We propose a logic of knowledge for impure simplicial complexes. Impure complexes represent distributed systems under uncertainty over which processes are still active (are alive) and have failed or crashed dead). Our work generalizes the pure complexes, where all alive, by Goubault et al. logical semantics has satisfaction relation defined simultaneously with definability relation. The latter ...

The training and the evaluation of learning algorithms depend critically on the quality of data samples. We denote as pure the samples that identify clearly and without any ambiguity the class of objects of interest. For instance, in pedestrian detection algorithms, we consider as pure samples the ones containing persons who are fully visible and are imaged at a good resolution (larger than the...