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Ross T. Brady [34]Ross Thomas Brady [1]
  1. Ross T. Brady (forthcoming). Simplified Gentzenizations for Contraction-Less Logics. Logique Et Analyse.
     
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  2. Ross T. Brady (2014). The Simple Consistency of Naive Set Theory Using Metavaluations. Journal of Philosophical Logic 43 (2-3):261-281.
    The main aim is to extend the range of logics which solve the set-theoretic paradoxes, over and above what was achieved by earlier work in the area. In doing this, the paper also provides a link between metacomplete logics and those that solve the paradoxes, by finally establishing that all M1-metacomplete logics can be used as a basis for naive set theory. In doing so, we manage to reach logics that are very close in their axiomatization to that of the (...)
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  3. Ross T. Brady & Andrea Meinander (2013). Distribution in the Logic of Meaning Containment and in Quantum Mechanics. In. In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. 223--255.
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  4. Ross T. Brady (2012). The Consistency of Arithmetic, Based on a Logic of Meaning Containment. Logique Et Analyse 55 (219).
     
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  5. Ross Thomas Brady (2010). Free Semantics. Journal of Philosophical Logic 39 (5):511 - 529.
    Free Semantics is based on normalized natural deduction for the weak relevant logic DW and its near neighbours. This is motivated by the fact that in the determination of validity in truth-functional semantics, natural deduction is normally used. Due to normalization, the logic is decidable and hence the semantics can also be used to construct counter-models for invalid formulae. The logic DW is motivated as an entailment logic just weaker than the logic MC of meaning containment. DW is the logic (...)
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  6. JC Beall, Ross T. Brady, A. P. Hazen, Graham Priest & Greg Restall (2006). Relevant Restricted Quantification. Journal of Philosophical Logic 35 (6):587 - 598.
    The paper reviews a number of approaches for handling restricted quantification in relevant logic, and proposes a novel one. This proceeds by introducing a novel kind of enthymematic conditional.
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  7. Ross T. Brady (2006). Normalized Natural Deduction Systems for Some Relevant Logics I: The Logic DW. Journal of Symbolic Logic 71 (1):35 - 66.
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  8. Ross T. Brady (2004). On the Formalization of the Law of Non-Contradiction. In Graham Priest, J. C. Beall & Bradley Armour-Garb (eds.), The Law of Non-Contradiction. Clarendon Press.
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  9. Ross Brady & Ross T. Brady (2004). Adelaide, Australia July 5–6, 2003. Bulletin of Symbolic Logic 10 (2).
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  10. Ross T. Brady (1996). Gentzenizations of Relevant Logics Without Distribution. I. Journal of Symbolic Logic 61 (2):353-378.
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  11. Ross T. Brady (1996). Gentzenizations of Relevant Logics Without Distribution. II. Journal of Symbolic Logic 61 (2):379-401.
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  12. Ross T. Brady (1996). Gentzenizations of Relevant Logics with Distribution. Journal of Symbolic Logic 61 (2):402-420.
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  13. Ross T. Brady (1996). Relevant Implication and the Case for a Weaker Logic. Journal of Philosophical Logic 25 (2):151 - 183.
    We collect together some misgivings about the logic R of relevant inplication, and then give support to a weak entailment logic $DJ^{d}$ . The misgivings centre on some recent negative results concerning R, the conceptual vacuousness of relevant implication, and the treatment of classical logic. We then rectify this situation by introducing an entailment logic based on meaning containment, rather than meaning connection, which has a better relationship with classical logic. Soundness and completeness results are proved for $DJ^{d}$ with respect (...)
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  14. Ross T. Brady (1996). Simple Gentzenizations for the Formal Formulae of Contraction-Less Logics. Journal of Symbolic Logic 61 (4):1321-1346.
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  15. Martin Bunder & Ross T. Brady (1996). Australasian Association for Logic 30th Anniversary Conference. Bulletin of Symbolic Logic 2:112.
     
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  16. Ross T. Brady (1994). Rules in Relevant Logic - I: Semantic Classification. [REVIEW] Journal of Philosophical Logic 23 (2):111 - 137.
    We provide five semantic preservation properties which apply to the various rules -- primitive, derived and admissible -- of Hilbert-style axiomatizations of relevant logics. These preservation properties are with respect to the Routley-Meyer semantics, and consist of various truth- preservations and validity-preservations from the premises to the conclusions of these rules. We establish some deduction theorems, some persistence theorems and some soundness and completeness theorems, for these preservation properties. We then apply the above ideas, as best we can, to the (...)
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  17. Ross T. Brady (1993). Rules in Relevant Logic — II: Formula Representation. Studia Logica 52 (4):565 - 585.
    This paper surveys the various forms of Deduction Theorem for a broad range of relevant logics. The logics range from the basic system B of Routley-Meyer through to the system R of relevant implication, and the forms of Deduction Theorem are characterized by the various formula representations of rules that are either unrestricted or restricted in certain ways. The formula representations cover the iterated form,A 1 .A 2 . ... .A n B, the conjunctive form,A 1&A 2 & ...A n (...)
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  18. Ross T. Brady (1992). Hierarchical Semantics for Relevant Logics. Journal of Philosophical Logic 21 (4):357 - 374.
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  19. Ross T. Brady (1991). Gentzenization and Decidability of Some Contraction-Less Relevant Logics. Journal of Philosophical Logic 20 (1):97 - 117.
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  20. Ross T. Brady (1990). The Gentzenization and Decidability of RW. Journal of Philosophical Logic 19 (1):35 - 73.
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  21. Ross T. Brady (1989). A Content Semantics for Quantified Relevant Logics. II. Studia Logica 48 (2):243 - 257.
    In part I, we presented an algebraic-style of semantics, which we called “content semantics,” for quantified relevant logics based on the weak systemBBQ. We showed soundness and completeness with respect to theunreduced semantics ofBBQ. In part II, we proceed to show soundness and completeness for extensions ofBBQ with respect to this type of semantics. We introducereduced semantics which requires additional postulates for primeness and saturation. We then conclude by showing soundness and completeness forBB d Q and its extentions with respect (...)
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  22. Ross T. Brady (1989). A Routley-Meyer Affixing Style Semantics for Logics Containing Aristotle's Thesis. Studia Logica 48 (2):235 - 241.
    We provide a semantics for relevant logics with addition of Aristotle's Thesis, ∼(A→∼A) and also Boethius,(A→B)→∼(A→∼B). We adopt the Routley-Meyer affixing style of semantics but include in the model structures a regulatory structure for all interpretations of formulae, with a view to obtaining a lessad hoc semantics than those previously given for such logics. Soundness and completeness are proved, and in the completeness proof, a new corollary to the Priming Lemma is introduced (c.f.Relevant Logics and their Rivals I, Ridgeview, 1982).
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  23. Ross T. Brady (1989). The Non-Triviality of Dialectical Set Theory. In G. Priest, R. Routley & J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag. 437--470.
     
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  24. Ross T. Brady (1988). A Content Semantics for Quantified Relevant Logics. I. Studia Logica 47 (2):111 - 127.
    We present an algebraic-style of semantics, which we call a content semantics, for quantified relevant logics based on the weak system BBQ. We show soundness and completeness for all quantificational logics extending BBQ and also treat reduced modelling for all systems containing BB d Q. The key idea of content semantics is that true entailments AB are represented under interpretation I as content containments, i.e. I(A)I(B) (or, the content of A contains that of B). This is opposed to the truth-functional (...)
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  25. Ross T. Brady (1984). Depth Relevance of Some Paraconsistent Logics. Studia Logica 43 (1-2):63 - 73.
    The paper essentially shows that the paraconsistent logicDR satisfies the depth relevance condition. The systemDR is an extension of the systemDK of [7] and the non-triviality of a dialectical set theory based onDR has been shown in [3]. The depth relevance condition is a strengthened relevance condition, taking the form: If DR- AB thenA andB share a variable at the same depth, where the depth of an occurrence of a subformulaB in a formulaA is roughly the number of nested ''s (...)
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  26. Ross T. Brady (1984). Reply to Priest on Berry's Paradox. Philosophical Quarterly 34 (135):157-163.
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  27. Robert K. Meyer, Steve Giambrone & Ross T. Brady (1984). Where Gamma Fails. Studia Logica 43 (3):247 - 256.
    A major question for the relevant logics has been, “Under what conditions is Ackermann's ruleγ from -A ∨B andA to inferB, admissible for one of these logics?” For a large number of logics and theories, the question has led to an affirmative answer to theγ problem itself, so that such an answer has almost come to be expected for relevant logics worth taking seriously. We exhibit here, however, another large and interesting class of logics-roughly, the Boolean extensions of theW — (...)
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  28. Ross T. Brady (1983). The Simple Consistency of a Set Theory Based on the Logic ${\Rm CSQ}$. Notre Dame Journal of Formal Logic 24 (4):431-449.
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  29. Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady (1982). Relevant Logics and Their Rivals. Ridgeview.
     
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  30. Ross T. Brady (1980). A Theory of Classes and Individuals Based on a $3$-Valued Significance Logic. [REVIEW] Notre Dame Journal of Formal Logic 21 (2):385-414.
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  31. Ross T. Brady (1980). Significance Range Theory. Notre Dame Journal of Formal Logic 21 (2):319-345.
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  32. Ross T. Brady (1980). Two Remarks On: The Logic of Significance and Context. Vol. I [Halsted, New York, 1973]. Notre Dame Journal of Formal Logic 21 (2):263-272.
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  33. Ross T. Brady (1976). Significance Logics. Notre Dame Journal of Formal Logic 17 (2):161-183.
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  34. Ross T. Brady (1972). The Relative Consistency of the Class Axioms of Abstraction and Extensionality and the Axioms of NBG in a Three-Valued Logic. Notre Dame Journal of Formal Logic 13 (2):161-176.
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  35. Ross T. Brady (1971). The Consistency of the Axioms of Abstraction and Extensionality in a Three-Valued Logic. Notre Dame Journal of Formal Logic 12 (4):447-453.
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