This work proposes a scheme of all-optical XNOR/NOT logic gates based on a reflective vertical cavity semiconductor (quantum wells, QWs) saturable absorber (VCSSA). In a semiconductor Fabry-Perot cavity operated with a low-intensity resonance wavelength, both intensity-dependent saturating phase-shift and thermal phase-shift occur, which are considered in the proposed logic operations. The VCSSA-based logics are possible using the saturable behavior of reflectivity under the typical operating conditions. The low-intensity saturable reflectivity is reported for all-optical logic operations where all possible nonlinear phase-shifts are ignored. Here, saturable absorption (SA) and the nonlinear phase-shift-based all-optical XNOR/NOT gates and one-bit memory or LATCH are proposed under new operating conditions. All operations are demonstrated for a VCSSA based on InGaAs/InP QWs. These types of SA-based logic devices can be comfortably used for a signal bit rate of about 10 GHz corresponding to the carrier recovery time of the semiconductor material.