Recently, with the emergence of mobile technology and mobile banking, debit and credit transactions have been the most common transactions that are widely spreading, using such technologies. In this research, we specify the concurrent debit and credit transactions in temporal logics such as CTL (Computational Tree Logic) and LTL (Linear-Time Temporal Logic). These specifications describe the infinite histories that may be produced by the iterations of such concurrent transactions infinitely many times. We represent the infinite histories as a model of temporal logics formulae. Then, model checkers, such as NuSMV or SPIN, can carry out exhaustive checks of the correctness of the concurrent debit and credit transactions. Moreover, in this paper, we presume that the serializability condition is too strict. Therefore, a relaxed condition has been suggested to keep the database consistent. Moreover, the relaxed condition is easier to encode into temporal logics formulae.