Related papers: Domains, Information Frames, Rough Sets: An Equiva…
In this paper we formalize the notions of information elements and information lattices, first proposed by Shannon. Exploiting this formalization, we identify a comprehensive parallelism between information lattices and subgroup lattices.…
Arrays are ubiquitous in the context of software verification. However, effective reasoning over arrays is still rare in CP, as local reasoning is dramatically ill-conditioned for constraints over arrays. In this paper, we propose an…
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…
For pixel-level crowd understanding, it is time-consuming and laborious in data collection and annotation. Some domain adaptation algorithms try to liberate it by training models with synthetic data, and the results in some recent works…
Our work is a fundamental study of the notion of approximation in V-categories and in (U,V)-categories, for a quantale V and the ultrafilter monad U. We introduce auxiliary, approximating and Scott-continuous distributors, the way-below…
Factual consistency is one of important summary evaluation dimensions, especially as summary generation becomes more fluent and coherent. The ESTIME measure, recently proposed specifically for factual consistency, achieves high correlations…
As Web sites are now ordinary products, it is necessary to explicit the notion of quality of a Web site. The quality of a site may be linked to the easiness of accessibility and also to other criteria such as the fact that the site is up to…
Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise)…
We present new information-theoretic generalization guarantees through the a novel construction of the "neighboring-hypothesis" matrix and a new family of stability notions termed sample-conditioned hypothesis (SCH) stability. Our approach…
Formal Concept Analysis (FCA) begins from a context, given as a binary relation between some objects and some attributes, and derives a lattice of concepts, where each concept is given as a set of objects and a set of attributes, such that…
Various frameworks that generalise the notion of contextuality in theories of physics have been proposed; one is the sheaf-theoretic approach by Abramsky and Brandenburger; an other is the equivalence-based approach by Spekkens. We show…
New Foundations ($\mathrm{NF}$) is a set theory obtained from naive set theory by putting a stratification constraint on the comprehension schema; for example, it proves that there is a universal set $V$. $\mathrm{NFU}$ ($\mathrm{NF}$ with…
Logic programming under the answer-set semantics nowadays deals with numerous different notions of program equivalence. This is due to the fact that equivalence for substitution (known as strong equivalence) and ordinary equivalence are…
We provide both a general framework for discretizing de Rham sequences of differential forms of high regularity, and some examples of finite element spaces that fit in the framework. The general framework is an extension of the previously…
Recently, Wang et al. discussed the properties of fuzzy information systems under homomorphisms in the paper [C. Wang, D. Chen, L. Zhu, Homomorphisms between fuzzy information systems, Applied Mathematics Letters 22 (2009) 1045-1050], where…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching…
Categorization axioms have been proposed to axiomatizing clustering results, which offers a hint of bridging the difference between human recognition system and machine learning through an intuitive observation: an object should be assigned…
Human ratings have become a crucial resource for training and evaluating machine learning systems. However, traditional elicitation methods for absolute and comparative rating suffer from issues with consistency and often do not distinguish…
Using the concepts of category and functor, we provide some insights and prove an intrinsic property of the category ${\bf AprS}$ of approximation spaces and relation-preserving functions, the category ${\bf RCls}$ of rough closure spaces…