I want to prove that $\neg(p\rightarrow q)\neq \neg p \rightarrow q$ and I have a proof example but I have lost the first step and I don't get the following one
- $w_iRw_i$ by hypothesis $R$ is reflexive
I don't get this worlds $w_i$ writings, what do they stand for ? In my last question I had a proof where in step 5, it was"choosing" a wj such that $w_iRw_j$ Does it means here that it is choosing a world where $w_iRw_i$ ?
The remaining of the question is :
- $\Box p,w_i$ from $R_{\neg\rightarrow}$ on 1 (which is missing)
- $\neg p,w_i$ from $R_{\neg\rightarrow}$ on 1 (which is missing)
- $p,w_i$ from $R_\Box$ on 3 which leads to a contradiction with 4.
$w_i$ is a "node or world" i.e. an element of the set $W$ of the Kripke frame $\langle W,R \rangle$ on which the so-called "accessibility relation" $R$ is defined.
The relation $R$ over $W$ is reflexive iff every element of $W$ is related to itself, i.e. $w_iRw_i$ for every $w_i \in W$.