Related papers: Abstract independence relations in neostability th…
A framework for quantifying dependence between random vectors is introduced. With the notion of a collapsing function, random vectors are summarized by single random variables, called collapsed random variables in the framework. Using this…
In dialogical argumentation it is often assumed that the involved parties always correctly identify the intended statements posited by each other, realize all of the associated relations, conform to the three acceptability states (accepted,…
This paper provides a full characterization for when the expansion of a complete o-minimal theory by a unary predicate that picks out a divisible dense and codense subgroup has a model companion. This result is motivated by criteria and…
We extend the treatment of functional dependence, the basic concept of dependence logic, to include the possibility of dependence with a limited number of exceptions. We call this approximate dependence. The main result of the paper is a…
In the first part we show a counterexample to a conjecture by Shelah regarding the existence of indiscernible sequences in dependent theories (up to the first inaccessible cardinal). In the second part we discuss generic pairs, and give an…
We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are non-nested and their intersection is a union of two marginal independences. We consider two sequences of such…
In any known description of nature, two physical systems are considered independent of each other if any action on one of the systems does not change the other system. From our classical intuitions about the world, we further conclude that…
We study dependence and independence concepts found in quantum physics, especially those related to hidden variables and non-locality, through the lens of team semantics and probabilistic team semantics, adapting a relational framework…
This paper takes a different look on the problem of testing the mutual independence of the components of a high-dimensional vector. Instead of testing if all pairwise associations (e.g. all pairwise Kendall's $\tau$) between the components…
An elementary rheory of concatenation is introduced and used to establish mutual interpretability of Robinson arithmetic, Minimal Predicative Set Theory, the quantifier-free part of Kirby's finitary set theory, and Adjunctive Set Theory,…
We observe that a simple condition suffices to describes non-forking independence over models in a stable theory. Under mild assumptions, this description can be extended to non-forking independence over algebraically closed subsets,…
We present a new scheme of defining invariant observables for general relativistic systems. The scheme is based on the introduction of an observer which endowes the construction with a straightforward physical interpretation. The…
We improve upon Huntington's affine geometry by showing that his independence proofs can be, in some cases, simplified. We carry out a systematic investigation of the strict notion of betweenness that Huntington employs (the three arguments…
The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic…
This work explores the connection between logical independence and the algebraic structure of quantum mechanics. Building on results by Brukner et al., it introduces the notion of \textit{onto-epistemic ignorance}: situations in which the…
We introduce a notion of non-commutative joint independence for multiple algebras in a non-commutative probability space. The pairwise relationships between these algebras are encoded by a graph with two edge sets -- a combinatorial…
As it was argued by Anderson [Science 177, 393 (1972)], the "reductionist" hypothesis does not by any means imply a "constructionist" one. Hence, in general, the behavior of large and complex aggregates of elementary components can not be…
We propose and axiomatize preferences on a product state space in light of uncertainty regarding the dependency of different payoff-relevant factors. Dependence structures allow to decompose probabilities and allow to pin down behavior…
We study model theoretic tree properties ($\text{TP}, \text{TP}_1, \text{TP}_2$) and their associated cardinal invariants ($\kappa_{\text{cdt}}, \kappa_{\text{sct}}, \kappa_{\text{inp}}$, respectively). In particular, we obtain a…
Syntax is a latent hierarchical structure which underpins the robust and compositional nature of human language. In this work, we explore the hypothesis that syntactic dependencies can be represented in language model attention…