Related papers: Essential Hereditary Undecidability

This dissertation introduces executable refinement types, which refine structural types by semi-decidable predicates, and establishes their metatheory and accompanying implementation techniques. These results are useful for undecidable type…

Existential rules, long known as tuple-generating dependencies in database theory, have been intensively studied in the last decade as a powerful formalism to represent ontological knowledge in the context of ontology-based query answering.…

Interpretability has arisen as a key desideratum of machine learning models alongside performance. Approaches so far have been primarily concerned with fixed dimensional inputs emphasizing feature relevance or selection. In contrast, we…

We study the variation of $\mu$-invariants of modular forms in a cuspidal Hida family in the case that the family intersects an Eisenstein family. We allow for intersections that occur because of "trivial zeros" (that is, because $p$…

In this paper we introduce a new homology theory devoted to the study of families such as semi-algebraic or subanalytic families and in general to any family definable in an o-minimal structure (such as Denjoy-Carleman definable or $ln-exp$…

We introduce the notions of definable amenability and extreme definable amenability for groups in continuous structures and conduct an extensive analysis of them, drawing parallels with the classical first-order case. We characterize both…

We use variational convergence to derive a hierarchy of one-dimensional rod theories, starting out from three-dimensional models in nonlinear elasticity subject to local volume-preservation. The densities of the resulting $\Gamma$-limits…

Many fundamental problems in extremal combinatorics are equivalent to proving certain polynomial inequalities in graph homomorphism densities. In 2011, a breakthrough result by Hatami and Norine showed that it is undecidable to verify…

For many practical problems, the regression models follow the strong heredity property (also known as the marginality), which means they include parent main effects when a second-order effect is present. Existing methods rely mostly on…

Supervised machine learning models boast remarkable predictive capabilities. But can you trust your model? Will it work in deployment? What else can it tell you about the world? We want models to be not only good, but interpretable. And yet…

We initiate the mathematical study of replicability as an algorithmic property in the context of reinforcement learning (RL). We focus on the fundamental setting of discounted tabular MDPs with access to a generative model. Inspired by…

We introduce the notion of a restricted exchangeable partition of $\mathbb{N}$. We obtain integral representations, consider associated fragmentations, embeddings into continuum random trees and convergence to such limit trees. In…

We investigate the logical strength of the cohesiveness principle when restricted to finite sequences of sets, denoted by fin-COH, over different base theories. Our main result shows that fin-COH entails $I\Sigma_1^0$ over the weaker base…

Access limitations are restrictions in the way in which the tuples of a relation can be accessed. Under access limitations, query answering becomes more complex than in the traditional case, with no guarantee that the answer tuples that can…

We prove the decidability of Ticket Entailment. Raised by Anderson and Belnap within the framework of relevance logic, this question is equivalent to the question of the decidability of type inhabitation in simply-typed combinatory logic…

In this work, we obtain an existence of nontrivial solutions to a minimization problem involving a fractional Hardy-Sobolev type inequality in the case of inner singularity. Precisely, for $\lambda>0$ we analyze the attainability of the…

Let $\Lambda$ be a Legendrian in the jet space of some manifold $X$. To a generating family presentation of $\Lambda$, we associate a constructible sheaf on $X \times \mathbb{R}$ whose singular support at infinity is $\Lambda$, and such…

Assuming a certain form of resolution of singularities, we prove a general existential Ax-Kochen/Ershov principle for tamely ramified fields in all characteristics. This specializes to well-known results in residue characteristic $0$ and…

Machine Learning explainability techniques have been proposed as a means of `explaining' or interrogating a model in order to understand why a particular decision or prediction has been made. Such an ability is especially important at a…

Similarity-sensitive entropy measures the uncertainty of a probability law relative to a similarity kernel that encodes the distinguishability between states. We develop a measure-theoretic treatment covering both finite similarity matrices…