Given a model $\mathbf{M} = (\mathbf{W}, \mathbf{R}, \mathbf{V})$ for a set of atomic formulae $\Omega$. We have possible worlds $\mathbf{w}, \mathbf{w'} \in \mathbf{W}$, access relation satisfies $(\mathbf{w}, \mathbf{w'}),(\mathbf{w'}, \mathbf{w})\in \mathbf{R}$, $p \in \Omega$.
Moreover, we define necessity operator and possibility operator as follows:Given $(\mathbf{w_1}, \mathbf{w_2}) \in \mathbf{R}$. If a proposition $\phi$ is true at $\mathbf{w_2}$ then $\Diamond{\phi}$ is true at $\mathbf w_1$. If $\Box \phi$ is true at $\mathbf w_1$, then $\phi$ is true at $\mathbf w_2$.
Question Can it be the case $p$,$\lnot p$ are true at $\mathbf w$ and $\mathbf w'$ respectively with $\mathbf w$ and $\mathbf w'$ have access to each other?
I think there is no incoherency, but remark 2 on page 29 of this note suggests otherwise.