Related papers: Natural Density and The Quantifier 'Most'
A quotient of a poset $P$ is a partial order obtained on the equivalence classes of an equivalence relation $\theta$ on $P$; $\theta$ is then called a congruence if it satisfies certain conditions, which vary according to different…
The term {\em complexity} is used informally both as a quality and as a quantity. As a quality, complexity has something to do with our ability to understand a system or object -- we understand simple systems, but not complex ones. On…
This article contains ideas and their elaboration for quantifiers, which appeared after checking in practice the experimental language of the formal knowledge representation YAFOLL [1]: - looking at for_all and exists quantifiers as…
This study is to review the approaches used for measuring sentences similarity. Measuring similarity between natural language sentences is a crucial task for many Natural Language Processing applications such as text classification,…
Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic…
The categorical compositional distributional model of natural language provides a conceptually motivated procedure to compute the meaning of sentences, given grammatical structure and the meanings of its words. This approach has…
Abstract upper densities are monotone and subadditive functions from the power set of positive integers into the unit real interval that generalize the upper densities used in number theory, including the upper asymptotic density, the upper…
A longstanding debate in semiotics centers on the relationship between linguistic signs and their corresponding semantics: is there an arbitrary relationship between a word form and its meaning, or does some systematic phenomenon pervade?…
\emph{Sentiment Quantification} (i.e., the task of estimating the relative frequency of sentiment-related classes -- such as \textsf{Positive} and \textsf{Negative} -- in a set of unlabelled documents) is an important topic in sentiment…
We isolate a new class of ultrafilters on N, called "quasi-selective" because they are intermediate between selective ultrafilters and P-points. (Under the Continuum Hypothesis these three classes are distinct.) The existence of…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
In this paper we introduce the notion of elementary numerosity as a special function defined on all subsets of a given set X which takes values in a suitable non-Archimedean field, and satisfies the same formal properties of finite…
We initiate the rigorous study of classification in semimetric spaces, which are point sets with a distance function that is non-negative and symmetric, but need not satisfy the triangle inequality. For metric spaces, the doubling dimension…
Compositionality in language models presents a problem when processing idiomatic expressions, as their meaning often cannot be directly derived from their individual parts. Although fine-tuning and other optimization strategies can be used…
Let $A$ be a nonempty finite subset of an additive abelian group $G$. Define $A + A := \{a + b : a, b \in A\}$ and $A \dotplus A := \{a + b : a, b \in A~\text{and}~ a \neq b\}$. The set $A$ is called a {\em sum-dominant (SD) set} if $|A +…
This document describes a possible approach that can be used to check the relevance of a summary / definition of an entity with respect to its name. This classifier focuses on the relevancy of an entity's name to its summary / definition,…
The Categorical Compositional Distributional (DisCoCat) framework models meaning in natural language using the mathematical framework of quantum theory, expressed as formal diagrams. DisCoCat diagrams can be associated with tensor networks…
We define the probability of an equation in a finite algebra as the proportion of tuples in its domain that satisfy it. We call the probabilistic spectrum of an algebra the set of probability values obtained when the equation varies. We…
We present a new Convolutional Neural Network (CNN) model for text classification that jointly exploits labels on documents and their component sentences. Specifically, we consider scenarios in which annotators explicitly mark sentences (or…
The concept of typicality refers to properties holding for the "overwhelming majority" of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate…