 Another early method for combining (modal) logics is the so-called product of modal logics. This mechanism, independently introduced in Segerberg 1973 and in Šehtman 1978, is appropriate to represent time-space information. Given two modal logics \({{\cal L}}_1\) and \({{\cal L}}_2\) as above, the product \({{\cal L}}_1 \times {{\cal L}}_2\) is the bimodal logic over the mixed signature (endowed with two boxes) characterized by the class of Kripke structures of the form   \[\langle W_1\times W_2,S_1,S_2,V_1 \times V_2 \rangle\]   defined from Kripke models \(\langle W_1,R_1,V_1\rangle\) and \(\langle W_2,R_2,V_2\rangle\) for \({{\cal L}}_1\) and \({{\cal L}}_2\), respectively. The accessibility relations \(S_1,S_2\subseteq ( W_1 \times W_2) \times (W_1 \times W_2)\) are defined as follows: