In this paper we propose the Tensor-based Reective Relational Learning System (TRRLS) as a first tensor-based approach to decision support in the area of ontology alignment. The system may be seen as realizing a probabilistic inference with regard to the relation representing the ‘semantic equivalence’ of ontology classes or their properties. Despite the fact that TRRLS is based on the new idea of algebraic modeling of multi-relational data, it provides similar results to the best approaches of the Ontology Alignment Evaluation Initiative (OAEI) competitors to the task of matching concepts of Adult Mouse Anatomy ontology and NCI Thesaurus ontology on the basis of partially known expert matches.