Relevance via decomposition

  • David Makinson London School of Economics

Abstract

We report on progress and an unsolved problem in our attempt to obtain a clear rationale for relevance logic via semantic decomposition trees. Suitable decomposition rules, constrained by a natural parity condition, generate a set of directly acceptable formulae that contains all axioms of the well-known system R, is closed under substitution and conjunction, satisfies the letter-sharing condition, but is not closed under detachment. To extend it, a natural recursion is built into the procedure for constructing decomposition trees. The resulting set of acceptable formulae has many attractive features, but it remains an open question whether it continues to satisfy the crucial letter-sharing condition.

Author Biography

David Makinson, London School of Economics

Philosophy Department

Professor

Published
2017-08-08
How to Cite
MAKINSON, David. Relevance via decomposition. The Australasian Journal of Logic, [S.l.], v. 14, n. 3, aug. 2017. ISSN 1448-5052. Available at: <https://ojs.victoria.ac.nz/ajl/article/view/4009>. Date accessed: 21 sep. 2019. doi: https://doi.org/10.26686/ajl.v14i3.4009.