Related papers: Lack of Finite Characterizations for the Distance-…
A vast and interesting family of natural semantics for belief revision is defined. Suppose one is given a distance d between any two models. One may then define the revision of a theory K by a formula a as the theory defined by the set of…
Prominent approaches to belief revision prescribe the adoption of a new belief that is as close as possible to the prior belief, in a process that, even in the standard case, can be described as attempting to minimize surprise. Here we…
As ontologies and description logics (DLs) reach out to a broader audience, several reasoning services are developed in this context. Belief revision is one of them, of prime importance when knowledge is prone to change and inconsistency.…
We lift metrics over words to metrics over word-to-word transductions, by defining the distance between two transductions as the supremum of the distances of their respective outputs over all inputs. This allows to compare transducers…
We characterize proximity operators, that is to say functions that map a vector to a solution of a penalized least squares optimization problem. Proximity operators of convex penalties have been widely studied and fully characterized by…
The main aim of this article is to prove that for any continuous function $f \colon X \to X$, where $X$ is metrizable (or, more generally, for any family $\mathcal{F}$ of such functions, satisfying an additional condition), there exists a…
When an Approximation Theorist looks at well-posed PDE problems or operator equations, and standard solution algorithms like Finite Elements, Rayleigh-Ritz or Trefftz techniques, methods of fundamental or particular solutions and their…
A perspective function is a construction which combines a base function defined on a given space with a nonlinear scaling function defined on another space and which yields a lower semicontinuous convex function on the product space. Since…
Evaluating large language models (LLMs) is fundamental, particularly in the context of practical applications. Conventional evaluation methods, typically designed primarily for LLM development, yield numerical scores that ignore the user…
This paper discusses belief revision under uncertain inputs in the framework of possibility theory. Revision can be based on two possible definitions of the conditioning operation, one based on min operator which requires a purely ordinal…
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…
Linear head reduction is a key tool for the analysis of reduction machines for lambda-calculus and for game semantics. Its definition requires a notion of redex at a distance named primary redex in the literature. Nevertheless, a clear and…
A formal framework is given for the characterizability of a class of belief revision operators, defined using minimization over a class of partial preorders, by postulates. It is shown that for partial orders characterizability implies a…
Proximal operators are now ubiquitous in non-smooth optimization. Since their introduction in the seminal work of Moreau, many papers have shown their effectiveness on a wide variety of problems, culminating in their use to construct…
We present a new proof of results of Kurdyka & Paunescu, and of Rainer, about real-analytic multi-parameters generalizations of classical results by Rellich and Kato about the reduction in families of univariate deformations of normal…
The paper considers various formalisms based on Automata, Temporal Logic and Regular Expressions for specifying queries over sequences. Unlike traditional binary semantics, the paper presents a similarity based semantics for thse…
An approximate program transformation is a transformation that can change the semantics of a program within a specified empirical error bound. Such transformations have wide applications: they can decrease computation time, power…
Here the definitions of nearest neighbor, robustness, concordance, and correlation, all of which feature in (Temple 2023) (henceforth abbreviated (T23)), are adjusted to make them completely mathematical while preserving their significance.…
The notions of distance and similarity play a key role in many machine learning approaches, and artificial intelligence (AI) in general, since they can serve as an organizing principle by which individuals classify objects, form concepts…
We present several operator versions of the Dunkl--Williams inequality with respect to the $p$-angular distance for operators. More precisely, we show that if $A, B \in \mathbb{B}(\mathscr{H})$ such that $|A|$ and $|B|$ are invertible,…