 Then, \(\langle h_1,h_2\rangle\) satisfies \(\varphi\), denoted by \(\langle h_1,h_2\rangle \Vdash \varphi\), if \(\langle h_1,h_2,m,w\rangle\Vdash \varphi\) for every \(m\in {{\cal M}}_1 \cup {{\cal M}}_2\) and \(w\in W_m\). Finally, \(\varphi\) is valid in the fibred semantics whenever \(\langle h_1,h_2\rangle \Vdash \varphi\) for every pair \(\langle h_1,h_2\rangle\) as above.