Related papers: A countable Boolean algebra that is Reichenbach's …

Reichenbach's principle states that in a causal structure, correlations of classical information can stem from a common cause in the common past or a direct influence from one of the events in correlation to the other. The difficulty of…

Causal sets are particular partially ordered sets which have been proposed as a basic model for discrete space-time in quantum gravity. We show that the class C of all countable past-finite causal sets contains a unique causal set (U,<)…

For every uncountable cardinal mu there is a ccc Boolean algebra whose topological density is mu .

We prove the following completeness result about classical realizability: given any Boolean algebra with at least two elements, there exists a Krivine-style classical realizability model whose characteristic Boolean algebra is elementarily…

Characterising cause-effect relationships in complex systems is fundamental to understanding their underlying mechanisms. Granger causality (GC) remains a widely used computational tool for identifying causal relationships in time series…

We show that there exists a canonical topology, naturally connected with the causal site of J. D. Christensen and L. Crane, a pointless algebraic structure motivated by quantum gravity. Taking a causal site compatible with Minkowski space,…

We prove the consistency of: if B_1, B_2 are Boolean algebra satisfying the c.c.c. and the 2^{aleph_0}-c.c. respectively then B_1 x B_2 satisfies the 2^{aleph_0}-c.c.

This paper presents correct algorithms for answering the following two questions; (i) Does there exist a causal explanation consistent with a set of background knowledge which explains all of the observed independence facts in a sample?…

Detecting commonsense causal relations (causation) between events has long been an essential yet challenging task. Given that events are complicated, an event may have different causes under various contexts. Thus, exploiting context plays…

We present necessary and sufficient conditions for the existence of a countably additive measure on a complete Boolean algebra.

Generalized quantum mechanics is used to examine a simple two-particle scattering experiment in which there is a bounded region of closed timelike curves (CTCs) in the experiment's future. The transitional probability is shown to depend on…

A completeness conjecture is advanced concerning the free small-colimit completion P(A) of a (possibly large) category A. The conjecture is based on the existence of a small generating-cogenerating set of objects in A. We sketch how the…

Causal inference revealing causal dependencies between variables from empirical data has found applications in multiple sub-fields of scientific research. A quantum perspective of correlations holds the promise of overcoming the limitation…

We study $C^*$-algebras arising from $C^*$-correspondences, which was introduced by the author. We prove the gauge-invariant uniqueness theorem, and obtain conditions for our $C^*$-algebras to be nuclear, exact, or satisfy the Universal…

For any second countable locally compact group G, we construct a simple G-C*-algebra whose full and reduced crossed product norms coincide. We then construct its G-equivariant representation on another simple G-C*-algebra without the…

In his late piece 'La nouvelle cuisine' (Bell 1990), John Bell describes the steps from an intuitive, informal principle of locality to a mathematical rule called Factorizability. This rule stipulates that when possible past causes are held…

Distinguishing cause from effect is a scientific challenge resisting solutions from mathematics, statistics, information theory and computer science. Compression-Complexity Causality (CCC) is a recently proposed interventional measure of…

The idea of this paper is to explore the existence of canonical countably saturated models for different classes of structures. It is well-known that, under CH, there exists a unique countably saturated linear order of cardinality…

Recent work has unveiled a theory for reasoning about the decisions made by binary classifiers: a classifier describes a Boolean function, and the reasons behind an instance being classified as positive are the prime-implicants of the…

We prove that many seemingly simple theories have Borel complete reducts. Specifically, if a countable theory has uncountably many complete 1-types, then it has a Borel complete reduct. Similarly, if $Th(M)$ is not small, then $M^{eq}$ has…