POWL 2.0 Language Evaluator $L(\psi)$ — Exact Mathematical Realization:

• Definition 3 [BPM25, p. 8]
• Definition 3.9 [PETRI25, p. 10]

Mathematical Definition

The language of a POWL 2.0 model $\psi$ is defined recursively:

1. $L(t) = \{\langle a \rangle\}$ for $t \in T$ with $l(t) = a \in \Sigma$.
2. $L(t) = \{\langle\rangle\}$ for $t \in T$ with $l(t) = \tau$.
3. $L(\circlearrowleft(\psi_1, \psi_2)) = L(\psi_1) \cdot (L(\psi_2) \cdot L(\psi_1))^*$.
4. $L(\prec(\psi_1, \dots, \psi_n)) = \{\sigma \in \prec\hspace{-0.6em}\odot(\sigma_1, \dots, \sigma_n) \mid \forall i, \sigma_i \in L(\psi_i)\}$.
5. $L(G) = \bigcup_{\langle x_1, \dots, x_k \rangle \in \vec{G}} L(x_1) \cdot L(x_2) \cdots L(x_k)$.