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- Title
An Avron rule for fragments of R-mingle.
- Authors
METCALFE, GEORGE
- Abstract
Axiomatic bases of admissible rules are obtained for fragments of the substructural logic R-mingle. In particular, it is shown that a 'modus-ponens-like' rule introduced by Arnon Avron forms a basis for the admissible rules of its implication and implication-fusion fragments, while a basis for the admissible rules of the full multiplicative fragment requires an additional countably infinite set of rules. Indeed, this latter case provides an example of a three-valued logic with a finitely axiomatizable consequence relation that has no finite basis for its admissible rules.
- Subjects
NATURAL deduction (Logic); AVRON, Arnon; TERNARY logic; PEDAGOGICAL content knowledge; INTUITIONISTIC mathematics; PERMUTATIONS
- Publication
Journal of Logic & Computation, 2016, Vol 26, Issue 1, p381
- ISSN
0955-792X
- Publication type
Article
- DOI
10.1093/logcom/ext031