The evolution of protoplanetary disks towards mature planetary systems is expected to include the formation of 'gaps' in the disk possibly due to planet formation. We studied the disks of four key intermediate mass (Herbig Ae/Be) stars in order to understand the influence of gaps to their observational appearance. We investigate mid-infrared images and perform radiative transfer modeling to examine the radial distribution of dust and PAHs. Our solutions constrain the sizes of the gaps. For one particular object, HD 97048, this is the first detection of a disk gap. The large gaps deplete the entire population of silicate particles with temperatures suitable for prominent mid-infrared feature emission, while small carbonaceous grains and PAHs can still show prominent emission at mid-infrared wavelengths. The absence of silicate emission features is due to the presence of large gaps in the critical temperature regime. Our results suggest that many, if not all Herbig disks with weak or no silicate features in the spectrum are disks with large gaps and can be characterized as (pre-)transitional. We conclude that the evolution of Herbig stars follows two different paths. Competition between the timescales of inner versus outer disk evolution determine whether young protoplanetary disks evolve into transitional disks (due to planet formation in the inner disk) or into flat disks (due to the grain growth and dust settling in the outer disk).