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RichardKennaway comments on Prisoner's dilemma tournament results - Less Wrong
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You just run the Prolog (or whatever logic system implements all this), and it either terminates with a failure or does not terminate within the time allowed by the competition. The time limit renders everything practically decidable.
Perhaps it terminates in the time required proving that A defects and B cooperates, even though the axioms were inconsistent, and one could also have proved that A cooperates and B defects.
The competitors know the deterministic proof-search algorithm (e.g. that of Prolog), and the first answer that produces within the time limit, that is the answer.