Visual cryptography (VC) is a powerful technique with perfect security and requires no PC or device to reconstruct the secret information. Progressive visual cryptography (PVC) is a variation of the VC scheme in which the quality of the reconstructed image is improved by increasing the number of shared images. Previous study focused directly on maximizing the value of the quality in the completely reconstructed image; thus, there is a difference in the quality of the shared images. In this paper, we focus on the aforementioned issue and propose a new approach based on inductive reasoning. Our basic idea is to maximize the quality of the reconstructed images each time the number of shared images increases. We call this method the Bottom-up approach . Moreover, hitherto, PVC has been evaluated based on the value of relative difference or by sight. Such evaluation methods are only subjective or difficult to execute without the knowledge of basis matrices. In addition, PVC users cannot easily confirm the effectiveness of their shared images. In this paper, we propose a new information-theoretic evaluation method for PVC, which only uses shared images, to solve the aforementioned problems. Our proposed method can objectively and quantitatively evaluate PVC based on the numerical value, and PVC users can easily confirm the effectiveness of their shared images.