Conditional Separation as a Binary Relation.

Jean-Philippe Chancelier (1) , Michel de Lara (1) , Benjamin Heymann (2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 Criteo [Paris]

The concept of d-separation holds a pivotal role in causality theory, serving as a fundamental tool for deriving conditional independence properties from causal graphs. Pearl defined the d-separation of two subsets conditionally on a third one. In this study, we present a novel perspective by showing i) how the d-separation can be extended beyond acyclic graphs, possibly infinite, and ii) how it can be expressed and characterized as a binary relation between vertices. Compared to the typical perspectives in causality theory, our equivalence opens the door to more compact and computational proofing techniques, because the language of binary relations is well adapted to equational reasoning. Additionally, and of independent interest, the proofs of the results presented in this paper are checked with the Coq proof assistant.

Mots clés: d-separation; causality; binary relations; conditional independence; Coq

Domaines: Mathématique discrète [cs.DM]; Mathématiques générales [math.GM]; Théorie de l'information et codage [math.IT]

Jean-Philippe Chancelier, Michel de Lara, Benjamin Heymann. Conditional Separation as a Binary Relation.: A Coq Assisted Proof. 2024. ⟨hal-03315809v3⟩