Related papers: Natural Density and The Quantifier 'Most'
Generic sentences express generalisations about the world without explicit quantification. Although generics are central to everyday communication, building a precise semantic framework has proven difficult, in part because speakers use…
Recent years have witnessed a renewed interest in Boolean function in explaining binary classifiers in the field of explainable AI (XAI). The standard approach of Boolean function is propositional logic. We present a modal language of a…
ZFC has sentences that quantify over all sets or all ordinals, without restriction. Some have argued that sentences of this kind lack a determinate meaning. We propose a set theory called TOPS, using Natural Deduction, that avoids this…
The density of a rational language can be understood as the frequency of some "pattern" in the shift space, for example a pattern like "words with an even number of a given letter." We study the density of group languages, i.e. rational…
Functional Distributional Semantics provides a computationally tractable framework for learning truth-conditional semantics from a corpus. Previous work in this framework has provided a probabilistic version of first-order logic, recasting…
A number of writers(Joseph Halpern and Fahiem Bacchus among them) have offered semantics for formal languages in which inferences concerning probabilities can be made. Our concern is different. This paper provides a formalization of…
We introduce a method to measure uncertainty in large language models. For tasks like question answering, it is essential to know when we can trust the natural language outputs of foundation models. We show that measuring uncertainty in…
Word meaning has different aspects, while the existing word representation "compresses" these aspects into a single vector, and it needs further analysis to recover the information in different dimensions. Inspired by quantum probability,…
Natural language semantics has recently sought to combine the complementary strengths of formal and distributional approaches to meaning. More specifically, proposals have been put forward to augment formal semantic machinery with…
Most research on natural language processing treats bias as an absolute concept: Based on a (probably complex) algorithmic analysis, a sentence, an article, or a text is classified as biased or not. Given the fact that for humans the…
Arithmetic quasi-densities are a large family of real-valued set functions partially defined on the power set of $\mathbb{N}$, including the asymptotic density, the Banach density, the analytic density, etc. Let $B \subseteq \mathbb{N}$ be…
A stereotype is a generalized perception of a specific group of humans. It is often potentially encoded in human language, which is more common in texts on social issues. Previous works simply define a sentence as stereotypical and…
A More Sums Than Differences (MSTD, or sum-dominant) set is a finite set $A\subset \mathbb{Z}$ such that $|A+A|<|A-A|$. Though it was believed that the percentage of subsets of $\{0,...,n\}$ that are sum-dominant tends to zero, in 2006…
Sentiment quantification is the task of training, by means of supervised learning, estimators of the relative frequency (also called ``prevalence'') of sentiment-related classes (such as \textsf{Positive}, \textsf{Neutral},…
We define {\em semantic complexity} using a new concept of {\em meaning automata}. We measure the semantic complexity of understanding of prepositional phrases, of an "in depth understanding system", and of a natural language interface to…
Let $\mathcal{P}$ and $\mathbb{N}$ be the sets of all primes and natural numbers, respectively. In this article, it is proved that there has a positive lower density of the natural numbers which can be represented by the form…
In a recent work, arXiv:2503.05884, we proposed a unified notion of nonclassicality that applies to arbitrary processes in quantum theory, including individual quantum states, measurements, channels, set of these, etc. This notion is…
During the last decades, a lot of effort was put into identifying decidable fragments of first-order logic. Such efforts gave birth, among the others, to the two-variable fragment and the guarded fragment, depending on the type of…
Classification is the task of predicting the class labels of objects based on the observation of their features. In contrast, quantification has been defined as the task of determining the prevalences of the different sorts of class labels…
Applications of large language models often involve the generation of free-form responses, in which case uncertainty quantification becomes challenging. This is due to the need to identify task-specific uncertainties (e.g., about the…