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A formal proof of the Sands-Sauer-Woodrow theorem using the Rocq prover and mathcomp/ssreflect
Jean-Philippe Chancelier
We present a formal proof of the Sands-Sauer-Woodrow (SSW) theorem using the Rocq proof assistant and the MathComp/SSReflect library. The SSW theorem states that in a directed grap…
Causal Inference Theory with Information Dependency Models
Benjamin Heymann, Michel de Lara, Jean-Philippe Chancelier
Inferring the potential consequences of an unobserved event is a fundamental scientific question. To this end, Pearl's celebrated do-calculus provides a set of inference rules to d…
Topological Conditional Separation
Michel de Lara, Jean-Philippe Chancelier, Benjamin Heymann
Pearl's d-separation is a foundational notion to study conditional independence between random variables. We define the topological conditional separation and we show that it is eq…
Conditional Separation as a Binary Relation. A Coq Assisted Proof
Jean-Philippe Chancelier, Michel de Lara, Benjamin Heymann
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 defin…