefinite direct objects; and (c) the syntax of 'adverbials'. We go on to consider Obenauer's work on 'quantification at a distance' and Battye's work on 'nominal quantification'. On the basis of this work, we posit that pas is generated lower in clause structure, either VP-adjoined or as the head of a determiner-less direct object DP

A Proof-Theoretic Approach to Scope Ambiguity in Compositional Vector Space Models

We investigate the extent to which compositional vector space models can be used to account for scope ambiguity in quantified sentences (of the form "Every man loves some woman"). Such sentences containing two quantifiers introduce two readings, a direct scope reading and an inverse scope reading. This ambiguity has been treated in a vector space model using bialgebras by (Hedges and Sadrzadeh, 2016) and (Sadrzadeh, 2016), though without an explanation of the mechanism by which the ambiguity arises. We combine a polarised focussed sequent calculus for the non-associative Lambek calculus NL, as described in (Moortgat and Moot, 2011), with the vector based approach to quantifier scope ambiguity. In particular, we establish a procedure for obtaining a vector space model for quantifier scope ambiguity in a derivational way.Comment: This is a preprint of a paper to appear in: Journal of Language Modelling, 201

Lambek vs. Lambek: Functorial Vector Space Semantics and String Diagrams for Lambek Calculus

The Distributional Compositional Categorical (DisCoCat) model is a mathematical framework that provides compositional semantics for meanings of natural language sentences. It consists of a computational procedure for constructing meanings of sentences, given their grammatical structure in terms of compositional type-logic, and given the empirically derived meanings of their words. For the particular case that the meaning of words is modelled within a distributional vector space model, its experimental predictions, derived from real large scale data, have outperformed other empirically validated methods that could build vectors for a full sentence. This success can be attributed to a conceptually motivated mathematical underpinning, by integrating qualitative compositional type-logic and quantitative modelling of meaning within a category-theoretic mathematical framework. The type-logic used in the DisCoCat model is Lambek's pregroup grammar. Pregroup types form a posetal compact closed category, which can be passed, in a functorial manner, on to the compact closed structure of vector spaces, linear maps and tensor product. The diagrammatic versions of the equational reasoning in compact closed categories can be interpreted as the flow of word meanings within sentences. Pregroups simplify Lambek's previous type-logic, the Lambek calculus, which has been extensively used to formalise and reason about various linguistic phenomena. The apparent reliance of the DisCoCat on pregroups has been seen as a shortcoming. This paper addresses this concern, by pointing out that one may as well realise a functorial passage from the original type-logic of Lambek, a monoidal bi-closed category, to vector spaces, or to any other model of meaning organised within a monoidal bi-closed category. The corresponding string diagram calculus, due to Baez and Stay, now depicts the flow of word meanings.Comment: 29 pages, pending publication in Annals of Pure and Applied Logi

Mathematical Foundations for a Compositional Distributional Model of Meaning

We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by Lambek. This mathematical framework enables us to compute the meaning of a well-typed sentence from the meanings of its constituents. Concretely, the type reductions of Pregroups are `lifted' to morphisms in a category, a procedure that transforms meanings of constituents into a meaning of the (well-typed) whole. Importantly, meanings of whole sentences live in a single space, independent of the grammatical structure of the sentence. Hence the inner-product can be used to compare meanings of arbitrary sentences, as it is for comparing the meanings of words in the distributional model. The mathematical structure we employ admits a purely diagrammatic calculus which exposes how the information flows between the words in a sentence in order to make up the meaning of the whole sentence. A variation of our `categorical model' which involves constraining the scalars of the vector spaces to the semiring of Booleans results in a Montague-style Boolean-valued semantics.Comment: to appea

A Paraconsistent Higher Order Logic

Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent logics in knowledge-based systems, logical semantics of natural language, etc. Higher order logics have the advantages of being expressive and with several automated theorem provers available. Also the type system can be helpful. We present a concise description of a paraconsistent higher order logic with countable infinite indeterminacy, where each basic formula can get its own indeterminate truth value (or as we prefer: truth code). The meaning of the logical operators is new and rather different from traditional many-valued logics as well as from logics based on bilattices. The adequacy of the logic is examined by a case study in the domain of medicine. Thus we try to build a bridge between the HOL and MVL communities. A sequent calculus is proposed based on recent work by Muskens.Comment: Originally in the proceedings of PCL 2002, editors Hendrik Decker, Joergen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/). Correcte