Entity linking (EL), the task of disambiguating mentions in text by linking them to entities in a knowledge graph, is crucial for text understanding, question answering or conversational systems. Entity linking on short text (e.g., single sentence or question) poses particular challenges due to limited context. While prior approaches use either heuristics or black-box neural methods, here we propose LNN-EL, a neuro-symbolic approach that combines the advantages of using interpretable rules based on first-order logic with the performance of neural learning. Even though constrained to using rules, LNN-EL performs competitively against SotA black-box neural approaches, with the added benefits of extensibility and transferability. In particular, we show that we can easily blend existing rule templates given by a human expert, with multiple types of features (priors, BERT encodings, box embeddings, etc), and even scores resulting from previous EL methods, thus improving on such methods. For instance, on the LC-QuAD-1.0 dataset, we show more than 4% increase in F1 score over previous SotA. Finally, we show that the inductive bias offered by using logic results in learned rules that transfer well across datasets, even without fine tuning, while maintaining high accuracy.