Problem Detail: I read in some sources that valid formulas are tautologies (valid under every evaluation). In the others, I read that these are formulas that have conclusions true when premises are true. Are these just equivalent definitions because ⊨ P → Q is equivalent to P ⊨ Q?
Asked By : Val
Answered By : Dave Clarke
Yes. These definitions are equivalent, noting that not all valid formula have the form $Pto Q$, though any formula $Q$ is equivalent to $topto Q$.
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