Related papers: Equilibria und weiteres Heiteres II
We investigate the notion of independence, which is at the basis of many, seemingly unrelated, properties of logic like Rational Monotony in non-monotonic logics, and interpolation theorems.
We investigate several technical and conceptual questions.
In this work in progress, we discuss independence and interpolation and related topics for classical, modal, and non-monotonic logics.
It has been widely acknowledged that probabilistic independence and logical independence cannot be coherently reconciled. By bridging these two notions, this paper addresses three long-standing problems that have puzzled the field of…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
We introduce the concepts of dependence and independence in a very general framework. We use a concept of rank to study dependence and independence. By means of the rank we identify (total) dependence with inability to create more…
We give an overview of some developments in dependence and independence logic. This is a tiny selection, intended for a newcomer, from a rapidly growing literature on the topic. Furthermore, we discuss conditional independence atoms and we…
Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…
We continue the work on the relations between independence logic and the model-theoretic analysis of independence, generalizing the results of [15] and [16] to the framework of abstract independence relations for an arbitrary AEC. We give a…
This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete…
Possibilistic conditional independence is investigated: we propose a definition of this notion similar to the one used in probability theory. The links between independence and non-interactivity are investigated, and properties of these…
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…
An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability…
A. Tarski proposed the study of infinitary consequence operations as the central topic of mathematical logic. He considered monotonicity to be a property of all such operations. In this paper, we weaken the monotonicity requirement and…
Meixner's historical remark in 1969 "... it can be shown that the concept of entropy in the absence of equilibrium is in fact not only questionable but that it cannot even be defined...." is investigated from today's insight. Several…
We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its…
A lattice-theoretic framework is introduced that permits the study of the conditional independence (CI) implication problem relative to the class of discrete probability measures. Semi-lattices are associated with CI statements and a…
A lattice-theoretic framework is introduced that permits the study of the conditional independence (CI) implication problem relative to the class of discrete probability measures. Semi-lattices are associated with CI statements and a…
Using the Hilbert-Bernays account as a spring-board, we first define four ways in which two objects can be discerned from one another, using the non-logical vocabulary of the language concerned. (These definitions are based on definitions…
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…