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

Hypothetical-reasoning and radical non-constituent coordination in categorical logic

The paper investigates the connection between non-constituent coordination, as implemented in categorial grammar by means of a polymorphic type-assignment to lexical conjunctions, and hypothetical reasoning in Categorial Logics. A way of extending the logic is suggested, so that coordination can be applied to types depending on undischarged assumptions. By a certain ``resource manipulation'' of assumptions (of hypothetical reasoning), a late-discharge is facilitated, leading to what is referred to as the {em radical non-constituent coordination, wherby only basic types (and not functional types of any kind) are coordinated

A Compositional Treatment of Polysemous Arguments in Categorial Grammar

We discuss an extension of the standard logical rules (functional application and abstraction) in Categorial Grammar (CG), in order to deal with some specific cases of polysemy. We borrow from Generative Lexicon theory which proposes the mechanism of {\em coercion}, next to a rich nominal lexical semantic structure called {\em qualia structure}. In a previous paper we introduced coercion into the framework of {\em sign-based} Categorial Grammar and investigated its impact on traditional Fregean compositionality. In this paper we will elaborate on this idea, mostly working towards the introduction of a new semantic dimension. Where in current versions of sign-based Categorial Grammar only two representations are derived: a prosodic one (form) and a logical one (modelling), here we introduce also a more detaled representation of the lexical semantics. This extra knowledge will serve to account for linguistic phenomena like {\em metonymy\/}.Comment: LaTeX file, 19 pages, uses pubsmacs, pubsbib, pubsarticle, leqn

Gapping as hypothetical reasoning

The scope anomaly observed in sentences like Mrs. J can’t live in Boston and Mr. J in LA (¬◊>∧) and No dog eats Whiskas or cat Alpo (¬∃>∨) is known to pose difficult challenges to many analyses of Gapping. We provide new arguments, based on both the basic syntactic patterns of Gapping and standard constituency tests, that the so-called ‘low VP coordination analysis’—the only extant analysis of Gapping in contemporary syntactic theories which accounts for this scope anomaly—is empirically untenable. We propose an explicit alternative analysis of Gapping in Hybrid Type-Logical Categorial Grammar, a variant of categorial grammar which builds on both the Lambek-inspired tradition and a more recent line of work modelling word order via a lambda calculus for the prosodic component. The flexible syntax-semantics interface of this framework enables us to characterize Gapping as an instance of like-category coordination, via a crucial use of the notion of hypothetical reasoning. This analysis of the basic syntax of Gapping is shown to interact with independently motivated analyses of scopal operators to immediately yield their apparently anomalous scopal properties in Gapping, offering, for the first time in the literature, a conceptually simple and empirically adequate solution for the notorious scope anomaly in Gapping

HPSG and categorial grammar

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Type-driven natural language analysis

The purpose of this thesis is in showing how recent developments in logic programming can be exploited to encode in a computational environment the features of certain linguistic theories. We are in this way able to make available for the purpose of natural language processing sophisticated capabilities of linguistic analysis directly justified by well developed grammatical frameworks. More specifically, we exploit hypothetical reasoning, recently proposed as one of the possible directions to widen logic programming, to account for the syntax of filler-gap dependencies along the lines of linguistic theories such as Generalized Phrase Structure Grammar and Categorial Grammar. Moreover, we make use, for the purpose of semantic analysis of the same kind of phenomena, of another recently proposed extension, interestingly related to the previous one, namely the idea of replacing first-order terms with the more expressive λ-terms of λ-Calculus

No context, no content, no problem

Recently, philosophers have offered compelling reasons to think that demonstratives are best represented as variables, sensitive not to the context of utterance, but to a variable assignment. Variablists typically explain familiar intuitions about demonstratives—intuitions that suggest that what is said by way of a demonstrative sentence varies systematically over contexts—by claiming that contexts initialize a particular assignment of values to variables. I argue that we do not need to link context and the assignment parameter in this way, and that we would do better not to

Pseudogapping as pseudo-VP ellipsis

Abstract In this paper, we propose an analysis of pseudogapping in Hybrid Type-Logical Categorial Grammar (Hybrid TLCG; Kubota 2010; Kubota and Levine 2012). Pseudogapping poses a particularly challenging problem for previous analyses in both the transformational and nontransformational literature. We argue that the flexible syntaxsemantics interface of Hybrid TLCG enables an analysis of pseudogapping that synthesizes the key insights of both transformational and nontransformational approaches, while at the same time overcoming the major difficulties of each type of approach. Keywords: pseudogapping, VP ellipsis, anaphora, syntactic identity, Hybrid Type-Logical Categorial Grammar 0 We are indebted to the following people for comments and discussions: Ai Kubota, Scott Martin, Philip Miller, Jordan Needle, Carl Pollard, and Daniel Puthawala. We would also like to thank the two LI reviewers for their insightful comments. We have presented parts of the present work at various venues, including LACL 2014, the syntax semantics group Synners at OSU, and the Semantics Workshop in Tokai (Nagoya). We would like to thank the audiences at these venues for their feedback

Meaning versus Grammar

This volume investigates the complicated relationship between grammar, computation, and meaning in natural languages. It details conditions under which meaning-driven processing of natural language is feasible, discusses an operational and accessible implementation of the grammatical cycle for Dutch, and offers analyses of a number of further conjectures about constituency and entailment in natural language