grammar:

where $p,r \in {P}$, $q \in {P}\setminus \{p\}$, and $a \in \Sigma$. We refer to ${\xi}$ as a *sentence*, to $\varphi$ as an *event formula*, and to $\pi$ as a *path formula*. We name the logic star-free because we use the operators $(\cup,\cap,{\mathsf{c}},\cdot)$ of star-free regular expressions instead of the regular-expression operators $(\cup,\cdot,\ast)$ of classical PDL. However, the formula ${\xrightarrow{\varphi}}$, whose semantics is explained below, can be seen as a restricted use of the construct $\pi^\ast$.

A sentence ${\xi}$ is evaluated wrt. an MSC $M =
(E,{\rightarrow},{\lhd},{\mathit{loc}},\lambda)$. An event formula $\varphi$ is evaluated wrt. $M$ and an event $e \in E$. Finally, a path formula $\pi$ is evaluated over *two* events. In other words, it defines a binary relation ${\llbracket {\pi} \rrbracket_{M}} \subseteq E \times E$. We often write $M,e,f \models \pi$ to denote $(e,f) \in {\llbracket {\pi} \rrbracket_{M}}$. Moreover, for $e \in E$, we let ${\llbracket {\pi} \rrbracket_{M}}(e) {:=}\{f \in E \mid (e,f) \in {\llbracket {\pi} \rrbracket_{M}}\}$. When $M$ is clear from the context, we may write ${\llbracket {\pi} \rrbracket}$ instead of ${\llbracket {\pi} \rrbracket_{M}}$. The semantics of sentences, event formulas, and path formulas is given in Table \[table:sem-PDL\].

$\begin{array}{ll}
\hline
\multicolumn{2}{l}{
M \models {\mathop{\mathsf{E}\vphantom{a}}\nolimits}\varphi \textup{ if } 