<p>Logical expressions are the main tools for describing various logical relationships in the real world, and the binary characteristic of either being "True" or "False" makes it the fundamental carrier for logical reasoning and conditional judgment. This paper proposes a new SNP system variant Π_DD, dual-channel and dual-spiking neural P system, which is inspired by the fact in biology. Based on Π_DD, a logical expression calculation SNP system Π_LE was designed. We have proven the correctness of Π_LE and verified its feasibility and effectiveness through examples. For the calculation of a logical expression containing <i>k</i> operations, 37 types of rules are used, the operation takes 3<i>k</i> + 4 time slices, and the maximum number of neurons required for Π_LE is 2<i>k</i> + 9. This study provides new ideas and methods for computational modeling of complex logical problems.</p>