The goal of this work is to contribute to a smooth and semantically sound inter-operability between the ICD-11 (International Classification of Diseases-11th revision Joint Linearization for Mortality, Morbidity and Statistics) and SNOMED CT (SCT). To guarantee such inter-operation between a classification, characterized by a single hierarchy of mutually exclusive and exhaustive classes, as is the JLMMS successor of ICD-10 on the one hand, and the multi-hierarchical, ontology-based clinical terminology SCT on the other hand, we use ontology axioms that logically express generalizable truths. This is expressed by the compositional grammar of SCT, together with queries on axiomsof SCT. We test the feasibility of the method on the circulatory chapter of ICD-11 JLMMS and present limitations and results.