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John Slaney [13]John K. Slaney [8]
  1. Greg Restall & John Slaney, Technical Report TR-ARP-2-95.
    In this paper we consider the implications for belief revision of weakening the logic under which belief sets are taken to be closed. A widely held view is that the usual belief revision functions are highly classical, especially in being driven by consistency. We show that, on the contrary, the standard representation theorems still hold for paraconsistent belief revision. Then we give conditions under which consistency is preserved by revisions, and we show that this modelling allows for the gradual revision (...)
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  2. 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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  3. John Slaney & Edward Walker (2014). The One-Variable Fragment of T→. Journal of Philosophical Logic 43 (5):867-878.
    We show that there are infinitely many pairwise non-equivalent formulae in one propositional variable p in the pure implication fragment of the logic T of “ticket entailment” proposed by Anderson and Belnap. This answers a question posed by R. K. Meyer.
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  4. Jc Beall, Ross Brady, J. Michael Dunn, A. P. Hazen, Edwin Mares, Robert K. Meyer, Graham Priest, Greg Restall, David Ripley, John Slaney & Richard Sylvan (2012). On the Ternary Relation and Conditionality. Journal of Philosophical Logic 41 (3):595 - 612.
    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 (...)
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  5. Tomasz Kowalski & John Slaney (2008). A Finite Fragment Of S3. Reports on Mathematical Logic.
    It is shown that the pure implication fragment of the modal logic [3] , pp. 385--387) has finitely many non-equivalent formulae in one variable. The exact number of such formulae is not known. We show that this finiteness result is the best possible, since the analogous fragment of S4, and therefore of [3], in two variables has infinitely many non-equivalent formulae.
     
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  6. John Slaney (2005). Semipositive LTL with an Uninterpreted Past Operator. Logic Journal of the Igpl 13 (2):211-229.
    $LTL is a version of linear temporal logic in which eventualities are not expressible, but in which there is a sentential constant $ intended to be true just at the end of some behaviour of interest—that is, to mark the end of the accepted words of some language. There is an effectively recognisable class of $LTL formulae which express behaviours, but in a sense different from the standard one of temporal logics like LTL or CTL. This representation is useful for (...)
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  7. John K. Slaney, Robert K. Meyer & Greg Restall (1996). Linear Arithmetic Desecsed. Logique Et Analyse 39:379-388.
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  8. John Slaney (1993). Sentential Constants in Systems Near R. Studia Logica 52 (3):443 - 455.
    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 (...)
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  9. John Slaney & Martin W. Bunder (1993). 1992 Annual Meeting of the Australasian Association for Logic. Journal of Symbolic Logic 58 (4):1477-1484.
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  10. John Slaney (1992). Realism in Mathematics. Philosophical Books 33 (1):61-62.
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  11. 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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  12. John Slaney (1990). A General Logic. Australasian Journal of Philosophy 68 (1):74 – 88.
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  13. A. General Logic & John Slaney (1989). Kh Sievers. International Philosophical Quarterly 29 (4).
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  14. John Slaney (1989). Solution to a Problem of Ono and Komori. Journal of Philosophical Logic 18 (1):103 - 111.
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  15. John Slaney (1988). A Logic for Vagueness. Australasian Journal of Logic 8:100-134.
    This paper presents F, substructural logic designed to treat vagueness. Weaker than Lukasiewicz’s infinitely valued logic, it is presented first in a natural deduction system, then given a Kripke semantics in the manner of Routley and Meyer's ternary relational semantics for R and related systems, but in this case, the points are motivated as degrees to which the truth could be stretched. Soundness and completeness are proved, not only for the propositional system, but also for its extension with first-order quantifiers. (...)
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  16. John Slaney (1988). A Note on 'Most'. Analysis 48 (3):134 - 135.
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  17. 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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  18. 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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  19. 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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  20. 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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  21. John K. Slaney (1981). 'Entailment' Survives Lewy's Paradoxes. Analysis 41 (4):188 - 191.
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