In other words, modus ponens is:
P(A=true)=1, P(B=true|A=true)=1 |- P(B=true) = 1
Let P'(A) be the distribution on A when we know nothing about B (in a world with only A and B). Plausible reasoning is possible through Bayes/joint-conditional probability rule and yields:
P(B=true|A=true)=1, P(B=true)=1 |- P(A=true) > P'(A=true)
where logic alone can't conclude (A->B, B |- ?)
Also:
P(B=true|A=true)=1, P(A=false)=1 |- P(B=true) < P'(B=true)
Let P'(A) be the distribution on A when we know nothing about B (in a world with only A and B). Plausible reasoning is possible through Bayes/joint-conditional probability rule and yields: P(B=true|A=true)=1, P(B=true)=1 |- P(A=true) > P'(A=true) where logic alone can't conclude (A->B, B |- ?) Also: P(B=true|A=true)=1, P(A=false)=1 |- P(B=true) < P'(B=true)