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LIT-1316: Abstracting Causal Models

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StatusActive — read 2026-10-21 (NOTE-1032) in full, from arXiv:1812.03789v4; worth reading for the examples that show exact transformation too permissive, for the characterization of exactness under every distribution as a context map commuting with every allowed intervention (THEORY-849), and for the ladder τ-abstraction, strong and constructive abstraction. Read it knowing that its Theorem 3.8 omits the countability its proof uses, that the context map is only required to exist, so high-level noise may hold what the coarse state drops, and that every strong abstraction being constructive is a conjecture.
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Tagscausality
Cited as “paper” byNOTE-1032 — Beckers and Halpern — Abstracting causal models
Cited as “source” byTHEORY-843 — Beckers, Eberhardt and Halpern's approximate abstraction error, the least over surjective context maps of the worst case over allowed interventions and contexts of the high-level distance between the coarse-grained low-level outcome and the high-level outcome, is zero exactly for τ-abstraction; an abstraction followed by an α-approximation of the high-level model is within α, an α-approximation of the low-level model followed by an abstraction only within kα, k the worst-case ratio of high- to low-level distances, and an approximate abstraction need not factor into an exact abstraction and an approximation, THEORY-847 — In a linear structural equation model whose exogenous micro-causes W₁, …, W_n drive effects Z = AW + F, with interventions that set all of W, all of Z or both, averaging each block is an exact transformation onto Ẑ = (an/m)Ŵ + F̂ if and only if every column of A sums to the same a, the column-equitability of the block of A from W to Z; the transformation is exact only for those whole-block interventions, THEORY-849 — For deterministic causal models with a countable set of allowed interventions, a high-level model reproduces the coarse-grained interventional law of a low-level one for every distribution on contexts exactly when some map τ_U on contexts commutes with every allowed intervention, τ(M_L(u, i)) = M_H(τ_U(u), ω(i)); exactness for one distribution is strictly weaker, since a well-chosen distribution lets unrelated models match, and τ-abstraction and strong abstraction are strictly stronger; the context map is only required to exist, so high-level exogenous variables may carry what the coarse state drops

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Beckers, S. & Halpern, J. Y. (2019). Abstracting Causal Models. Proceedings of the AAAI Conference on Artificial Intelligence 33(01): 2678–2685. doi:10.1609/aaai.v33i01.33012678. Preprint: arXiv:1812.03789 (10 December 2018).

Read in full (NOTE-1032).

Why this is here

The middle step of A25’s lineage, “different strengths of causal abstraction”. Which strength governance-response sufficiency needs is part of what CLAIM-407 and CLAIM-409 have to say. LIT-038’s status note already points a reader to Beckers–Halpern.

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