Notation for tautology, inconsistency and contingency A tautology can be indicated like so: $\models \phi$ What is the notation for an inconsistency? $\not \models \phi$? What is the notation for a contingency?

Inconsistency is not $\
ot \vDash \phi$, because that is merely saying that $\phi$ is not a tautology, so it could still be either an inconsistency or a contingeny.

Instead, an inconsistency is: $\phi \vDash \bot$

When $\
ot \vDash \phi$ _and_ $\
ot \vDash \
eg \phi$, then $\phi$ is a contingency. I personally have not seen one symbol for this.