For instance, $x = x + 1[0.3]x+2$ sets $x$ to $x + 1$ with probability $0.3$ and to $x+2$ with probability $0.7$.
If I use notation used in the paper "An Analysis of First-Order Logics of Probability" of Joseph Y. Halpern.
Given a formula $\varphi$ in the logic, he also allows formulas of the form $W_x(\varphi)\geq 1/2$, which can be interpreted as "the probability that a randomly chosen $x$ in the domain satisfies $\varphi$ is greater than or equal to 1/2".
Is my representation of the above probabilistic assignment presented below correct?
$W_x(\varphi_1)\geq 0.3 \land W_x(\varphi_2)< 0.3$ where $\varphi_1$ is $x=x+1$ and $\varphi_2$ is $x=x+2$
Please guide me in this regard?