Related papers: Vector spaces as Kripke frames

Distributed representations of words and paragraphs as semantic embeddings in high dimensional data are used across a number of Natural Language Understanding tasks such as retrieval, translation, and classification. In this work, we…

While important properties of word vector representations have been studied extensively, far less is known about the properties of sentence vector representations. Word vectors are often evaluated by assessing to what degree they exhibit…

We introduce the algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as the natural extension of the algebraic entropy for endomorphisms of discrete vector spaces. We show that the…

The aim of this paper is to study the topological properties of algebraic sets with zero divisors. We impose a subbasic topology on the set of proper ideals of a $k$-algebra and this new ``$k$-space'' becomes a generalization of the…

Two variations of classical Urysohn lemma for subsets of topological vector spaces are obtained in this article. The continuous functions constructed in these lemmas are of quasi-convex type.

In our paper "Uniformity and the Taylor expansion of ordinary lambda-terms" (with Laurent Regnier), we studied a translation of lambda-terms as infinite linear combinations of resource lambda-terms, from a calculus similar to Boudol's…

Many properties of a module can be expressed in terms of the dimension of the vector space obtained by applying a finitely presented functor to that module. For example, the dimension of the kernel, image or cokernel of the multiplication…

Learning representations for semantic relations is important for various tasks such as analogy detection, relational search, and relation classification. Although there have been several proposals for learning representations for individual…

This paper deals with some basic constructions of linear and multilinear algebra on finite-dimensional diffeological vector spaces. We consider the diffeological dual formally checking that the assignment to each space of its dual defines a…

Human cognition excels at symbolic reasoning, deducing abstract rules from limited samples. This has been explained using symbolic and connectionist approaches, inspiring the development of a neuro-symbolic architecture that combines both…

To formalize calculations in linear algebra for the development of efficient algorithms and a framework suitable for functional programming languages and faster parallelized computations, we adopt an approach that treats elements of linear…

We give a classification theorem of certain geometric objects, called torsors over the sheaf of K-theory spaces, in terms of Tate vector bundles. This allows us to present a very natural and simple, alternative approach to the Tate central…

Distributional semantic models learn vector representations of words through the contexts they occur in. Although the choice of context (which often takes the form of a sliding window) has a direct influence on the resulting embeddings, the…

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…

We introduce Latent Vector Grammars (LVeGs), a new framework that extends latent variable grammars such that each nonterminal symbol is associated with a continuous vector space representing the set of (infinitely many) subtypes of the…

Data-driven representation learning for words is a technique of central importance in NLP. While indisputably useful as a source of features in downstream tasks, such vectors tend to consist of uninterpretable components whose relationship…

This paper is devoted to a new approach of the arithmetic of intervals. We present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any…

Motivated by the theory of locally definable groups, we study the theory of $K$-vector spaces with a predicate for the union $X$ of an infinite family of independent subspaces. We show that if $K$ is infinite then the theory is complete and…

Connectionist approaches to machine learning, \emph{i.e.} neural networks, are enjoying a considerable vogue right now. However, these methods require large volumes of data and produce models that are uninterpretable to humans. An…

This paper explores proof-theoretic aspects of hybrid type-logical grammars , a logic combining Lambek grammars with lambda grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property and also…