153 research outputs found
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
A Quick Overview on the Quantum Control Approach to the Lambda Calculus
In this short overview, we start with the basics of quantum computing,
explaining the difference between the quantum and the classical control
paradigms. We give an overview of the quantum control line of research within
the lambda calculus, ranging from untyped calculi up to categorical and
realisability models. This is a summary of the last 10+ years of research in
this area, starting from Arrighi and Dowek's seminal work until today.Comment: In Proceedings LSFA 2021, arXiv:2204.0341
Call-by-value non-determinism in a linear logic type discipline
We consider the call-by-value lambda-calculus extended with a may-convergent
non-deterministic choice and a must-convergent parallel composition. Inspired
by recent works on the relational semantics of linear logic and non-idempotent
intersection types, we endow this calculus with a type system based on the
so-called Girard's second translation of intuitionistic logic into linear
logic. We prove that a term is typable if and only if it is converging, and
that its typing tree carries enough information to give a bound on the length
of its lazy call-by-value reduction. Moreover, when the typing tree is minimal,
such a bound becomes the exact length of the reduction
Evaluating Composition Models for Verb Phrase Elliptical Sentence Embeddings
Ellipsis is a natural language phenomenon where part of a sentence is missing and its information must be recovered from its surrounding context, as in âCats chase dogs and so do foxes.â. Formal semantics has different methods for resolving ellipsis and recovering the missing information, but the problem has not been considered for distributional semantics, where words have vector embeddings and combinations thereof provide embeddings for sentences. In elliptical sentences these combinations go beyond linear as copying of elided information is necessary. In this paper, we develop different models for embedding VP-elliptical sentences. We extend existing verb disambiguation and sentence similarity datasets to ones containing elliptical phrases and evaluate our models on these datasets for a variety of non-linear combinations and their linear counterparts. We compare results of these compositional models to state of the art holistic sentence encoders. Our results show that non-linear addition and a non-linear tensor-based composition outperform the naive non-compositional baselines and the linear models, and that sentence encoders perform well on sentence similarity, but not on verb disambiguation
Variational Approximation of Functionals Defined on 1-dimensional Connected Sets: The Planar Case
In this paper we consider variational problems involving 1-dimensional connected sets in the Euclidean plane, such as the classical Steiner tree problem and the irrigation (Gilbert--Steiner) problem. We relate them to optimal partition problems and provide a variational approximation through Modica--Mortola type energies proving a -convergence result. We also introduce a suitable convex relaxation and develop the corresponding numerical implementations. The proposed methods are quite general and the results we obtain can be extended to -dimensional Euclidean space or to more general manifold ambients, as shown in the companion paper [M. Bonafini, G. Orlandi, and E. Oudet, Variational Approximation of Functionals Defined on 1-Dimensional Connected Sets in , preprint, 2018]
Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model
In a recent paper, a realizability technique has been used to give a
semantics of a quantum lambda calculus. Such a technique gives rise to an
infinite number of valid typing rules, without giving preference to any subset
of those. In this paper, we introduce a valid subset of typing rules, defining
an expressive enough quantum calculus. Then, we propose a categorical semantics
for it. Such a semantics consists of an adjunction between the category of
semi-vector spaces of value distributions (that is, linear combinations of
values in the lambda calculus), and the category of sets of value
distributions.Comment: 26 pages plus appendi
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