A Frobenius Algebraic Analysis for Parasitic Gaps

The interpretation of parasitic gaps is an ostensible case of non-linearity in natural language composition. Existing categorial analyses, both in the typelogical and in the combinatory traditions, rely on explicit forms of syntactic copying. We identify two types of parasitic gapping where the duplication of semantic content can be confined to the lexicon. Parasitic gaps in adjuncts are analysed as forms of generalized coordination with a polymorphic type schema for the head of the adjunct phrase. For parasitic gaps affecting arguments of the same predicate, the polymorphism is associated with the lexical item that introduces the primary gap. Our analysis is formulated in terms of Lambek calculus extended with structural control modalities. A compositional translation relates syntactic types and derivations to the interpreting compact closed category of finite dimensional vector spaces and linear maps with Frobenius algebras over it. When interpreted over the necessary semantic spaces, the Frobenius algebras provide the tools to model the proposed instances of lexical polymorphism.Comment: SemSpace 2019, to appear in Journal of Applied Logic

On shared indefinite expressions in coordinative structures

The paper shows that shared indefinite expressions in coordinative constructions may differ with respect to their referential properties. This is due to their being either in a focused or in a nonfocused shared constituent. Their different information-structural status follows from Rooth's theory on focus interpretation. Thus it follows that focused shared constitutents must be beyond the actual coordination and that coordinative constructions with unfocused shared constituents can be represented as ellipsis. In a focused shared constituent indefinite expressions may have a specific and an non specific unique reading as well as an non specific distributive one. For the latter we outline the idea that subjects and objects in the actual coordination form a pair of sets to which a distributing operator is attached. The set formation is further supported by plural pronouns referring to the respective set and by plural verb agreement in subsequent expressions

Comparing and evaluating extended Lambek calculi

Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a logical theory). However, though it was successful in giving at least a basic treatment of many linguistic phenomena, it was also clear that a slightly more expressive logical calculus was needed for many other cases. Therefore, many extensions and variants of the Lambek calculus have been proposed, since the eighties and up until the present day. As a result, there is now a large class of calculi, each with its own empirical successes and theoretical results, but also each with its own logical primitives. This raises the question: how do we compare and evaluate these different logical formalisms? To answer this question, I present two unifying frameworks for these extended Lambek calculi. Both are proof net calculi with graph contraction criteria. The first calculus is a very general system: you specify the structure of your sequents and it gives you the connectives and contractions which correspond to it. The calculus can be extended with structural rules, which translate directly into graph rewrite rules. The second calculus is first-order (multiplicative intuitionistic) linear logic, which turns out to have several other, independently proposed extensions of the Lambek calculus as fragments. I will illustrate the use of each calculus in building bridges between analyses proposed in different frameworks, in highlighting differences and in helping to identify problems.Comment: Empirical advances in categorial grammars, Aug 2015, Barcelona, Spain. 201

On quantifier raising in German

The status of quantifier raising in German and other languages where scope is fairly rigid is debated. The first part of this paper argues that quantifiers in German can undergo covert extraction out of coordinations, and therefore that quantifier raising is available in German. The second part argues that quantifier raising in German is constrained to never move one DP across another. This result might provide part of an explanation of scope rigidity in German

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

Linearization and Coordination in German

This paper attempts a novel approach to certain coordination constructions in German and other Germanic languages. It will be shown that virtually all previous attempts at describing such constructions involve asymmetric conjuncts, in violation of the general like category constraint on coordination. While independent evidence for the kinds of mechanisms that license such asymmetry is weak, these analyses in addition are incapable of reflecting the close relationship of the constructions in question with another type of coordination. Since the reason for the asymmetry is essentially the insistence on phrase structure as the sole means of describing syntactic structure (i.e. by relating structure and surface representation in terms of the terminal yield of a tree), we will develop an alternative analysis that is empirically adequate and respects the like category constraint necessitating a different relation between structure and surface string which we will call "Linearization"

The use of and-coordination in terms of its syntactic (a)symmetry in argumentative essays : a corpus-based study of three university learner groups in MICUSP and NUCLE.

Studies found EL learners overuse and as an additive connector at the sentence-initial position (Bolton, Hung, & Nelson, 2002), and they underuse and as a coordinator (Leung, 2005). Generally, the use of the and-coordinator has often been overlooked in corpus research and in English teaching because of its seemingly simplicity. To test previous findings about the and-coordinator and to examine the influence of English proficiency on the use of and in academic writing, three learner corpora--MICUSP-NNS (advanced level), MICUSP-NS (advanced level), and NUCLE-NNS (upper-intermediate) were compared, with regard to the use of (a)symmetric structures of the and-coordination. Each corpus contains 31 argumentative essays written by 31 university students