A Causal Markov Condition for Value

Olav Benjamin Vassend
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:6862-6884, 2026.

Abstract

This paper proposes a causal independence principle for *value*—the *value Causal {Markov} Condition* (v-CMC)—and develops the conceptual and mathematical foundations of a "causal value theory" linking causality and utility. After motivating a local formulation of the v-CMC, we introduce a probability–value duality that translates standard causal-inference results into the value setting. In particular, we formulate local, global, and decomposition versions of the v-CMC and prove their equivalence. We also define $v$-separation and show that it is sound and complete for conditional value independence. Furthermore, we derive a {Bellman}-type recursion as a special case of the v-CMC, thereby generalizing standard {Bellman} recursion from linear chains to causal DAGs. Finally, we show how the v-CMC supports modular transfer and updating of utility information across causal contexts and develop algorithms for causally structured utility elicitation and canonical influence-diagram construction.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-vassend26a, title = {A Causal {Markov} Condition for Value}, author = {Vassend, Olav Benjamin}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {6862--6884}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/vassend26a/vassend26a.pdf}, url = {https://proceedings.mlr.press/v337/vassend26a.html}, abstract = {This paper proposes a causal independence principle for *value*—the *value Causal {Markov} Condition* (v-CMC)—and develops the conceptual and mathematical foundations of a "causal value theory" linking causality and utility. After motivating a local formulation of the v-CMC, we introduce a probability–value duality that translates standard causal-inference results into the value setting. In particular, we formulate local, global, and decomposition versions of the v-CMC and prove their equivalence. We also define $v$-separation and show that it is sound and complete for conditional value independence. Furthermore, we derive a {Bellman}-type recursion as a special case of the v-CMC, thereby generalizing standard {Bellman} recursion from linear chains to causal DAGs. Finally, we show how the v-CMC supports modular transfer and updating of utility information across causal contexts and develop algorithms for causally structured utility elicitation and canonical influence-diagram construction.} }
Endnote
%0 Conference Paper %T A Causal Markov Condition for Value %A Olav Benjamin Vassend %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-vassend26a %I PMLR %P 6862--6884 %U https://proceedings.mlr.press/v337/vassend26a.html %V 337 %X This paper proposes a causal independence principle for *value*—the *value Causal {Markov} Condition* (v-CMC)—and develops the conceptual and mathematical foundations of a "causal value theory" linking causality and utility. After motivating a local formulation of the v-CMC, we introduce a probability–value duality that translates standard causal-inference results into the value setting. In particular, we formulate local, global, and decomposition versions of the v-CMC and prove their equivalence. We also define $v$-separation and show that it is sound and complete for conditional value independence. Furthermore, we derive a {Bellman}-type recursion as a special case of the v-CMC, thereby generalizing standard {Bellman} recursion from linear chains to causal DAGs. Finally, we show how the v-CMC supports modular transfer and updating of utility information across causal contexts and develop algorithms for causally structured utility elicitation and canonical influence-diagram construction.
APA
Vassend, O.B.. (2026). A Causal Markov Condition for Value. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:6862-6884 Available from https://proceedings.mlr.press/v337/vassend26a.html.

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