Abstract We study higher analogues of the classical independence number on $\omega $ . For $\kappa regular uncountable, we denote by $i(\kappa )$ minimal size a maximal -independent family. establish ZFC relations between and standard some cardinal characteristics, e.g., $\mathfrak {r}(\kappa )\leq \mathfrak {i}(\kappa {d}(\kappa measurable, assuming that $2^{\kappa }=\kappa ^{+}$ construct fam...

This paper studies the interrelations between independence or conditional independence and causal relations, defined in terms of functional dependence, that hold among variables of interest within the settable system framework of White and Chalak. We provide formal conditions ensuring the validity of Reichenbach’s principle of common cause and introduce a new conditional counterpart, the condit...

Mutual stochastic independences among-algebras and mutual algebraic inde-pendences among elements of semimodular lattices are observed to have a very similar behaviour. We suggest abstract independence structures called I-relations describing it. Presented examination of I-relations resembles a theory of abstract connectedness: a dual characterization of I-relations by families of connected set...

Knowledge about complex events is usually incomplete in practice. Zeros can be utilized to capture such events within probability models. In this article, Geiger and Pearl’s conditional probabilistic independence statements are investigated in the presence of zeros. Random variables can be specified to be zero-free, i.e., to disallow zeros in their domains. Zero-free random variables provide an...

BACKGROUND Progressive independence is a traditional premise of clinical training. Recently, issues such as managed care, work hours limitation, and patient safety have begun to impact the degree of autonomy afforded to clinical trainees. This article reviews empirical evidence and theory pertaining to the role of progressive autonomy in clinical learning. METHOD A computerized literature sea...

The current ubiquity of multi-core processors has brought renewed interest in program parallelization. Logic programs allow studying the parallelization of programs with complex, dynamic data structures with (declarative) pointers in a comparatively simple semantic setting. In this context, automatic parallelizers which exploit and-parallelism rely on notions of independence in order to ensure ...