92 research outputs found
The Hidden Structural Rules of the Discontinuous Lambek Calculus
The sequent calculus sL for the Lambek calculus L (lambek 58) has no
structural rules. Interestingly, sL is equivalent to a multimodal calculus mL,
which consists of the nonassociative Lambek calculus with the structural rule
of associativity. This paper proves that the sequent calculus or hypersequent
calculus hD of the discontinuous Lambek calculus (Morrill and Valent\'in),
which like sL has no structural rules, is also equivalent to an omega-sorted
multimodal calculus mD. More concretely, we present a faithful embedding
translation between mD and hD in such a way that it can be said that hD absorbs
the structural rules of mD.Comment: Submitted to Lambek Festschrift volum
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
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
The Grail theorem prover: Type theory for syntax and semantics
As the name suggests, type-logical grammars are a grammar formalism based on
logic and type theory. From the prespective of grammar design, type-logical
grammars develop the syntactic and semantic aspects of linguistic phenomena
hand-in-hand, letting the desired semantics of an expression inform the
syntactic type and vice versa. Prototypical examples of the successful
application of type-logical grammars to the syntax-semantics interface include
coordination, quantifier scope and extraction.This chapter describes the Grail
theorem prover, a series of tools for designing and testing grammars in various
modern type-logical grammars which functions as a tool . All tools described in
this chapter are freely available
Spurious ambiguity and focalization
Spurious ambiguity is the phenomenon whereby distinct derivations in grammar may assign the same structural reading, resulting in redundancy in the parse search space and inefficiency in parsing. Understanding the problem depends on identifying the essential mathematical structure of derivations. This is trivial in the case of context free grammar, where the parse structures are ordered trees; in the case of type logical categorial grammar, the parse structures are proof nets. However, with respect to multiplicatives, intrinsic proof nets have not yet been given for displacement calculus, and proof nets for additives, which have applications to polymorphism, are not easy to characterize. In this context we approach here multiplicative-additive spurious ambiguity by means of the proof-theoretic technique of focalization.Peer ReviewedPostprint (published version
Grammar logicised: relativisation
Many variants of categorial grammar assume an underlying logic which is associative and linear. In relation to left extraction, the former property is challenged by island domains, which involve nonassociativity, and the latter property is challenged by parasitic gaps, which involve nonlinearity. We present a version of type logical grammar including ‘structural inhibition’ for nonassociativity and ‘structural facilitation’ for nonlinearity and we give an account of relativisation including islands and parasitic gaps and their interaction.Peer ReviewedPostprint (published version
Gapping as Constituent Coordination
A number of coordinate constructions in natural languages conjoin sequences which do not appear to correspond to syntactic constituents in the traditional sense. One striking instance of the phenomenon is afforded by the gapping construction of English, of which the following sentence is a simple example: (1) Harry eats beans, and Fred, potatoes Since all theories agree that coordination must in fact be an operation upon constituents, most of them have dealt with the apparent paradox presented by such constructions by supposing that such sequences as the right conjunct in the above example, Fred, potatoes, should be treated in the grammar as traditional constituents, of type S, but with pieces missing or deleted
A Compositional Vector Space Model of Ellipsis and Anaphora.
PhD ThesisThis thesis discusses research in compositional distributional semantics: if words
are defined by their use in language and represented as high-dimensional vectors
reflecting their co-occurrence behaviour in textual corpora, how should words be
composed to produce a similar numerical representation for sentences, paragraphs
and documents? Neural methods learn a task-dependent composition by generalising
over large datasets, whereas type-driven approaches stipulate that composition
is given by a functional view on words, leaving open the question of what those
functions should do, concretely.
We take on the type-driven approach to compositional distributional semantics
and focus on the categorical framework of Coecke, Grefenstette, and Sadrzadeh
[CGS13], which models composition as an interpretation of syntactic structures as
linear maps on vector spaces using the language of category theory, as well as the
two-step approach of Muskens and Sadrzadeh [MS16], where syntactic structures
map to lambda logical forms that are instantiated by a concrete composition model.
We develop the theory behind these approaches to cover phenomena not dealt with
in previous work, evaluate the models in sentence-level tasks, and implement a tensor
learning method that generalises to arbitrary sentences.
This thesis reports three main contributions. The first, theoretical in nature, discusses
the ability of categorical and lambda-based models of compositional distributional
semantics to model ellipsis, anaphora, and parasitic gaps; phenomena that
challenge the linearity of previous compositional models. Secondly, we perform an
evaluation study on verb phrase ellipsis where we introduce three novel sentence
evaluation datasets and compare algebraic, neural, and tensor-based composition
models to show that models that resolve ellipsis achieve higher correlation with humans.
Finally, we generalise the skipgram model [Mik+13] to a tensor-based setting
and implement it for transitive verbs, showing that neural methods to learn tensor
representations for words can outperform previous tensor-based methods on compositional
tasks
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