[FOM] question about relevance and variable-sharing

[Edwin Mares]

Neil,

I think perhaps the *deepest* such results are Ross Brady's depth relevance theorems (in Studia Logica 1984, Volume 43, Issue 1-2 and in the JPL in 1992). The idea is that for logics around DW, that lack nested transitivity ((A->B)->((B->C)->(A->C)), and the like) but include conjunctive transitivity: (((A->B)&(B->C))->(A->C)) the following holds: if A->B is a theorem, then A and B share a variable at each depth, where the depth of a subformula is how deeply it is buried in nested implications within the formula. I think Brady may have republished the proofs in his book, Universal Logic.

Cheers,
Ed


Edwin Mares
Philosophy
Victoria University of Wellington
P.O. Box 600
Wellington, New Zealand
+64 (0)4 4635234
________________________________________
From: fom-bounces at cs.nyu.edu [fom-bounces at cs.nyu.edu] on behalf of Neil Tennant [neilpmb at yahoo.com]
Sent: 22 November 2013 07:37
To: fom at cs.nyu.edu
Subject: [FOM] question about relevance and variable-sharing

Could any member of this list please let me know what they judge to be the best/most important/deepest result about  variable-sharing that has ever been established for any (propositional) relevance logic of note?
Thanks--
Neil Tennant

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