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 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.
