I try to model a decision process in which I first need to decide about a binary variable $x$. In case $x=1$, I also need to decide upon variable $y$ and the value of $y$ is not defined otherwise. Especially, I do not know how to correctly introduce constraints. Assume that I want to model a constraint that states that $y$ needs to be greater than 5. Of course I could then just state: \begin{equation}\label{eq:cap} y > 5 \end{equation} But this would suggest that $y$ has a defined value, which does not need to be the case (if $x = 0$).
Is there a standard way how to introduce such a variable and associated constraints (e.g. in an IP or MDP)?