5.6 Causal discovery as identification in a causal category

Fixed doctrine.

A causal discovery system begins with a category of causal hypotheses: for example directed acyclic graphs, structural causal models, or mechanism families, together with maps preserving the variables and interventions of interest. Its presentation may contain observational samples, interventions, or both. Its query doctrine may ask for conditional independences, interventional distributions, counterfactuals, or transport across environments [ Pearl , 2009 , Peters et al. , 2017 ] .

That category is already highly structured. Depending on the method, its doctrine may include acyclicity, a causal Markov factorization, faithfulness, independent noise, causal sufficiency, modular mechanisms, a fixed variable ontology, or a restricted functional family. Constraint-based search, score-based search, and functional causal modeling use different internal solution constructions because they inherit different subsets of these commitments. None infers causal direction from an unconstrained category of all joint distributions.

The quotient is decisive. Observational data alone often identify only a Markov-equivalence class. Interventional evidence can refine that quotient, but only relative to the available intervention targets and causal assumptions. UOCL describes this as a change in the separating power of the presentation and query doctrine. It does not turn categorical universality into causal identification: intervention semantics and assumptions such as causal sufficiency remain additional declarations.

Causal discovery also illustrates doctrinal accommodation. A contradiction may require changing an edge, a mechanism, or a latent-variable realization within the current causal category. More severe evidence may reject acyclicity, causal sufficiency, modularity, or the chosen variable ontology. The latter is a repair of the hypothesis doctrine, not a better estimate inside the original model class.

Doctrinal audit.

The structural doctrine supplies mechanisms and interventions; observational and experimental samples form the presentation; conditional-independence, interventional, or counterfactual inference supplies the solver; and Markov or interventional equivalence supplies the quotient. ORACLE begins where a causal learner can compare those background commitments rather than merely choose another graph satisfying them.