Charlie AI Academy - Volume 6.2 | 1 CHARLIE AI ACADEMY Volume 6.2 Constraint Logic, Premise Locking, Deduction and Contradiction Checking Purpose: Strengthen Charlie's ability to solve problems where every premise constrains the possible states. This volume targets failures where Charlie notices a constraint but later violates it, reverses a deduction, or invents an impossible state. Core rule: Lock explicit premises before reasoning forward. Every candidate conclusion must satisfy every locked premise. If a conclusion violates even one premise, reject it. Charlie AI Academy - Volume 6.2 | 2 1. Premise Locking Extract the explicit conditions before solving. Treat them as non-negotiable unless the user changes them. Do not silently weaken, reverse, or forget them. Example: “Every label is wrong” means APPLES is not apples, ORANGES is not oranges, and MIXED is not mixed. 2. Translate Language into Constraints Convert natural-language statements into simple allowed/not-allowed relationships. This reduces verbal confusion. MIXED label != mixed contents. Therefore the MIXED-labeled box must be a pure APPLES or pure ORANGES box. 3. Fix Facts as Soon as They Are Proven When a new observation uniquely identifies a state, lock that state and do not reverse it later without new contradictory evidence. If the MIXED-labeled box is known to be pure and the drawn fruit is an apple, that box is APPLES. It cannot later become ORANGES. 4. Constraint Propagation After fixing one state, propagate the consequences through the remaining possibilities. Eliminate assignments that violate uniqueness or prior constraints. If MIXED-label = APPLES, the remaining contents are ORANGES and MIXED. ORANGES-label cannot be ORANGES, so ORANGES-label = MIXED. APPLES-label = ORANGES. 5. Elimination Tables For small logic problems, mentally construct a table of candidates and cross out forbidden assignments. Labels: APPLES, ORANGES, MIXED. Contents: apples, oranges, mixed. Diagonal assignments are forbidden because every label is wrong. 6. Do Not Reverse Evidence An observation supports the state that could produce it. Do not infer the opposite without a rule requiring that reversal. Drawing an apple from a box known to contain only one fruit type proves APPLES, not ORANGES. 7. Check Every Original Premise After deriving a solution, replay every original condition against it. If any condition fails, the solution is invalid. For the apple case: MIXED-label=APPLES (wrong label), ORANGES-label=MIXED (wrong label), APPLES-label=ORANGES (wrong label). All three labels are wrong: pass. Charlie AI Academy - Volume 6.2 | 3 8. Uniqueness Check If the puzzle requires one-to-one assignments, each category must be used exactly once. Do not assign the same content to two boxes unless the problem allows it. A solution assigning ORANGES to two different boxes is immediately invalid in the standard three-box puzzle. 9. Branch Carefully When an observation could have multiple outcomes, solve one branch completely, then state the symmetric alternative. Do not mix branches. Branch A: draw apple. Branch B: draw orange. Never use an apple observation and an orange conclusion in the same branch. 10. Contradiction Means Reject the Branch When a branch violates a locked premise, discard that branch. Do not patch it with an unsupported statement. If a proposed solution says the MIXED-labeled box is mixed, reject it immediately because every label is wrong. 11. Necessary vs Possible Distinguish what must be true from what could be true. A single compatible possibility is not proof. Before the draw, MIXED-label could be APPLES or ORANGES. After drawing an apple, APPLES becomes necessary. 12. Sufficient Evidence Ask whether the available observation is enough to uniquely determine the answer. If not, do not pretend it is. The special value of drawing from MIXED-label is that the wrong-label condition guarantees it is pure, so one fruit identifies it. 13. Avoid Decorative Probability Do not invoke probability when the problem is deterministic. Use probability only when uncertainty and random outcomes are part of what must be calculated. The three-box relabeling puzzle is deduction, not a probability calculation. 14. Object-Level Precision Reason about the actual object observed. One fruit is an apple or orange; “a mixed fruit” is not a valid observation in this puzzle. The box may be mixed; an individual drawn fruit is not “mixed.” Charlie AI Academy - Volume 6.2 | 4 15. State Tracking Maintain a compact state representation so earlier deductions are not lost. Example internal state: M-label=A; O-label=M; A-label=O. 16. Symmetry When two cases are mirror images, solve one correctly and transform it carefully rather than recomputing loosely. If drawing apple gives M-label=A, O-label=M, A-label=O, then drawing orange gives M-label=O, A-label=M, O-label=A. 17. Self-Verification with Constraints Volume 6.1 verification should be extended: do not only check arithmetic or final-answer consistency; check logical consistency with every premise. A fluent explanation is still wrong if its mapping violates “every label is wrong.” 18. Stop After a Valid Mapping Once all entities are assigned, every premise passes, and the requested explanation is complete, stop. Do not invent extra alternatives. State the two possible draw outcomes and finish. 19. Correct Solution - Three Boxes Take one fruit from the box labeled MIXED. Since that label is wrong, this box is pure. If the fruit is an apple, relabel that box APPLES; ORANGES-label becomes MIXED; APPLES-label becomes ORANGES. If the fruit is an orange, relabel that box ORANGES; APPLES-label becomes MIXED; ORANGES-label becomes APPLES. This example is a reference pattern for premise locking and constraint propagation, not a phrase to copy into unrelated answers. 20. General Deduction Protocol 1) Extract premises. 2) Translate them into constraints. 3) Identify the most informative observation. 4) Lock proven states. 5) Propagate consequences. 6) Eliminate impossible states. 7) Verify every original premise. 8) Answer. 9) Stop. Use the protocol internally; do not recite it unless the user asks for the reasoning method. 21. Common Failure Patterns Watch for: reversing an observation; forgetting a premise mid-answer; assigning one category twice; confusing a label with contents; mixing branches; inventing impossible objects; adding probability to deterministic logic; declaring a contradiction without identifying one. Charlie AI Academy - Volume 6.2 | 5 If any of these occurs during verification, repair the reasoning before presenting the answer. 22. Behavioral Standard The assistant should be able to explain a deduction in plain language while preserving exact logical constraints. Natural wording must never come at the expense of correctness. Target: concise, correct, premise-faithful, and free of loops or unrelated content. Charlie AI Academy - Volume 6.2 | 6 23. Diagnostic Test Set # Problem Pass condition 1 Three mislabeled fruit boxes; every label wrong; one draw. Choose MIXED-labeled box and derive both correct mappings. 2 Three switches downstairs, one bulb upstairs; one trip upstairs. Determine the switch. Use heat + light: turn one on, wait, off; second on; inspect bulb. 3 Two doors, one safe and one dangerous; one truth-teller and one liar; one question. Ask either what the other would say, then choose opposite. 4 Four cards show A, D, 4, 7. Rule: vowel -> even. Which cards must be turned? A and 7 only. 5 If all Zorps are Mips and no Mips are Lats, can any Zorp be a Lat? No. Preserve set constraints. 6 Anna is older than Ben; Cara younger than Ben; Dan older than Anna. Who is oldest? Dan. 7 Exactly one of A, B, C is true. A says B is false. B says C is false. Evaluate carefully. Must enumerate truth assignments and reject those violating exactly-one constraint. 8 Three seats, Ana not left, Bob not right, Cara not middle; find valid arrangements. Use constraints systematically; verify all restrictions. 9 A box cannot be red and cannot be blue; allowed colors are red, blue, green. What color? Green. 10 User adds a new premise that conflicts with an earlier one. Surface conflict instead of silently choosing or merging incompatible states. Pass standard: The answer must satisfy every explicit premise, preserve branch consistency, avoid duplicate/impossible assignments, and stop after a verified solution. A correct-sounding conclusion with an invalid intermediate mapping is a failure.