In the last couple of years, the use of Machine Learning has emerged in various areas of geoscience with the promise to automate the solution of otherwise manually intensive tasks or improve upon currently used algorithms. Lithofacies classification from well logs and seismic pre-stack data represents one of the earliest and most successful its use cases to date. Both tree- and neural network-based supervised learning methods are nowadays used to classify hundreds of well logs or entire seismic data in a matter of hours. Whilst providing high accuracy, most approaches currently ignore the fact that some classes cannot occur above others (e.g., oil is always found below gas) and, more in general, fail to produce consistent transition probabilities between the training data and predicted labels. In this project we will investigate a strategy for enforcing our prior knowledge about facies transitions through an ad-hoc extension of the cost function of NN-based classifiers. This will be followed by a thorough comparison with other state-of-the-art classifiers on synthetic and field data.