## Notre Dame Journal of Formal Logic

### Admissible Rules and the Leibniz Hierarchy

James G. Raftery

#### Abstract

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

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

Dates
Accepted: 20 June 2013
First available in Project Euclid: 1 September 2016

https://projecteuclid.org/euclid.ndjfl/1472746139

Digital Object Identifier
doi:10.1215/00294527-3671151

Mathematical Reviews number (MathSciNet)
MR3565538

Zentralblatt MATH identifier
1357.03041

#### Citation

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. https://projecteuclid.org/euclid.ndjfl/1472746139

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