We address the problem of handling provenance information in ELHr ontologies. We consider a setting recently introduced for ontology-based data access, based on semirings and extending classical data provenance, in which ontology axioms are annotated with provenance tokens. A consequence inherits the provenance of the axioms involved in deriving it, yielding a provenance polynomial as an annotation. We analyse the semantics for the ELHr case and show that the presence of conjunctions poses various difficulties for handling provenance, some of which are mitigated by assuming multiplicative idempotency of the semiring. Under this assumption, we study three problems: ontology completion with provenance, computing the set of relevant axioms for a consequence, and query answering.

翻译：我们研究了处理描述逻辑 ELHr 本体中溯源信息的问题。考虑一种近期提出的、基于半环并扩展经典数据溯源的本体数据访问框架，其中本体公理带有溯源标记。结论继承推导过程中所涉及公理的溯源，从而产生一个作为注释的溯源多项式。我们分析了 ELHr 情况下的语义，并表明合取的存在给溯源处理带来了诸多困难，其中部分困难可通过假设半环的乘法幂等性得以缓解。在此假设下，我们研究了三个问题：带溯源的本体补全、计算结论的相关公理集以及查询回答。