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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?

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  • $\begingroup$ Your formula is also satisfied by the assignment $x = x+1$. $\endgroup$ – Yuval Filmus Nov 12 '19 at 16:54
  • $\begingroup$ Thanks a lot. should the connector be $\lor$? $\endgroup$ – Tom Nov 13 '19 at 1:11
  • $\begingroup$ I’ll let you figure that out. $\endgroup$ – Yuval Filmus Nov 13 '19 at 6:00
  • $\begingroup$ We discourage "please check whether my answer is correct" questions, as only "yes/no" answers are possible, which won't help you or future visitors. See here and here. Can you ask about a specific conceptual issue you're uncertain about? As a rule of thumb, a good conceptual question should be useful even to someone who isn't looking at the problem you happen to be working on. If you just need someone to check your work, you might seek out a friend, classmate, or teacher. $\endgroup$ – D.W.♦ Nov 14 '19 at 6:57
  • $\begingroup$ point noted thanks a lot $\endgroup$ – Tom Nov 14 '19 at 10:41

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