Dear Editors, Please find our manuscript entitled "Lattice-based ALC ontology embeddings with saturation" for your consideration. We submit this manuscript for the NeSy 2024 special issue as an extended version of the manuscript "Lattice-based ALC ontology embeddings" published at the NeSy 2024 conference. Some neurosymbolic methods have aimed to capture the semantics of logical axioms in embedding spaces to aid knowledge base completion. In our previous work at the NeSy 2024 conference, we introduced an ontology embedding method for ALC description logic. Our approach materializes a lattice structure of ontology concepts with an order-preserving embedding, distinguishing it from prior geometric and fuzzy logic methods. In this extended version, we extend our method to incorporate partial saturation rules that increase the information within the materialized lattice by adding new elements and morphisms to it. We show that the additional information can enhance the knowledge base completion task. Please do not hesitate to contact us should you require any further information. Thank you for considering our work. Sincerely, The authors.