Related papers: Ellipses and Lambda Definability
We give a principled method for decomposing the predictive uncertainty of a model into aleatoric and epistemic components with explicit semantics relating them to the real-world data distribution. While many works in the literature have…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
In this paper we extend a decision procedure for the Boolean algebra of finite sets with cardinality constraints ($\mathcal{L}_{\lvert\cdot\rvert}$) to a decision procedure for $\mathcal{L}_{\lvert\cdot\rvert}$ extended with set terms…
It is known that the alternation hierarchy of least and greatest fixpoint operators in the mu-calculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of…
Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous…
Dependently typed lambda calculi such as the Logical Framework (LF) are capable of representing relationships between terms through types. By exploiting the "formulas-as-types" notion, such calculi can also encode the correspondence between…
Learning an embedding for a large collection of items is a popular approach to overcome the computational limitations associated to one-hot encodings. The aim of item embedding is to learn a low dimensional space for the representations,…
Graded modalities have been proposed in recent work on programming languages as a general framework for refining type systems with intensional properties. In particular, continuous endomaps of the discrete time scale, or time warps, can be…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
Allen's Interval Algebra constitutes a framework for reasoning about temporal information in a qualitative manner. In particular, it uses intervals, i.e., pairs of endpoints, on the timeline to represent entities corresponding to actions,…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
Generalization problems in languages with binders involve computing the most common structure between expressions while respecting bound variable renaming and freshness constraints. These problems often lack a least general solution.…
Existing sample-based methods, like influence functions and representer points, measure the importance of a training point by approximating the effect of its removal from training. As such, they are skewed towards outliers and points that…
Ellipse and ellipsoid fitting has been extensively researched and widely applied. Although traditional fitting methods provide accurate estimation of ellipse parameters in the low-noise case, their performance is compromised when the noise…
This paper illustrates the richness of the concept of regular sets of time bounds and demonstrates its application to problems of computational complexity. There is a universe of bounds whose regular subsets allow to represent several time…
Lattice-theoretic ideals have been used to define and generate non granular rough approximations over general approximation spaces over the last few years by few authors. The goal of these studies, in relation based rough sets, have been to…
We present a coherent collection of finite mathematical theorems some of which can only be proved by going well beyond the usual axioms for mathematics. The proofs of these theorems illustrate in clear terms how one uses the well studied…
Characterizing rectifiability of Radon measures in Euclidean space has led to fundamental contributions to geometric measure theory. Conditions involving existence of principal values of certain singular integrals…
Accurately quantifying uncertainty in large language models (LLMs) is crucial for their reliable deployment, especially in high-stakes applications. Current state-of-the-art methods for measuring semantic uncertainty in LLMs rely on strict…
Indirect Inference (I-I) estimation of structural parameters $\theta$ {{requires matching observed and simulated statistics, which are most often generated using an auxiliary model that depends on instrumental parameters $\beta$.}} {The…