rob@anwar.UUCP (Robert R Stegmann) (04/03/85)
[munch, munch] It has been asserted by Chris Stassen, of TRW, Redondo Beach CA that, given the premises: 1) Real Men play AD&D 2) Munchkins play anything by TSR and 3) AD&D is a TSR game one can deduce that 4) Real Men are Munchkins. However, by using Wang's Algorithm, one can show that the given premises allow no such deduction. Let the following symbols be defined: M = membership in the set of Real Men A = membership in the set of AD&D players T = membership in the set of TSR game players C = membership in the set of Munchkins (children) The original premises can be represented symbolically by the implications: 1) M -> A 2) C -> T 3) A -> T and the proposed theorem by: 4) M -> C Since Wang's Algorithm can be applied only to premises in conjunctive normal form, we must simplify the implications using the equivalence: a -> b = ~a V b to get: 1) ~M V A, ~C V T, ~A V T -> ~M V C Applying Wang's Algorithm: 2) ~M V A, ~C V T, ~A V T -> ~M , C (simplify right-V to comma) 3) ~M V A, ~C V T, ~A V T, M -> C (negate negation and move to other side) (split left-V) 3a.1) ~M, ~C V T, ~A V T, M -> C 3a.2) ~C V T, ~A V T, M -> C, M (negate and move - proved by M -> M) 3b.1) A, ~C V T, ~A V T, M -> C (split left-V) 3b.1a.1) A, ~C V T, ~A, M -> C 3b.1a.2) A, ~C V T, M -> C, A (negate and move - proved by A -> A) 3b.1b.1) A, ~C V T, T, M -> C (split left-V) 3b.1b.1a.1) A, ~C, T, M -> C 3b.1b.1a.1) A, T, M -> C (negate and move - ignore duplicates) This is irreducible and unprovable - therefore the original theorem is false. Presented for your entertainment. rob Robert Stegmann @ HHB-Softron, Mahwah, NJ