Related papers: Continuous Sentences Preserved Under Reduced Produ…
This article introduces the novel notion of dimension preserving approximation for continuous functions defined on $[0,1]$ and initiates the study of it. Restrictions and extensions of continuous functions in regards to fractal dimensions…
This work lists and describes the main recent strategies for building fixed-length, dense and distributed representations for words, based on the distributional hypothesis. These representations are now commonly called word embeddings and,…
In this paper, we will first summarize known results concerning continued fractions. Then we will limit our consideration to continued fractions of quadratic numbers. The second author described periods and sometimes precise form of…
A branch of generalizations of the Banach Fixed Point Theorem replaces contractivity by a weaker but still effective property. The aim of the present note is to extend the contraction principle in this spirit for such complete semimetric…
A brief overview of dimensional reductions for diffeomorphism invariant theories is given. The distinction between the physical idea of compactification and the mathematical problem of a consistent truncation is discussed, and the typical…
In this paper, we introduce a family of topological spaces that captures the existence of preservation theorems. The structure of those spaces allows us to study the relativisation of preservation theorems under suitable definitions of…
We extend the classical Feferman-Vaught theorem to logic for metric structures. This implies that the reduced powers of elementarily equivalent structures are elementarily equivalent, and therefore they are isomorphic under the Continuum…
Sentence embeddings from transformer models encode in a fixed length vector much linguistic information. We explore the hypothesis that these embeddings consist of overlapping layers of information that can be separated, and on which…
In continuous logic, there are plenty of examples of interesting stable metric structures. However, on the other side of the SOP line, there are only a few metric structures where order is relevant, and orders often appear in different…
We answer the question if the continuous product of square matrices $M(t)$ over $t\in [0,1]$ can be correctly defined. The case where all $M(t)$ are taken from a finite set $\Sigma$ is studied. We find necessary and sufficient conditions on…
Finite-state transducers give efficient representations of many Natural Language phenomena. They allow to account for complex lexicon restrictions encountered, without involving the use of a large set of complex rules difficult to analyze.…
Characterizations of paracompact finite $C$-spaces via continuous selections are given. We apply these results to obtain some properties of finite $C$-spaces. Factorization theorems and a completion theorem for finite $C$- spaces are also…
This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…
We give conditions under which a product of topological spaces satisfies some local property. The conditions are necessary and sufficient when the corresponding global property is preserved under finite products. Further examples include…
In this article, we investigate the status of the homomorphism preservation property amongst restricted classes of finite relational structures and algebraic structures. We show that there are many homomorphism-closed classes of finite…
After surveying some known properties of compact convex sets in the plane, we give a two rigorous proofs of the general feeling that supporting lines can be slide-turned slowly and continuously. Targeting a wide readership, our treatment is…
Sentence embeddings can be decoded to give approximations of the original texts used to create them. We explore this effect in the context of text simplification, demonstrating that reconstructed text embeddings preserve complexity levels.…
The paper studies the local geometry of embedding clouds induced by \emph{controlled local classes of semantically close sentences}. The central question is how controlled paraphrase-like semantic variation is organized in sentence…
This paper studies nested sequents for quantified modal logics. In particular, it considers extensions of the propositional modal logics definable by the axioms D, T, B, 4, and 5 with varying, increasing, decreasing, and constant domains.…
As speakers turn their thoughts into sentences, they maintain a balance between the complexity of words and syntax. However, it is unclear whether this syntax-lexicon tradeoff is unique to the spoken language production that is under the…