While deep learning models excel in various applications, their black-box nature hampers understanding, especially in critical domains like healthcare and autonomous vehicles. Current explainability methods fall short in providing meaningful insights into model decisions. Concept-based explanations offer a promising alternative by explaining predictions in terms of human-understandable concepts. Concept-based models, however, either reduce the generalization capability of the model (as in Concept-bottleneck Models), or provide uninterpretable task predictions (as in Concept Embedding Models). In this paper, we propose a Linearly Interpretable CEMs (LICEM) addressing both issues. Building upon existing literature on logic rules, LICEM generates linear equations over concept embeddings to provide interpretable predictions over concept scores. We showcase its competitive performance over existing methods in a number of tasks.