Related papers: Natural Density and The Quantifier 'Most'
The concept of majority domination in graphs has been defined in at least two different ways: As a function and as a set. In this work we extend the latter concept to digraphs, while the former was extended in another paper. Given a digraph…
The Chapter starts with introductory information about quantitative linguistics notions, like rank--frequency dependence, Zipf's law, frequency spectra, etc. Similarities in distributions of words in texts with level occupation in quantum…
Many organizations describe their processes as consensus-driven, but there is no consensus on the definition of consensus. Qualitative definitions of consensus prioritize social phenomena like "unity" that are not necessarily measurable.…
Compositionality in language refers to how much the meaning of some phrase can be decomposed into the meaning of its constituents and the way these constituents are combined. Based on the premise that substitution by synonyms is…
Sentences are important semantic units of natural language. A generic, distributional representation of sentences that can capture the latent semantics is beneficial to multiple downstream applications. We observe a simple geometry of…
Single document summarization has enjoyed renewed interests in recent years thanks to the popularity of neural network models and the availability of large-scale datasets. In this paper we develop an unsupervised approach arguing that it is…
Language modeling, a central task in natural language processing, involves estimating a probability distribution over strings. In most cases, the estimated distribution sums to 1 over all finite strings. However, in some pathological cases,…
For a probability distribution $P$ on an at most countable alphabet $\mathcal A$, this article gives finite sample bounds for the expected occupancy counts $\mathbb E K_{n,r}$ and probabilities $\mathbb E M_{n,r}$. Both upper and lower…
Probability densities that are not uniquely determined by their moments are said to be "moment-indeterminate", or "M-indeterminate". Determining whether or not a density is M-indeterminate, or how to generate an M-indeterminate density, is…
A repeated claim in linguistics is that the majority of linguistic utterances are unique. For example, Pinker (1994: 10), summarizing an argument by Noam Chomsky, states that "virtually every sentence that a person utters or understands is…
We improve a recent result by giving the optimal conclusion possible both to the frequent universality criterion and the frequent hypercyclicity criterion using the notion of A-densities, where A refers to some weighted densities sharper…
Density operators allow for representing ambiguity about a vector representation, both in quantum theory and in distributional natural language meaning. Formally equivalently, they allow for discarding part of the description of a composite…
We propose a probabilistic approach to select a subset of a \textit{target domain representative keywords} from a candidate set, contrasting with a context domain. Such a task is crucial for many downstream tasks in natural language…
Given $\mathscr{B}\subseteq \mathbb{N}$, let $\mathcal{M}_\mathscr{B}=\bigcup_{b\in\mathscr{B}}b\mathbb{Z}$ be the correspoding set of multiples. We say that $\mathscr{B}$ is taut if the logarithmic density of $\mathcal{M}_\mathscr{B}$…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
The density matrix formalism which is widely used in the theory of measurements, quantum computing, quantum description of chemical and biological systems always imply the averaging over the states of the environment. In practice this is…
We relate two measures of complexity of regular languages. The first is syntactic complexity, that is, the cardinality of the syntactic semigroup of the language. That semigroup is isomorphic to the semigroup of transformations of states…
Theoretically as well as experimentally it is investigated how people represent their knowledge in order to make decisions or to share their knowledge with others. Experiment 1 probes into the ways how people 6ather information about the…
We introduce the notion of density of a rational language with respect to a sequence of probability measures. We prove that if $(\mu_n)$ is a sequence of Bernoulli measures converging to a positive Bernoulli measure $\overline{\mu}$, the…
A semi-measure is a generalization of a probability measure obtained by relaxing the additivity requirement to super-additivity. We introduce and study several randomness notions for left-c.e. semi-measures, a natural class of effectively…