Protoplanetary disks with cavities in their dust distribution, also named transitional disks, are expected to be in the middle of active evolution and possibly planet formation. In recent years, millimeter-dust rings observed by ALMA have been suggested to have their origin in dust traps, caused by pressure bumps. One of the ways to generate these is by the presence of planets, which lower the gas density along their orbit and create pressure bumps at the edge. We present spatially resolved ALMA Cycle 0 and Cycle 1 observations of CO and CO isotopologues of several famous transitional disks. Gas is found to be present inside the dust cavities, but at a reduced level compared with the gas surface density profile of the outer disk. The dust and gas emission are quantified using the physical-chemical modeling code DALI. In the majority of these disks we find clear evidence for a drop in gas density of at least a factor of 10 inside the cavity, whereas the dust density drops by at least a factor 1000. The CO isotopologue observations reveal that the gas cavities are significantly smaller than the dust cavities. These gas structures suggest clearing by one or more planetary-mass companions.