aqora

Characterizing common cause closedness of quantum probability theories

Yuichiro Kitajima, Miklós Rédei

arXiv:1503.04410Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern PhysicsSep 8, 20154 citations

Causal Completeness in General Probability Theories

Balázs Gyenis, Miklós Rédei

Springer eBooksSep 21, 20109 citations

Common Cause Completability of Classical and Quantum Probability Spaces

Gábor Hofer‐Szabó, Miklós Rédei, László E. Szabó

International Journal of Theoretical PhysicsMar 1, 200022 citations

Causal completeness of probability theories — Results and open problems

Miklós Rédei, Balázs Gyenis

The aim of this paper is to give a review of the known results and open problems concerning causal completeness (closedness) of classical and non-classical (quantum) probability spaces. Causal closedness of a probabilistic theory means that the theory is causally rich enough to be able to explain causally all the correlations it predicts. It is natural to ask whether probabilistic theories are causally closed if one assumes that Reichenbach’s Common Cause Principle holds: this principle states that if two events A and B are probabilistically correlated then either the correlation is due to a causal interaction between A and B, or, if A and B are causally independent, Rind(A,B), then there exists a third event C, a so-called common cause that explains the correlation by being related to A and B probabilistically in a specific way (see Definition 1). Causal closedness of a probabilistic theory is intended to express that the theory complies with the Common Cause Principle; accordingly, and more precisely, a probability theory is defined to be causally closed with respect to a causal independence relationThe aim of this paper is to give a review of the known results and open problems concerning causal completeness (closedness) of classical and non-classical (quantum) probability spaces. Causal closedness of a probabilistic theory means that the theory is causally rich enough to be able to explain causally all the correlations it predicts. It is natural to ask whether probabilistic theories are causally closed if one assumes that Reichenbach’s Common Cause Principle holds: this principle states that if two events A and B are probabilistically correlated then either the correlation is due to a causal interaction between A and B, or, if A and B are causally independent, Rind(A,B), then there exists a third event C, a so-called common cause that explains the correlation by being related to A and B probabilistically in a specific way (see Definition 1). Causal closedness of a probabilistic theory is intended to express that the theory complies with the Common Cause Principle; accordingly, and more precisely, a probability theory is defined to be causally closed with respect to a causal independence relation

Oxford University Press eBooksMar 17, 20113 citations

Completion of the Causal Completability Problem

Michał Marczyk, Leszek Wroński

We give a few results concerning the notions of causal completability and causal closedness of classical probability spaces (Hofer-Szabó et al. [1999]; Gyenis and Rédei [2004]). We prove that (i) any classical probability space has a causally closed extension; (ii) any finite classical probability space with positive rational probabilities on the atoms of the event algebra can be extended to a causally up-to-three-closed finite space; and (iii) any classical probability space can be extended to a space in which all correlations between events that are logically independent modulo measure zero event have a countably infinite common-cause system. Collectively, these results show that it is surprisingly easy to find Reichenbach-style ‘explanations' for correlations, underlining doubts as to whether this approach can yield a philosophically relevant account of causality. 1 Introduction2 Basic Definitions and Results in the Literature3 Causal Completability the Easy Way: ‘Splitting the Atom’4 Causal Completability of Classical Probability Spaces: The General Case5 Infinite Statistical Common-Cause Systems for Arbitrary Pairs6 Conclusion Appendix AWe give a few results concerning the notions of causal completability and causal closedness of classical probability spaces (Hofer-Szabó et al. [1999]; Gyenis and Rédei [2004]). We prove that (i) any classical probability space has a causally closed extension; (ii) any finite classical probability space with positive rational probabilities on the atoms of the event algebra can be extended to a causally up-to-three-closed finite space; and (iii) any classical probability space can be extended to a space in which all correlations between events that are logically independent modulo measure zero event have a countably infinite common-cause system. Collectively, these results show that it is surprisingly easy to find Reichenbach-style ‘explanations' for correlations, underlining doubts as to whether this approach can yield a philosophically relevant account of causality. 1 Introduction2 Basic Definitions and Results in the Literature3 Causal Completability the Easy Way: ‘Splitting the Atom’4 Causal Completability of Classical Probability Spaces: The General Case5 Infinite Statistical Common-Cause Systems for Arbitrary Pairs6 Conclusion Appendix A

The British Journal for the Philosophy of ScienceMar 23, 201417 citations

When Can Statistical Theories Be Causally Closed?

Balázs Gyenis, Miklós Rédei

Foundations of PhysicsSep 1, 200422 citations

A Note on Strong Causal Closedness and Completability of Classical Probability Spaces

Related papers

A Note on Strong Causal Closedness and Completability of Classical Probability Spaces

Related papers