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  1. John K. Slaney, Robert K. Meyer & Greg Restall, Technical Report TR-ARP-2-96.
    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 desecsed. A formula A which entails 0 = 0 is a secondary equation; one entailed by 0 6= 0 is a secondary unequation. A (...)
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  2. John K. Slaney, Robert K. Meyer & Greg Restall (1996). Linear Arithmetic Desecsed. Logique Et Analyse 39:379-388.
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  3. John K. Slaney & Robert K. Meyer (1992). A Structurally Complete Fragment of Relevant Logic. Notre Dame Journal of Formal Logic 33 (4):561-566.
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  4. John K. Slaney (1988). On the Structure of De Morgan Monoids with Corollaries on Relevant Logic and Theories. Notre Dame Journal of Formal Logic 30 (1):117-129.
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  5. John K. Slaney (1987). Reduced Models for Relevant Logics Without ${\Rm WI}$. Notre Dame Journal of Formal Logic 28 (3):395-407.
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  6. John K. Slaney (1985). 3088 Varieties a Solution to the Ackermann Constant Problem. Journal of Symbolic Logic 50 (2):487-501.
    It is shown that there are exactly six normal DeMorgan monoids generated by the identity element alone. The free DeMorgan monoid with no generators but the identity is characterised and shown to have exactly three thousand and eighty-eight elements. This result solves the "Ackerman constant problem" of describing the structure of sentential constants in the logic R.
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  7. John K. Slaney (1984). A Metacompleteness Theorem for Contraction-Free Relevant Logics. Studia Logica 43 (1-2):159 - 168.
    I note that the logics of the relevant group most closely tied to the research programme in paraconsistency are those without the contraction postulate(A.AB).AB and its close relatives. As a move towards gaining control of the contraction-free systems I show that they are prime (that wheneverA B is a theorem so is eitherA orB). The proof is an extension of the metavaluational techniques standardly used for analogous results about intuitionist logic or the relevant positive logics.
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  8. John K. Slaney (1981). 'Entailment' Survives Lewy's Paradoxes. Analysis 41 (4):188 - 191.
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