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“New Order” Microscenario #1 (“no distractor” version)

“New Order” Microscenario #1 (“no distractor” version). John H. was killed by a member of the Al-Qaeda cell 'The New Order'. The only members of 'The New Order' were John H., Majed H., and Essid D.

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“New Order” Microscenario #1 (“no distractor” version)

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  1. “New Order” Microscenario #1(“no distractor” version) John H. was killed by a member of the Al-Qaeda cell 'The New Order'. The only members of 'The New Order' were John H., Majed H., and Essid D. Within-cell killings only occur when the attacker believes the victim is a traitor, and never when the attacker is of lower rank. Essid D. believes that nobody is a traitor who John H. believes is a traitor. John H. believes everyone except Majed H. is a traitor. Majed H. believes that everyone who is not of lower rank than John H. is a traitor. Majed H. believes everyone is a traitor who John H. believes is a traitor. No one believes everyone in 'The New Order' is a traitor. ‘John H.’ is not an alias for ‘Majed H.’, nor vice versa. In addition, ‘Majed’ isn’t an alias for ‘Essid’ (nor, again, vice versa).

  2. Solved By Hand in Hyperproof

  3. Using Athena to: Find out who killed; automatically obtain a proof; construct and check a natural deduction-style proof (define culprit-property (forall ?x (iff (culprit ?x) (killed ?x John)))) (assert culprit-property) (find-model (add (exists ?x (culprit ?x)) (ab))) (!prove (killed John John)) ((killed John John) BY (!by-contradiction (assume (not (killed John John)) (dlet ((disjunction (!derive (or (killed Essid John) (killed Majed John)) [(not (killed John John)) premise1 premise2]))) (!by-cases (assume (killed Essid John) (dlet ((S1 (!derive (believesTraitor Essid John) [premise3 premise2 (killed Essid John)])) (S2 (!derive (believesTraitor John John) [premise5 premise9])) (S3 (!derive (not (believesTraitor Essid John)) [S2 premise4]))) (!derive false [S1 S3]))) (assume (killed Majed John) (dlet ((S1 (!derive (believesTraitor Majed John) [premise3 premise2 (killed Majed John)])) (S2 (!derive (believesTraitor John John) [premise5 premise9])) (S3 (!derive (believesTraitor John Essid) [premise5 premise9])) (S4 (!derive (believesTraitor Majed Essid) [S3 premise7])) (S5 (!derive (not (believesTraitor Majed Majed)) [S1 S4 premise8 premise2])) (S6 (!derive (not (lowerRank Majed John)) [(killed Majed John) premise2 premise3])) (S7 (!derive (believesTraitor Majed Majed) [S6 premise6]))) (!derive false [S5 S7]))) [disjunction])))))

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