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Robert K. Meyer [91]Robert Kenneth Meyer [1]
  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. Robert K. Meyer & Greg Restall, “Strenge” Arithmetics.
    In Entailment, Anderson and Belnap motivated their modification E of Ackermann’s strenge Implikation Π Π’ as a logic of relevance and necessity. The kindred system R was seen as relevant but not as modal. Our systems of Peano arithmetic R# and omega arithmetic R## were based on R to avoid fallacies of relevance. But problems arose as to which arithmetic sentences were (relevantly) true. Here we base analogous systems on E to solve those problems. Central to motivating E is the (...)
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  3. 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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  4. Robert K. Meyer (2008). Ai, Me and Lewis (Abelian Implication, Material Equivalence and C I Lewis 1920). Journal of Philosophical Logic 37 (2):169 - 181.
    C I Lewis showed up Down Under in 2005, in e-mails initiated by Allen Hazen of Melbourne. Their topic was the system Hazen called FL (a Funny Logic), axiomatized in passing in Lewis 1921. I show that FL is the system MEN of material equivalence with negation. But negation plays no special role in MEN. Symbolizing equivalence with → and defining ∼A inferentially as A→f, the theorems of MEN are just those of the underlying theory ME of pure material equivalence. (...)
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  5. Robert K. Meyer (2008). Fallacies of Division. Proceedings of the Xxii World Congress of Philosophy 13:71-80.
    What do well-known theories look like if formulated with a relevant rather than a standard classical or intuitionist logic? Do familiar reconstructions of these theories go through, or do we change the reconstruction when we change the logic? I show in this paper that a new class of fallacies arises when we take the familiar Peano postulates as the foundation for a relevant theory of the natural numbers N. For these postulates fail in the relevant context to establish the relevant (...)
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  6. L. Wos, G. W. Pieper & Robert K. Meyer (2007). REVIEWS-A Fascinating Country in the World of Computing--Your Guide to Automated Reasoning. Bulletin of Symbolic Logic 13 (3):359-361.
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  7. Koushik Pal & Robert K. Meyer (2005). Basic Relevant Theories for Combinators at Levels I and II. Australasian Journal of Logic 3 (14-32):14-32.
    The system B+ is the minimal positive relevant logic. B+ is trivially extended to B+T on adding a greatest truth T. If we leave ∨ out of the formation apparatus, we get the fragment B∧T. It is known that the set of ALL B∧T theories provides a good model for the combinators CL at Level-I, which is the theory level. Restoring ∨ to get back B+T was not previously fruitful at Level-I, because the set of all B+T theories is NOT (...)
     
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  8. Robert K. Meyer (2004). Ternary Relations and Relevant Semantics. Annals of Pure and Applied Logic 127 (1-3):195-217.
    Modus ponens provides the central theme. There are laws, of the form A→C. A logic L collects such laws. Any datum A provides input to the laws of L. The central ternary relation R relates theories L,T and U, where U consists of all of the outputs C got by applying modus ponens to major premises from L and minor premises from T. Underlying this relation is a modus ponens product operation on theories L and T, whence RLTU iff LTU. (...)
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  9. Yoko Motohama, Robert K. Meyer & Mariangiola Dezani-Ciancaglini (2002). The Semantics of Entailment Omega. Notre Dame Journal of Formal Logic 43 (3):129-145.
    This paper discusses the relation between the minimal positive relevant logic B and intersection and union type theories. There is a marvelous coincidence between these very differently motivated research areas. First, we show a perfect fit between the Intersection Type Discipline ITD and the tweaking BT of B, which saves implication and conjunction but drops disjunction . The filter models of the -calculus (and its intimate partner Combinatory Logic CL) of the first author and her coauthors then become theory models (...)
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  10. Edwin D. Mares & Robert K. Meyer (2001). Relevant Logics. In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Blackwell Publishers 280--308.
     
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  11. Robert K. Meyer (1998). ⊃E is Admissible in “True” Relevant Arithmetic. Journal of Philosophical Logic 27 (4):327 - 351.
    The system R## of "true" relevant arithmetic is got by adding the ω-rule "Infer VxAx from AO, A1, A2, ...." to the system R# of "relevant Peano arithmetic". The rule ⊃E (or "gamma") is admissible for R##. This contrasts with the counterexample to ⊃E for R# (Friedman & Meyer, "Whither Relevant Arithmetic"). There is a Way Up part of the proof, which selects an arbitrary non-theorem C of R## and which builds by generalizing Henkin and Belnap arguments a prime theory (...)
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  12. Robert K. Meyer (1998). ŠƒE is Admissible in €œTrue” Relevant Arithmetic. Journal of Philosophical Logic 27 (4):327-351.
    The system R## of "true" relevant arithmetic is got by adding the ω-rule "Infer VxAx from AO, A1, A2, ...." to the system R# of "relevant Peano arithmetic". The rule ⊃E (or "gamma") is admissible for R##. This contrasts with the counterexample to ⊃E for R# (Friedman & Meyer, "Whither Relevant Arithmetic"). There is a Way Up part of the proof, which selects an arbitrary non-theorem C of R## and which builds by generalizing Henkin and Belnap arguments a prime theory (...)
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  13. Robert K. Meyer (1998). In Memoriam: Richard (Routley) Sylvan, 1935-1996. Bulletin of Symbolic Logic 4 (3):338-340.
  14. Anita Feferman, Solomon Feferman, Robert Goldblatt, Yuri Gurevich, Klaus Grue, Sven Ove Hansson, Lauri Hella, Robert K. Meyer & Petri Mäenpää (1997). Stål Anderaa (Oslo), A Traktenbrot Inseparability Theorem for Groups. Peter Dybjer (G Öteborg), Normalization by Yoneda Embedding (Joint Work with D. Cubric and PJ Scott). Abbas Edalat (Imperial College), Dynamical Systems, Measures, Fractals, and Exact Real Number Arithmetic Via Domain Theory. [REVIEW] Bulletin of Symbolic Logic 3 (4).
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  15. John K. Slaney, Robert K. Meyer & Greg Restall (1996). Linear Arithmetic Desecsed. Logique Et Analyse 39:379-388.
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  16. Robert K. Meyer & Hiroakira Ono (1994). The Finite Model Property for BCK and BCIW. Studia Logica 53 (1):107 - 118.
    This paper shows that both implicational logics BCK and BCIW have the finite model property. The proof of the finite model property for BCIW, which is equal to the relevant logic $\text{R}_{\rightarrow}$ , was originally given by the first author in his unpublished paper [6] in 1973. The finite model property for BCK can be obtained by modifying the proof of that for BCIW. Here, both of these proofs will be given in a unified form and the difference between them (...)
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  17. Edwin D. Mares & Robert K. Meyer (1993). The Semantics Ofr. Journal of Philosophical Logic 22 (1):95 - 110.
    The Logic R4 is obtained by adding the axiom □(A v B) → (◇A v □B) to the modal relevant logic NR. We produce a model theory for this logic and show completeness. We also show that there is a natural embedding of a Kripke model for S4 in each R4 model structure.
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  18. Harvey Friedman & Robert K. Meyer (1992). Whither Relevant Arithmetic? Journal of Symbolic Logic 57 (3):824-831.
    Based on the relevant logic R, the system R# was proposed as a relevant Peano arithmetic. R# has many nice properties: the most conspicuous theorems of classical Peano arithmetic PA are readily provable therein; it is readily and effectively shown to be nontrivial; it incorporates both intuitionist and classical proof methods. But it is shown here that R# is properly weaker than PA, in the sense that there is a strictly positive theorem QRF of PA which is unprovable in R#. (...)
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  19. Edwin D. Mares & Robert K. Meyer (1992). The Admissibility of $\Gamma$ in ${\Rm R}4$. Notre Dame Journal of Formal Logic 33 (2):197-206.
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  20. Robert K. Meyer & Errol P. Martin (1992). On Establishing the Converse. Logique Et Analyse 139:207-222.
     
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  21. 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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  22. Robert K. Meyer (1990). Peirced Clean Through. Bulletin of the Section of Logic 19 (3):100-101.
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  23. Robert K. Meyer, Georg Dorn & P. Weingartner (1990). A Farewell to Entailment. Journal of Symbolic Logic 55 (1):352-353.
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  24. Steve Giambrone & Robert K. Meyer (1989). Completeness and Conservative Extension Results for Some Boolean Relevant Logics. Studia Logica 48 (1):1 - 14.
    This paper presents completeness and conservative extension results for the boolean extensions of the relevant logic T of Ticket Entailment, and for the contractionless relevant logics TW and RW. Some surprising results are shown for adding the sentential constant t to these boolean relevant logics; specifically, the boolean extensions with t are conservative of the boolean extensions without t, but not of the original logics with t. The special treatment required for the semantic normality of T is also shown along (...)
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  25. Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady (1989). Relevant Logics and Their Rivals. Part I. The Basic Philosophical and Semantical Theory. Journal of Symbolic Logic 54 (1):293-296.
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  26. Robert K. Meyer, Errol P. Martin, Steve Giambrone & Alasdair Urquhart (1988). Further Results on Proof Theories For Semilattice Logics. Mathematical Logic Quarterly 34 (4):301-304.
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  27. Richard Routley, Robert K. Meyer, Val Plumwood & Ross T. Brady (1988). Relevant Logics and Their Rivals: Part 1. The Basic Philosophical and Semantical Theory. Studia Logica 47 (2):169-172.
     
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  28. Paul B. Thistlewaite, M. A. Mcrobbie & Robert K. Meyer (1988). Automated Theorem-Proving in Non-Classical Logics. Monograph Collection (Matt - Pseudo).
     
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  29. God Exists, Robert K. Meyer & Materialism Rorty (1987). McCall and Counter/Actuals, Richard Otte. Philosophical Quarterly 37 (147).
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  30. Steve Giambrone, Robert K. Meyer & Alasdair Urquhart (1987). A Contractionless Semilattice Semantics. Journal of Symbolic Logic 52 (2):526-529.
  31. Robert K. Meyer (1987). Curry's Philosophy of Formal Systems. Australasian Journal of Philosophy 65 (2):156 – 171.
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  32. Robert K. Meyer (1987). God Exists! Noûs 21 (3):345-361.
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  33. Robert K. Meyer (1986). Idempotents in R. Mathematical Logic Quarterly 32 (25‐30):407-408.
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  34. Robert K. Meyer (1986). Sentential Constants in R and R⌝. Studia Logica 45 (3):301 - 327.
    In this paper, we shall confine ourselves to the study of sentential constants in the system R of relevant implication.In dealing with the behaviour of the sentential constants in R, we shall think of R itself as presented in three stages, depending on the level of truth-functional involvement.
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  35. Robert K. Meyer & Errol P. Martin (1986). Logic on the Australian Plan. Journal of Philosophical Logic 15 (3):305 - 332.
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  36. Robert K. Meyer & Igor Urbas (1986). Conservative Extension in Relevant Arithmetic. Mathematical Logic Quarterly 32 (1‐5):45-50.
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  37. Robert K. Meyer & Adrian Abraham (1984). A Model for the Modern Malaise. Philosophia 14 (1-2):25-40.
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  38. 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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  39. Robert K. Meyer & Chris Mortensen (1984). Inconsistent Models for Relevant Arithmetics. Journal of Symbolic Logic 49 (3):917-929.
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  40. Robert K. Meyer (1983). A Note on ${\Rm R}_{\Rightarrow}$ Matrices. Notre Dame Journal of Formal Logic 24 (4):450-472.
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  41. Robert K. Meyer, Errol P. Martin & Robert Dwyer (1983). The Fundamental ${\Rm S}$-Theorem---A Corollary. Notre Dame Journal of Formal Logic 24 (4):509-516.
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  42. Robert K. Meyer, Ermanno Bencivenga & Karel Lambert (1982). The Ineliminability of E! In Free Quantification Theory Without Identity. Journal of Philosophical Logic 11 (2):229 - 231.
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  43. Robert K. Meyer & Michael A. McRobbie (1982). Multisets and Relevant Implication I. Australasian Journal of Philosophy 60 (2):107 – 139.
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  44. Robert K. Meyer & Michael A. McRobbie (1982). Multisets and Relevant Implication II. Australasian Journal of Philosophy 60 (3):265 – 281.
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  45. Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady (1982). Relevant Logics and Their Rivals. Ridgeview.
     
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  46. Robert K. Meyer & S. Giambrone (1981). Strict Implication In T. Logique Et Analyse 24 (June):267-269.
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  47. Robert K. Meyer (1980). Sentential Constants in Relevance Implication. Bulletin of the Section of Logic 9 (1):33-36.
    Sentential constants have been part of the R environment since Church [1]. They have had diverse uses in explicating relevant ideas and in sim- plifying them technically. Of most interest have been the Ackermann pair of constants t; f, functioning conceptually as a least truth, and as a greatest , under the ordering of propositions under true impli- cation. Also interesting have been the Church constants F; T, functioning similarly as least greatest propositions.
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  48. Robert K. Meyer (1980). Syntactical Treatment of Negation. Analysis 40 (2):74 - 78.
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  49. Robert K. Meyer (1980). Career Induction for Quantifiers. Notre Dame Journal of Formal Logic 21 (3):539-548.
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  50. Robert K. Meyer & Steve Giambrone (1980). R+ is Contained in T. Bulletin of the Section of Logic 9 (1):30-32.
    Although the system T of ticket entailment is obviously related to its cousins E and R , it is motivated along quite distinctive lines in Anderson and Belnap [1975]. It would seem, accordingly, that T is more nearly akin to the system P W studied in Martin [1978] than to E and R. The result presented here, however, at least suggests the contrary.
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