Raftery, James G.2016-11-302016-11-302016Raftery, JG 2016, 'Admissible rules and the Leibniz hierarchy', Notre Dame Journal of Formal Logic , vol. 57, no. 4, pp. 569-606.0029-4527 (print)1939-0726 (online)10.1215/00294527-3671151http://hdl.handle.net/2263/58313This paper provides a semantic analysis of admissible rules and associated completeness conditions for arbitrary deductive systems, using the framework of abstract algebraic logic. Algebraizability is not assumed, so the meaning and signi cance of the principal notions vary with the level of the Leibniz hierarchy at which they are presented. As a case study of the resulting theory, the non-algebraizable fragments of relevance logic are considered.en© Duke University PressDeductive systemAdmissible ruleReduced matrixStructural completenessLeibniz hierarchy[Order] algebraizable logicBCIWPostprint Article