Answer by lemontree for Show $\vDash \phi \to \psi \Leftrightarrow \{\phi\}...
Starting with the assumption that $[[\phi]]_v = 1$ is correct.The $[[\psi]]_v$ in your first sub-bullet point is strange; that's just an unknown number (a yet to be determined truth value) standing...
View ArticleShow $\vDash \phi \to \psi \Leftrightarrow \{\phi\} \vDash \psi$.
Dirk van Dalen. "Logic and Structure (Universitext)" (p. 29)Definition 1.2.1 A mapping $v : PROP \to \{0, 1\}$ is a valuation if$v(\phi \land \psi) = min(v(\phi), v(\psi)),\\v(\phi \lor \psi) =...
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