 In order to exemplify the technique of categorial fibring (without entering into technical details), suppose that \({{\cal L}}_1\) and \({{\cal L}}_2\) are two modal logics defined through Hilbert calculi over the same signatures \(C_1\) and \(C_2\) of subsections  4.1  and  4.2,  respectively, such that both logics contain the rules of Modus Ponens and necessitation. Then \(C_1 \oplus C_2\) consists of two negations \(\neg_1\) and \(\neg_2\), two implications \(\to_1\) and \(\to_2\) and two boxes \(\square_1\) and \(\square_2\). The unconstrained fibring \({{\cal L}}_1 \oplus {{\cal L}}_2\) of \({{\cal L}}_1\) and \({{\cal L}}_2\) is, therefore, the Hilbert calculus over \(C_1 \oplus C_2\) defined by joining up the axiom schemas and inference rules of both calculi. This logic has, among other axioms and inference rules, two versions of Modus Ponens (one for each implication) as well as two versions of the necessitation rule (one for each box). It should be noted that, by using a fixed set of schema variables for writing the axioms and rules of every calculus, the calculi obtained by fibring are also formed by schematic axioms and inference rules. Thus, for instance, in the rule of Modus Ponens in \({{\cal L}}\):   \[\frac{\xi_1 \hspace{1cm} (\xi_1 \to_1 \xi_2)}{\xi_2}\]   the schema variables \(\xi_1\) and \(\xi_2\) can be replaced by mixed formulas. Instances such as   \[\frac{\neg_2 p \hspace{1cm} (\neg_2 p \to_1 \square_2(q \to_2 \square_1 r))}{\square_2(q \to_2 \square_1 r)}\]   are new, because the formulas \(\neg_2 p\) and \(\square_2(q \to_2 \square_1 r)\) do not belong to the language of \({{\cal L}}_1\). Analogous replacements apply, of course, to other inference rules and axioms of \({{\cal L}}_1 \oplus {{\cal L}}_2\).