Abstract We present an abstract development of Gödel’s incompleteness theorems, performed with the help Isabelle/HOL proof assistant. analyze sufficient conditions for applicability our theorems to a partially specified logic. In addition usual benefits generality, perspective enables comparison between alternative approaches from literature. These include Rosser’s variation first theorem, Jero...

Despite the success of deep learning methods in medical image segmentation tasks, human-level performance relies on massive training data with high-quality annotations, which are expensive and time-consuming to collect. The fact is that there exist low-quality annotations label noise, leads suboptimal learned models. Two prominent directions for noisy labels include pixel-wise noise robust imag...