Charlie AI Academy - Volume 7.3.2 | 1
CHARLIE AI ACADEMY
Volume 7.3.2
Exhaustive Completion + Proposition-vs-Truth Discipline
Purpose: Repair two remaining failure modes: (1) treating a proposition as true merely because it exists in the
problem statement, and (2) stopping after finding one valid candidate before all candidate rows have been
checked.
Core rule: A report is only a proposition until evaluated against a specific candidate state. A solution is not
complete until every candidate has been evaluated or logically eliminated.

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1. Proposition Is Not Truth
A statement such as “C is RED” is a proposition. It becomes true or false only after evaluating C in the current
candidate row.
Never say “Y says C is RED, therefore Y is true.” First inspect the candidate value of C.

2. Truth Is Row-Local
The truth value of X, Y, or Z belongs to a specific candidate row. It may change in another row.
Y can be false in A=RED,B=GREEN,C=BLUE and true in A=GREEN,B=BLUE,C=RED.

3. Conditional Rules Do Not Create Truth
Y -> X does not make Y true and does not make X true by itself. It only constrains which truth-value
combinations are allowed.
Y=false satisfies Y->X regardless of X. Y=true requires X=true.

4. Evaluate, Then Infer
First determine X, Y, Z from A/B/C. Only then apply counts and implications.
State -> proposition truth -> constraint checks -> row result.

5. Exhaustive Completion
When the state space is small, do not stop after the first valid row. Continue until every row has been
evaluated.
For 3 colors across 3 boxes, check all 6 permutations.

6. Survivor Count Is Part of the Answer
After all rows are checked, count survivors. One survivor means unique; multiple survivors mean ambiguity;
zero survivors means inconsistent constraints.
The integrated A/B/C problem has two survivors.

7. Never Promote a Candidate Early
A candidate that looks promising is provisional until all constraints pass and all other candidates have been
checked.
Do not write “therefore the solution is...” before matrix completion.

8. Exact Label Verification
A printed label is correct only if actual contents match the printed value for that same box.
For A=GREEN,B=BLUE,C=RED, only B label is correct.

9. Exact Report Verification

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X: A != BLUE. Y: C = RED. Z: B = GREEN. Evaluate exactly these expressions.
If A=BLUE, X=false. If B=GREEN, Z=true.

10. No Negation Drift
Do not replace a proposition with its opposite while discussing it.
Z is “B is GREEN,” not “B is not GREEN.”

11. Final Answer Must Reflect All Survivors
The final response must list every passing candidate exactly as verified.
Do not provide one valid solution when two rows pass.

12. Discriminating Information
If multiple survivors remain, state what new observation would distinguish them.
In the integrated test, learning A actual color would distinguish RED from GREEN.

13. Completion Audit
Before sending, ask: Have all candidate rows been checked? Have all survivors been listed? Did I treat every
report as evaluated rather than assumed?
If any answer is no, the solution is incomplete.

14. Reference Survivor 1
A=RED, B=GREEN, C=BLUE.
Label matches=1; X=true; Y=false; Z=true; exactly two reports true; Y->X passes.

15. Reference Survivor 2
A=GREEN, B=BLUE, C=RED.
Label matches=1; X=true; Y=true; Z=false; exactly two reports true; Y->X passes.

16. Reference Rejection: A=BLUE,B=GREEN,C=RED
This row has X=false, Y=true, Z=true.
It fails Y->X and has zero correct printed labels. Reject.

17. No Memory-Based Shortcuts
Even if a familiar puzzle has known survivors, re-evaluate from the current premises.
If any report, label, or rule changes, rebuild the matrix.

18. Final Operating Discipline

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Finish the matrix, count survivors, then explain. Do not infer truth from wording and do not stop early.
Proposition -> evaluate -> row result -> exhaustive completion -> final answer.

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19. Mandatory Reference Matrix
Row A B C Label # X Y Z True # Y->X Result
1 RED BLUE GREEN 3 T F F 1 Pass Reject
2 RED GREEN BLUE 1 T F T 2 Pass VALID
3 BLUE RED GREEN 1 F F F 0 Pass Reject
4 BLUE GREEN RED 0 F T T 2 FAIL Reject
5 GREEN BLUE RED 1 T T F 2 Pass VALID
6 GREEN RED BLUE 0 T F F 1 Pass Reject
Required conclusion for these exact premises: exactly two solutions survive: Row 2 and Row 5. A
unique-answer response is incomplete.

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20. Diagnostic Transfer Tests

# Test Pass requirement
1 Same puzzle, but change Y to “C is BLUE.” Re-evaluate Y in every row; do not reuse old truth values.
2 Same puzzle, but require exactly one report true. Check all six rows and list every survivor.
3 Same reports, but replace Y->X with X->Y. Apply the new directional implication row by row.
4 Finite puzzle with three valid candidates. Return all three, not the first one found.
5 Finite puzzle with no valid candidates. Report inconsistency after exhaustive checking.
6 User asks “is Y true?” without providing a candidate state. Explain that Y is a proposition whose truth depends on C actual value.
Final instruction: Do not confuse a statement with its truth value. Do not stop at the first valid candidate.
Complete the state space, preserve every survivor, and only then conclude.