In order to interact with people in a natural way, a robot must be able to link words to objects and actions. Although previous studies in the literature have investigated grounding, they did not consider grounding of unknown synonyms. In this paper, we introduce a probabilistic model for grounding unknown synonymous object and action names using cross-situational learning. The proposed Bayesian learning model uses four different word representations to determine synonymous words. Afterwards, they are grounded through geometric characteristics of objects and kinematic features of the robot joints during action execution. The proposed model is evaluated through an interaction experiment between a human tutor and HSR robot. The results show that semantic and syntactic information both enable grounding of unknown synonyms and that the combination of both achieves the best grounding.