## Selected papers on Relevant Logic## John Slaney
One-variable Ticket Implication This is the abstract of the paper: John Slaney and Edward Walker.
We show that there are infinitely many pairwise non-equivalent formulae
in one propositional variable
This is the abstract of the paper: JC Beall, Ross Brady, Mike Dunn, Allen Hazen, Ed Mares, Roberty Meyer, Graham Priest, Greg Restall, David Ripley, John Slaney and Richard Sylvan. One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley-Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close by briefly discussing a general conception of conditionality that may unify the three given conceptions.
This is the abstract of the paper: John K. Slaney, Robert K. Meyer and Greg Restall.
In classical and intuitionistic arithmetics, any formula implies a true
equation, and a false equation implies anything. In weaker logics fewer
implications hold. In this paper we rehearse known results about the
relevant arithmetic R#, and we show that in linear arithmetic LL# by
contrast false equations never imply true ones. As a result, linear
arithmetic is
Sentential Constants in Systems Near R This is the abstract of the paper: John Slaney. An Ackermann constant is a formula of sentential logic built up from the sentential constant t by closing under connectives. It is known that there are only finitely many non-equivalent Ackermann constants in the relevant logic R. In this paper it is shown that the most natural systems close to R but weaker than it - in particular the non-distributive system LR and the modalised system NR - allow infinitely many Ackermann constants to be distinguished. The argument in each case proceeds by construction of an algebraic model, infinite in the case of LR and of arbitrary finite size in the case of NR. The search for these models was aided by the computer program MaGIC (Matrix Generator for Implication Connectives) developed by the author at the Australian National University.
A Structurally Complete Fragment of Relevant Logic This is the introduction to the paper: John K Slaney and Robert K Meyer.
This note contains a proof that the implication-conjunction fragment of the
relevant logic R is
The Ackermann Constant Problem This is the abstract of the paper: John K Slaney.
This is a report on researches carried out at the Australian National
University some ten years ago which led to proofs of the results reported in
[Slaney,
On the Structure of De Morgan Monoids This is the abstract of the paper: John K Slaney.
A De Morgan monoid is
This is the abstract of the paper: John K Slaney. It is shown that there are exactly six normal De Morgan monoids generated by the identity element alone. The free De Morgan monoid with no generators but the identity is characterised and shown to have exactly three thousand and eighty-eight elements. This result solves the "Ackermann constant problem" of describing the structure of sentential constants in the logic R.
Dr J K Slaney Phone (Aus.): (026) 125 8607 Theory Group Phone (Int.): +61 26 125 8607 Research School of Computer Science Fax (Aus.): (026) 125 8651 Australian National University Fax (Int.): +61 26 125 8651 Canberra, ACT, 0200, AUSTRALIA |