Reducing Causality to Functions with Structural Models
This work addresses a foundational issue in philosophy and statistics by offering a novel functional approach to causality, potentially impacting fields like AI and causal inference.
The paper tackles the open problem of defining causality by proposing a reductive definition based on Structural Functional Models (SFM), which maps causes to effects as functions, and demonstrates its application across various causal scenarios and downstream problems.
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.