Notre Dame Journal of Formal Logic

Admissible Rules and the Leibniz Hierarchy

James G. Raftery

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This 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 significance 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 nonalgebraizable fragments of relevance logic are considered.

Article information

Notre Dame J. Formal Logic, Volume 57, Number 4 (2016), 569-606.

Received: 1 May 2012
Accepted: 20 June 2013
First available in Project Euclid: 1 September 2016

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Zentralblatt MATH identifier

Primary: 03B22: Abstract deductive systems 03G27: Abstract algebraic logic
Secondary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52} 08C10: Axiomatic model classes [See also 03Cxx, in particular 03C60]

deductive system admissible rule reduced matrix structural completeness Leibniz hierarchy [order] algebraizable logic BCIW


Raftery, James G. Admissible Rules and the Leibniz Hierarchy. Notre Dame J. Formal Logic 57 (2016), no. 4, 569--606. doi:10.1215/00294527-3671151.

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