DanielLC comments on Paraconsistency and relevance: avoid logical explosions - Less Wrong Discussion
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Using probabilities seems to get around it. A→B would seem to mean P(B|A)≈1. P(Rafael Delago was elected president of Ecuador in 2005|The moon is made of cheese) is low, so I would not say that if the moon is made of cheese, then Rafael Delago was elected president of Ecuador in 2005.
Probabilities are usually defined in terms of events. P(B|A) = P(B,A) / P(A). If A = "the moon is made of cheese" then the measure P(A) = 0, and also P(B,A) = 0. So the conditional probability would be undefined.
You could adopt the position that probabilities should never be exactly 0 or 1. The moon might be made out of cheese after all, just with probability 1e-(1e1000). And quantum uncertainty pretty much guarantees that it is possible. Then what you are saying makes a lot of sense.
I'm not sure they should never be zero or one, but there is definitely a non-zero (and much higher than 1e-(1e1000) chance that the moon is made of cheese.
Yep, I feel that's the most promising avenue - but relevance logics deserve at least a glance.