  Learning from noisy labels is an important concern in plenty of real-world
scenarios. Various approaches for this concern first make corrections
corresponding to potentially noisy-labeled instances, and then update
predictive model with information of the made corrections. However, in specific
areas, such as medical histopathology whole slide image analysis (MHWSIA), it
is often difficult or impossible for experts to manually achieve the noisy-free
ground-truth labels which leads to labels with complex noise. This situation
raises two more difficult problems: 1) the methodology of approaches making
corrections corresponding to potentially noisy-labeled instances has
limitations due to the complex noise existing in labels; and 2) the appropriate
evaluation strategy for validation/testing is unclear because of the great
difficulty in collecting the noisy-free ground-truth labels. For the problem
1), we present one-step abductive multi-target learning (OSAMTL) that imposes a
one-step logical reasoning upon machine learning via a multi-target learning
procedure to constrain the predictions of the learning model to be subject to
our prior knowledge about the true target. For the problem 2), we propose a
logical assessment formula (LAF) that evaluates the logical rationality of the
outputs of an approach by estimating the consistencies between the predictions
of the learning model and the logical facts narrated from the results of the
one-step logical reasoning of OSAMTL. Based on the Helicobacter pylori (H.
pylori) segmentation task in MHWSIA, we show that OSAMTL enables the machine
learning model achieving logically more rational predictions, which is beyond
various state-of-the-art approaches in handling complex noisy labels.
