Related papers: Dependence and Independence
This paper investigates formal logics for reasoning about determinacy and independence. Propositional Dependence Logic D and Propositional Independence Logic I are recently developed logical systems, based on team semantics, that provide a…
Atomism is the view that everything is composed of atoms. The view within the framework of the contemporary formal approach is expressed on the ground of mereology with the use of the primitive notion of being a part as every object has at…
We investigate operator-valued monotone independence, a noncommutative version of independence for conditional expectation. First we introduce operator-valued monotone cumulants to clarify the whole theory and show the moment-cumulant…
Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…
In this paper we construct an entire function of two variables having the property that its values and its partial derivatives of any order at any distinct algebraic points are algebraically independent. Such an entire function is generated…
A recently proposed axiom system for Andr\'e's central translation structures is improved upon. First, one of its axioms turns out to be dependent (derivable from the other axioms). Without this axiom, the axiom system is indeed…
Two known results on the relationship between conditional and unconditional independence are obtained as a consequence of the main result of this paper, a theorem that uses independence of Markov kernels to obtain a minimal condition which…
We examine the relationship between Dependence Logic and game logics. A variant of Dynamic Game Logic, called Transition Logic, is developed, and we show that its relationship with Dependence Logic is comparable to the one between…
Any scientific attempt to explain consciousness is tasked with reconciling the third person objective perspective of science with our first person subjective experience of the world. A good point of departure is to consider situations in…
Conditional independence has been widely used in AI, causal inference, machine learning, and statistics. We introduce categoroids, an algebraic structure for characterizing universal properties of conditional independence. Categoroids are…
Intuitionistic dependence logic was introduced by Abramsky and Vaananen (2009) as a variant of dependence logic under a general construction of Hodges' (trump) team semantics. It was proven that there is a translation from intuitionistic…
We present Lilac, a separation logic for reasoning about probabilistic programs where separating conjunction captures probabilistic independence. Inspired by an analogy with mutable state where sampling corresponds to dynamic allocation, we…
Understanding and quantifying causal relationships between variables is essential for reasoning about the physical world. In this work, we develop a resource-theoretic framework to do so. Here, we focus on the simplest nontrivial setting --…
Both propositional dependence logic and inquisitive logic are expressively complete. As a consequence, every formula with intuitionistic disjunction or intuitionistic implication can be translated equivalently into a formula in the language…
Mathematical proof aims to deliver confident conclusions, but a very similar process of deduction can be used to make uncertain estimates that are open to revision. A key ingredient in such reasoning is the use of a "default" estimate of…
We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…
We establish a generic result concerning order independence of a dominance relation on finite games. It allows us to draw conclusions about order independence of various dominance relations in a direct and simple way.
In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular…
We postulate a principle stating that the initial condition of a physical system is typically algorithmically independent of the dynamical law. We argue that this links thermodynamics and causal inference. On the one hand, it entails…
Recognizing, quantifying and visualizing associations between two variables is increasingly important. This paper investigates how a new function-valued measure of dependence, the quantile dependence function, can be used to construct tests…