A Logical Characterization of Constraint-Based Causal Discovery
Abstract
Proof. As the edges in GC represent causal relations, a path of length 0 (no edge) is not considered a causal relation, and existence of a directed path from a variable back to itself would contravene the causal DAG assumption, hence: irreflexive and acyclic (or, more accurate, asymmetric). Transitivity follows immediately, by concatenation, from the sequence 〈X, .., Y, .., Z〉, in which each node is parent of its successor, hence a directed path from X to Z in GC .
Cite
Text
Claassen and Heskes. "A Logical Characterization of Constraint-Based Causal Discovery." Conference on Uncertainty in Artificial Intelligence, 2011.Markdown
[Claassen and Heskes. "A Logical Characterization of Constraint-Based Causal Discovery." Conference on Uncertainty in Artificial Intelligence, 2011.](https://mlanthology.org/uai/2011/claassen2011uai-logical/)BibTeX
@inproceedings{claassen2011uai-logical,
title = {{A Logical Characterization of Constraint-Based Causal Discovery}},
author = {Claassen, Tom and Heskes, Tom},
booktitle = {Conference on Uncertainty in Artificial Intelligence},
year = {2011},
pages = {135-144},
url = {https://mlanthology.org/uai/2011/claassen2011uai-logical/}
}