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\paragraph*{HML}
Let $\varphi, \psi$ be HML expressions: 
\begin{equation*}
    \varphi, \psi \Coloneqq 
    \top\ |\ \bot\ |\ \neg \varphi\ |\ \varphi \wedge \psi\ |\ 
    \varphi \vee \psi \ |\ \langle A\rangle \Phi \ |\ [A] \Phi
\end{equation*}
where $\Phi$ denotes predicates. 

We omit explanation of familiar syntactic elements from FOL. Besides them: 
\begin{align*}
    P \models [A]\Phi &\iff 
    \forall Q: (\exists a \in A: P \xrightarrow{a} Q) \implies (Q \models \Phi) \\
    P \models \langle A\rangle \Phi &\iff 
    \exists Q: \exists a \in A: P \xrightarrow{a} Q \wedge Q \models \Phi
\end{align*}

\begin{example}[deadlock in HML]
    Given set of all actions $A$, a process $P$ deadlocks if this holds:  
    \begin{equation*}
        P \models [A]\bot
    \end{equation*}
\end{example}

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