Neuro-symbolic integration aims at harnessing the power of symbolic knowledge representation combined with the learning capabilities of deep neural networks. In particular, Logic Tensor Networks (LTNs) allow to incorporate background knowledge in the form of logical axioms by grounding a first order logic language as differentiable operations between real tensors. Yet, few studies have investigated the potential benefits of this approach to improve zero-shot learning (ZSL) classification. In this study, we present the Fuzzy Logic Visual Network (FLVN) that formulates the task of learning a visual-semantic embedding space within a neuro-symbolic LTN framework. FLVN incorporates prior knowledge in the form of class hierarchies (classes and macro-classes) along with robust high-level inductive biases. The latter allow, for instance, to handle exceptions in class-level attributes, and to enforce similarity between images of the same class, preventing premature overfitting to seen classes and improving overall performance. FLVN reaches state of the art performance on the Generalized ZSL (GZSL) benchmarks AWA2 and CUB, improving by 1.3% and 3%, respectively. Overall, it achieves competitive performance to recent ZSL methods with less computational overhead.