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Modus tollens probabilized. (English) Zbl 1062.03015
Summary: We establish a probabilized version of modus tollens, deriving from \(p(E\mid H)=a\) and \(p(\overline E)=b\) the best possible bounds on \(p(\overline H)\). In particular, we show that \(p(\overline H)\to 1\) as \(a,b\to 1\), and also as \(a,b\to 0\).

03A05 Philosophical and critical aspects of logic and foundations
03B48 Probability and inductive logic
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