# Reducing Causality to Functions with Structural Models

arXiv: https://arxiv.org/abs/2307.07524 · HTML: https://mlsanity.com/paper/2307.07524/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 77 references that are in the map.
- First posted on arXiv 11 Jul 2023.

## Builds on (most cited first, 3 of 3)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Graded Causation and Defaults](https://mlsanity.com/paper/1309.1226/) (2013)
- [On Dependence Logic](https://mlsanity.com/paper/1305.5948/) (2013)

## Abstract (arXiv)

The precise definition of causality is currently an open problem in philosophy and statistics. We believe causality should be defined as functions (in mathematics) that map causes to effects. We propose a reductive definition of causality based on Structural Functional Model (SFM). Using delta compression and contrastive forward inference, SFM can produce causal utterances like "X causes Y" and "X is the cause of Y" that match our intuitions. We compile a dataset of causal scenarios and use SFM in all of them. SFM is compatible with but not reducible to probability theory. We also compare SFM with other theories of causation and apply SFM to downstream problems like free will, causal explanation, and mental causation.