diff options
Diffstat (limited to 'Assignment1/semantics.tex')
| -rw-r--r-- | Assignment1/semantics.tex | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/Assignment1/semantics.tex b/Assignment1/semantics.tex index d99e636..05e96fb 100644 --- a/Assignment1/semantics.tex +++ b/Assignment1/semantics.tex @@ -41,8 +41,8 @@ The information about $A_0$ is not lost, so whether $\Xop\phi$ holds for $\sigma \sigma &\vDash_i & \phi_1\land\phi_2 &\text{iff} & \text{$\sigma\vDash_i\phi_1$ and $\sigma\vDash_i\phi_2$}\\ \sigma &\vDash_i & \lnot\phi &\text{iff} & \sigma \nvDash_i \phi\\ \sigma &\vDash_i & \Xop\phi &\text{iff} & \sigma \vDash_{i+1} \phi\\ - \sigma &\vDash_i & \phi_1\Uop\phi_2 &\text{iff} & \exists_{j \ge i}.\text{$\sigma \vDash_j \phi_2$ and $\sigma \vDash_k \phi_1$ for all $i \le k < j$}\\ - \sigma &\vDash_i & \phi_1\Sop\phi_2 &\text{iff} & \exists_{0 \le j \le i}.\text{$\sigma \vDash_j \phi_2$ and $\sigma \vDash_k \phi_1$ for all $j < k \le i$}\\ + \sigma &\vDash_i & \phi_1\Uop\phi_2 &\text{iff} & \exists_{j \ge i}\big[\text{$\sigma \vDash_j \phi_2$ and $\sigma \vDash_k \phi_1$ for all $i \le k < j$}\big]\\ + \sigma &\vDash_i & \phi_1\Sop\phi_2 &\text{iff} & \exists_{0 \le j \le i}\big[\text{$\sigma \vDash_j \phi_2$ and $\sigma \vDash_k \phi_1$ for all $j < k \le i$}\big]\\ \sigma &\vDash_i & \Pop\phi &\text{iff} & \text{$i \geq 1$ and $\sigma \vDash_{i-1} \phi$} \end{matrix*} \] |