Reconstruction

After this lesson, the reader should understand:

• 01State the extractability thesis, and the claim it deliberately does not make.
• 02Explain why several rule sets can be equally consistent with the same behaviour.
• 03Express a reconstructed boundary with its uncertainty attached.

Two rules, one behaviour

A reconstruction yields "escalate above £48,000". An equally consistent reading is "escalate when the approver is not a director". How is the ambiguity resolved?

Not by the data alone. If directors happen to hold the higher approval limits, the two rules produce identical behaviour across every record in the log, and no further volume of the same evidence will separate them. This is the non-identifiability problem familiar from inverse reinforcement learning: behaviour under-determines the rule that generated it. The discipline's answer is not to silently pick the more plausible reading. It is to surface both, name the confound explicitly, and route the question back to the institution — which knows which of the two it meant, and is the only party entitled to say.

• What should a reconstruction do when two readings fit the evidence equally well?
• Is a reconstruction an accusation, a hypothesis, or a finding?
• Who owns a rule that was inferred rather than authored?
• How much confidence should a reconstruction carry before anyone acts on it?

Reconstruct a boundary, then attack your own result.

1. 01Infer a boundary from a real decision log.
2. 02Write it out as an explicit rule.
3. 03Propose a second rule that fits the same data equally well.
4. 04Identify the evidence that would separate the two.
5. 05State what you would require before presenting the first as a finding.

• Inverse reinforcement learning — non-identifiability of reward from behaviour (Ng & Russell; Ziebart et al.).
• Causal inference — confounding and identification.
• Philosophy of science — under-determination of theory by evidence.
• Operational Logic, §8 — the extractability thesis.