On Open-Universe Causal Reasoning

Duligur Ibeling; Thomas Icard

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arXiv · 1907.02170

On Open-Universe Causal Reasoning

Duligur Ibeling·Thomas Icard

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Abstract

We extend two kinds of causal models, structural equation models and simulation models, to infinite variable spaces. This enables a semantics for conditionals founded on a calculus of intervention, and axiomatization of causal reasoning for rich, expressive generative models -- including those in which a causal representation exists only implicitly -- in an open-universe setting. Further, we show that under suitable restrictions the two kinds of models are equivalent, perhaps surprisingly as their axiomatizations differ substantially in the general case. We give a series of complete axiomatizations in which the open-universe nature of the setting is seen to be essential.

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Duligur Ibeling, Thomas Icard. 2019-07-04. On Open-Universe Causal Reasoning. https://arxiv.org/abs/1907.02170

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