The Topology of Causality
Stefano Gogioso, Nicola Pinzani

TL;DR
This paper develops a comprehensive, theory-independent framework for understanding causality, non-locality, and contextuality using sheaf theory, extending previous models to include arbitrary causal orders and revealing new phenomena like causally-induced contextuality.
Contribution
It introduces a unified operational framework for causality that encompasses arbitrary causal orders and extends sheaf-theoretic approaches to include dynamical and indefinite causal structures.
Findings
Causality is equivalent to continuity in the lowerset topology.
Causal functions can be organized into a presheaf, but may not always form a sheaf.
Causally-induced contextuality can arise when causal constraints are context-dependent.
Abstract
We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. Our work has its roots in the sheaf-theoretic framework for contextuality by Abramsky and Brandenburger, which it extends to include arbitrary causal orders (be they definite, dynamical or indefinite). We define a notion of causal function for arbitrary spaces of input histories, and we show that the explicit imposition of causal constraints on joint outputs is equivalent to the free assignment of local outputs to the tip events of input histories. We prove factorisation results for causal functions over parallel, sequential, and conditional sequential compositions of the underlying spaces. We prove that causality is equivalent to continuity with respect to the lowerset topology on the underlying spaces, and we show that…
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Taxonomy
TopicsPhilosophy and History of Science · Bayesian Modeling and Causal Inference
