Determinability Checker

Causal Sufficiency Determinability Checker — Meta-Skill Gatekeeper based on JEP Paper CheckDeterminability Algorithm

Causal Sufficiency Determinability Checker

Algorithm implementation based on the paper Target Determinability under Partial Causal Observation (Wang, 2026).

Core Question

Before an Agent calls other skills, it asks itself:

"Based on current evidence, am I sufficient to make this judgment?"

Determinability Results

Result	Meaning	Agent Action
DETERMINED	Evidence is sufficient; target is zero-error determinable	Execute immediately; no wasted tokens
NOT_DETERMINED	Evidence is insufficient; indistinguishable counterexample exists	Return missing-evidence list; guide next skill to call

Theoretical Foundation

• Theorem 10.1 (Finite Model Checking): The algorithm returns Determined if and only if the target is zero-error determinable; returns NotDetermined with a counterexample pair certificate.
• Theorem 8.2 (Constrained Evidence Coverage): An evidence subset covers all conflict edges if and only if the target becomes determinable from the joint observation.
• Quotient Factorization (Lemma 7.1): D is determinable from Omega if and only if D is constant on every observation equivalence class, if and only if D = g composed with Omega.

Usage Example

Request

json

{
  "session_id": "audit-001",
  "question": "Does the final output have a valid verification event?",
  "configs": [
    {"config_id": "C1", "tool": "code", "has_verif": true, "verif_hash": "valid", "output": "correct", "target": 1},
    {"config_id": "C2", "tool": "code", "has_verif": false, "verif_hash": "none", "output": "correct", "target": 0}
  ],
  "omega_field": "output",
  "target_field": "target",
  "evidence_fields": ["tool", "has_verif", "verif_hash"]
}

Response

json

{
  "session_id": "audit-001",
  "question": "Does the final output have a valid verification event?",
  "determinability": "NOT_DETERMINED",
  "can_proceed": false,
  "counterexample": {
    "config1": "C1",
    "config2": "C2",
    "observation": "correct",
    "target1": 1,
    "target2": 0
  },
  "missing_evidence": ["tool", "has_verif", "verif_hash"],
  "next_skill_suggestion": "Supplement the following evidence items: tool, has_verif, verif_hash",
  "message": "Non-determinability proven: configs C1 and C2 share observation correct but differ on target (1 vs 0)."
}

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Cognitive Emergence Lab
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