Q: (Logics) If well-formed formula $q , \not\vDash q \text{, then } \vDash \lnot q$ If well-formed formula without free variables $q , \not\vDash q \text{, then }\vDash \lnot q$. Is it true?

$\
ot\models q$ is equivalent to "$q$ isn't a tautology," or "In _some_ interpretations, $q$ _may_ not true".

$\models \
eg q$ is equivalent to "$q$ is a contradiction," or "In _all_ interpretations, $q$ _can_ not true."