Affordances enable robots to have a semantic understanding of their surroundings. This allows them to have more acting flexibility when completing a given task. Capturing object affordances in a machine learning model is a difficult task, because of their dependence on contextual information. Markov Logic Networks (MLN) combine probabilistic reasoning with logic that is able to capture such context. Mobile robots operate in partially known environments wherein unseen object affordances can be observed. This new information must be incorporated into the existing knowledge, without having to retrain the MLN from scratch. We introduce the MLN Cumulative Learning Algorithm (MLN-CLA). MLN-CLA learns new relations in various knowledge domains by retaining knowledge and only updating the changed knowledge, for which the MLN is retrained. We show that MLN-CLA is effective for accumulative learning and zero-shot affordance inference, outperforming strong baselines.