If we cannot recognize another community's practices as logic without shared inferential norms, then 'incompatible logics' is not a coherent cross-cultural description but a failure of translation.
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incompatible logics(as used in cross-cultural philosophy)
Different reasoning systems that seem to contradict each other or follow completely different rules about what counts as valid reasoning.
inferential norms(as the key to solving the puzzle)
The unwritten rules that tell us what conclusions we can logically draw from a statement—basically, the patterns of reasoning that language users naturally follow.