Unless the soil/gravel under the floor has been covered by a vapour barrier, there's no stopping water vapour moving into the basement outside of treatments that can be quite costly. To see if you have excessive moisture moving upward, you can use the plastic sheet test.

The Plastic Sheet Test (ASTM-D-4263) is an eighteen inch by eighteen inch square of clear plastic sheeting that is sealed to the concrete surface with tape on all four sides. After sixteen hours, if any condensation is found on the underside of the plastic or if the concrete surface is darkened, the concrete is considered too wet. In cooler conditions, the test may not work and the reliability of the results can be influenced by differences in the temperature. An obvious appearance of moisture, however, will always indicate excessive moisture flow.

Bob Cain, Concrete Network

I would keep the rugs to a minimum and be sure to move and launder them frequently. If the moisture is slight, you won't see it, but you will smell any mould the moisture is nourishing in the rugs. Thin synthetic rugs with no rubber backing work best.

Epoxy paint coat. Do this in summer only the fumes are not tolerable in winter. I agree to do the plastic sheet test.