$$\newcommand{\sslash}{\mathbin{/\mkern-6mu/}}$$
$$\newcommand{\defeq}{\stackrel{\text{def}}{=}}$$
$$\require{bussproofs}$$
$$\newcommand{\counterfactual}
{~\Box\kern-1.5pt\raise1pt\hbox{$\mathord{\rightarrow}$}~}
\newcommand{\countermight}
{~\mathord{\Diamond}\kern-1.5pt\raise0.5pt\hbox{$\mathord{\rightarrow}$}~}$$
$$\newcommand{\Dashv}{\mathbin{\style{display: inline-block; transform: scaleX(-1)}{\vDash}}}$$