Related papers: Natural Density and The Quantifier 'Most'
Quantitative characterizations and estimations of uncertainty are of fundamental importance in optimization and decision-making processes. Herein, we propose intuitive scores, which we call certainty and doubt, that can be used in both a…
With the recent proliferation of the use of text classifications, researchers have found that there are certain unintended biases in text classification datasets. For example, texts containing some demographic identity-terms (e.g., "gay",…
We consider the case of a domain expert who wishes to explore the extent to which a particular idea is expressed in a text collection. We propose the task of semantically matching the idea, expressed as a natural language proposition,…
The density of state for a complex $N\times N$ random matrix coupled to an external deterministic source is considered for a finite N, and a compact expression in an integral representation is obtained.
Estimating the parameters of probabilistic models of language such as maxent models and probabilistic neural models is computationally difficult since it involves evaluating partition functions by summing over an entire vocabulary, which…
In this paper, we derive a notion of 'word meaning in context' that characterizes meaning as both intensional and conceptual. We introduce a framework for specifying local as well as global constraints on word meaning in context, together…
Sentence extraction based summarization methods has some limitations as it doesn't go into the semantics of the document. Also, it lacks the capability of sentence generation which is intuitive to humans. Here we present a novel method to…
For any set $A$ of natural numbers with positive upper Banach density and any $k\geq 1$, we show the existence of an infinite set $B\subset{\mathbb N}$ and a shift $t\geq0$ such that $A-t$ contains all sums of $m$ distinct elements from $B$…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
In concurrency theory, weak bisimilarity is often used to relate processes exhibiting the same observable behaviour. The probabilistic environment gives rise to several generalisations; we study the infinitary semantics, which abstracts…
The density topology $\cal T$ is a topology on the real line, finer than the usual topology, having as its open sets the measurable subsets of ${\mathbb R}$, which are of density 1 at each of their points. The aim of this paper is to…
This paper investigates the natural density and structural relationships within Fibonacci words, the density of a Fibonacci word is $\operatorname{DF}(F_k)=n/(n+m),$ where $m$ denote the number of zeros in a Fibonacci word and $n$ denote…
A family of m independent identically distributed random variables indexed by a chemical potential \phi\in[0,\gamma] represents piles of particles. As \phi increases to \gamma, the mean number of particles per site converges to a maximal…
Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite number of points. In this paper, firstly a general approach to this process is outlined using…
We study the sequences of numbers corresponding to lambda terms of given sizes, where the size is this of lambda terms with de Bruijn indices in a very natural model where all the operators have size 1. For plain lambda terms, the sequence…
Considering that words with different characteristic in the text have different importance for classification, grouping them together separately can strengthen the semantic expression of each part. Thus we propose a new text representation…
Measuring text complexity is an essential task in several fields and applications (such as NLP, semantic web, smart education, etc.). The semantic layer of text is more tacit than its syntactic structure and, as a result, calculation of…
The behavior of a quantum system depends on how it is measured. How much of what is observed comes from the structure of the quantum system itself and how much from the observer's choice of measurement? We explore these questions by…
We identify complete fragments of the Simple Theory of Types with Infinity ($\mathrm{TSTI}$) and Quine's $\mathrm{NF}$ set theory. We show that $\mathrm{TSTI}$ decides every sentence $\phi$ in the language of type theory that is in one of…
Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite set. In this article, we consider a probability distribution generated by an infinite system of…