Related papers: Some thoughts upon axiomatized languages with este…
Query expansion is an effective approach for mitigating vocabulary mismatch between queries and documents in information retrieval. One recent line of research uses language models to generate query-related contexts for expansion. Along…
This paper studies the complexity of languages of finite words using automata theory. To go beyond the class of regular languages, we consider infinite automata and the notion of state complexity defined by Karp. Motivated by the seminal…
In the principles-and-parameters framework, the structural features of languages depend on parameters that may be toggled on or off, with a single parameter often dictating the status of multiple features. The implied covariance between…
We first study probabilistic dynamical systems from logical perspective. To this purpose, we introduce the finitary dynamic probability logic} ($\mathsf{DPL}$), as well as its infinitary extension $\mathsf{DPL}_{\omega_1}\!$. Both these…
Languages are not created randomly but rather to communicate information. There is a strong association between languages and their underlying meanings, resulting in a sparse joint distribution that is heavily peaked according to their…
Large language models (LLMs) are increasingly used in group decision-making, but their influence risks fostering conformity and reducing epistemic vigilance. Drawing on the Argumentative Theory of Reasoning, we argue that confirmation bias,…
The compound Poisson process and the Dirichlet process are the pillar structures of Renewal theory and Bayesian nonparametric theory, respectively. Both processes have many useful extensions to fulfill the practitioners needs to model the…
We derive new explicit bounds for the total variation distance between two convolution products of $n$ probability distributions, one of which having identical convolution factors. Approximations by finite signed measures of arbitrary order…
A reasonably complete theory of the approximation of an irrational by rational fractions whose numerators and denominators lie in prescribed arithmetic progressions is developed in this paper. Results are both, on the one hand, from a…
The multinomial language model has been one of the most effective models of retrieval for over a decade. However, the multinomial distribution does not model one important linguistic phenomenon relating to term-dependency, that is the…
We survey the classical results of the Dirichlet Approximation Theorem.
The paper presents probabilistic extensions of interval temporal logic (ITL) and duration calculus (DC) with infinite intervals and complete Hilbert-style proof systems for them. The completeness results are a strong completeness theorem…
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…
Eilenberg-type correspondences, relating varieties of languages (e.g. of finite words, infinite words, or trees) to pseudovarieties of finite algebras, form the backbone of algebraic language theory. Numerous such correspondences are known…
We came across an unexpected connection between a remarkable grammar of Dumont for the joint distribution of $(\exc, \fix)$ over $S_n$ and a beautiful theorem of Diaconis-Evans-Graham on successions and fixed points of permutations. With…
Recent developments in the theory and application of the Hardy-Littlewood method are discussed, concentrating on aspects associated with diagonal diophantine problems. Recent efficient differencing methods for estimating mean values of…
We give an algorithmic-bijective proof of Macdonald's reduced word identity in the theory of Schubert polynomials, in the special case where the permutation is dominant. Our bijection uses a novel application of David Little's generalized…
Distributed linguistic representations are powerful tools for modelling the uncertainty and complexity of preference information in linguistic decision making. To provide a comprehensive perspective on the development of distributed…
We establish arithmetical properties and provide essential bounds for bi-sequences of approximation coefficients associated with the natural extension of maps, leading to continued fraction-like expansions. These maps are realized as the…
We consider the classical problem of discrete distribution estimation using i.i.d. samples in a novel scenario where additional side information is available on the distribution. In large alphabet datasets such as text corpora, such side…