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Profile: Jon Michael Dunn (Indiana University)
  1. Katalin Bimbó & J. Michael Dunn (2014). Extracting BB′IW Inhabitants of Simple Types From Proofs in the Sequent Calculus {LT_to^{T}} for Implicational Ticket Entailment. Logica Universalis 8 (2):141-164.
    The decidability of the logic of pure ticket entailment means that the problem of inhabitation of simple types by combinators over the base { B, B′, I, W } is decidable too. Type-assignment systems are often formulated as natural deduction systems. However, our decision procedure for this logic, which we presented in earlier papers, relies on two sequent calculi and it does not yield directly a combinator for a theorem of ${T_\to}$ . Here we describe an algorithm to extract an (...)
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  2. Katalin Bimbó & J. Michael Dunn (2013). On the Decidability of Implicational Ticket Entailment. Journal of Symbolic Logic 78 (1):214-236.
    The implicational fragment of the logic of relevant implication, $R_\to$ is known to be decidable. We show that the implicational fragment of the logic of ticket entailment, $T_\to$ is decidable. Our proof is based on the consecution calculus that we introduced specifically to solve this 50-year old open problem. We reduce the decidability problem of $T_\to$ to the decidability problem of $R_\to$. The decidability of $T_\to$ is equivalent to the decidability of the inhabitation problem of implicational types by combinators over (...)
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  3. J. Michael Dunn (2013). A Guide to the Floridi Keys. Metascience 22 (1):93-98.
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  4. J. Michael Dunn (2013). A Guide to the Floridi Keys: Luciano Floridi: The Philosophy of Information. Oxford: Oxford University Press, 2011, Xx+ 405pp,£ 37.50 HB (Essay Review). [REVIEW] Metascience 22 (1):93-98.
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  5. J. Michael Dunn, Lawrence S. Moss & Zhenghan Wang (2013). Editors' Introduction: The Third Life of Quantum Logic: Quantum Logic Inspired by Quantum Computing. [REVIEW] Journal of Philosophical Logic 42 (3):443-459.
  6. 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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  7. Katalin Bimbó & J. Michael Dunn (2012). New Consecution Calculi for $R^{T}_{\To}$. Notre Dame Journal of Formal Logic 53 (4):491-509.
    The implicational fragment of the logic of relevant implication, $R_{\to}$ is one of the oldest relevance logics and in 1959 was shown by Kripke to be decidable. The proof is based on $LR_{\to}$ , a Gentzen-style calculus. In this paper, we add the truth constant $\mathbf{t}$ to $LR_{\to}$ , but more importantly we show how to reshape the sequent calculus as a consecution calculus containing a binary structural connective, in which permutation is replaced by two structural rules that involve $\mathbf{t}$ (...)
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  8. Katalin Bimbó & J. Michael Dunn (2012). New Consecution Calculi for $R^{T}_{To}$. Notre Dame Journal of Formal Logic 53 (4):491-509.
    The implicational fragment of the logic of relevant implication, $R_{\to}$ is one of the oldest relevance logics and in 1959 was shown by Kripke to be decidable. The proof is based on $LR_{\to}$, a Gentzen-style calculus. In this paper, we add the truth constant $\mathbf{t}$ to $LR_{\to}$, but more importantly we show how to reshape the sequent calculus as a consecution calculus containing a binary structural connective, in which permutation is replaced by two structural rules that involve $\mathbf{t}$. This calculus, (...)
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  9. J. Michael Dunn (2010). Contradictory Information: Too Much of a Good Thing. [REVIEW] Journal of Philosophical Logic 39 (4):425 - 452.
    Both I and Belnap, motivated the "Belnap-Dunn 4-valued Logic" by talk of the reasoner being simply "told true" (T) and simply "told false" (F), which leaves the options of being neither "told true" nor "told false" (N), and being both "told true" and "told false" (B). Belnap motivated these notions by consideration of unstructured databases that allow for negative information as well as positive information (even when they conflict). We now experience this on a daily basis with the Web. But (...)
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  10. Katalin Bimbó & J. Michael Dunn (2009). Symmetric Generalized Galois Logics. Logica Universalis 3 (1):125-152.
    Symmetric generalized Galois logics (i.e., symmetric gGl s) are distributive gGl s that include weak distributivity laws between some operations such as fusion and fission. Motivations for considering distribution between such operations include the provability of cut for binary consequence relations, abstract algebraic considerations and modeling linguistic phenomena in categorial grammars. We represent symmetric gGl s by models on topological relational structures. On the other hand, topological relational structures are realized by structures of symmetric gGl s. We generalize the weak (...)
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  11. Katalin Bimbó, J. Michael Dunn & Roger D. Maddux (2009). Relevance Logics and Relation Algebras. Review of Symbolic Logic 2 (1):102-131.
    Relevance logics are known to be sound and complete for relational semantics with a ternary accessibility relation. This paper investigates the problem of adequacy with respect to special kinds of dynamic semantics (i.e., proper relation algebras and relevant families of relations). We prove several soundness results here. We also prove the completeness of a certain positive fragment of R as well as of the first-degree fragment of relevance logics. These results show that some core ideas are shared between relevance logics (...)
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  12. J. Michael Dunn, Mai Gehrke & Alessandra Palmigiano (2005). Canonical Extensions and Relational Completeness of Some Substructural Logics. Journal of Symbolic Logic 70 (3):713 - 740.
    In this paper we introduce canonical extensions of partially ordered sets and monotone maps and a corresponding discrete duality. We then use these to give a uniform treatment of completeness of relational semantics for various substructural logics with implication as the residual(s) of fusion.
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  13. J. Michael Dunn, Tobias J. Hagge, Lawrence S. Moss & Zhenghan Wang (2005). Quantum Logic as Motivated by Quantum Computing. Journal of Symbolic Logic 70 (2):353 - 359.
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  14. J. Michael Dunn & Chunlai Zhou (2005). Negation in the Context of Gaggle Theory. Studia Logica 80 (2-3):235 - 264.
    We study an application of gaggle theory to unary negative modal operators. First we treat negation as impossibility and get a minimal logic system Ki that has a perp semantics. Dunn's kite of different negations can be dealt with in the extensions of this basic logic Ki. Next we treat negation as “unnecessity” and use a characteristic semantics for different negations in a kite which is dual to Dunn's original one. Ku is the minimal logic that has a (...)
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  15. J. Michael Dunn (2001). Algebraic Methods in Philosophical Logic. Oxford University Press.
    This comprehensive text demonstrates how various notions of logic can be viewed as notions of universal algebra.
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  16. J. Michael Dunn & Katalin Bimb� (2001). Four-Valued Logic. Notre Dame Journal of Formal Logic 42 (3):171-192.
    Four-valued semantics proved useful in many contexts from relevance logics to reasoning about computers. We extend this approach further. A sequent calculus is defined with logical connectives conjunction and disjunction that do not distribute over each other. We give a sound and complete semantics for this system and formulate the same logic as a tableaux system. Intensional conjunction (fusion) and its residuals (implications) can be added to the sequent calculus straightforwardly. We extend a simplified version of the earlier semantics for (...)
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  17. Yaroslav Shramko, J. Michael Dunn & Tatsutoshi Takenaka (2001). The Trilaticce of Constructive Truth Values. Journal of Logic and Computation 11 (1):761--788.
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  18. J. Michael Dunn (2000). Partiality and its Dual. Studia Logica 66 (1):5-40.
    This paper explores allowing truth value assignments to be undetermined or "partial" (no truth values) and overdetermined or "inconsistent" (both truth values), thus returning to an investigation of the four-valued semantics that I initiated in the sixties. I examine some natural consequence relations and show how they are related to existing logics, including ukasiewicz's three-valued logic, Kleene's three-valued logic, Anderson and Belnap's (first-degree) relevant entailments, Priest's "Logic of Paradox", and the first-degree fragment of the Dunn-McCall system "R-mingle". None of these (...)
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  19. J. Michael Dunn (1997). A Logical Framework for the Notion of Natural Property. In John Earman & John Norton (eds.), The Cosmos of Science. University of Pittsburgh Press. 6--458.
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  20. J. Michael Dunn (1996). Generalized Onrno Negation. In H. Wansing (ed.), Negation: A Notion in Focus. W. De Gruyter. 7--3.
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  21. J. Michael Dunn (1996). Is Existence a (Relevant) Predicate? Philosophical Topics 24 (1):1-34.
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  22. J. Michael Dunn (1995). Positive Modal Logic. Studia Logica 55 (2):301 - 317.
    We give a set of postulates for the minimal normal modal logicK + without negation or any kind of implication. The connectives are simply , , , . The postulates (and theorems) are all deducibility statements . The only postulates that might not be obvious are.
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  23. Gerard Allwein & J. Michael Dunn (1993). A Kripke Semantics for Linear Logic. Journal of Symbolic Logic 58:514-545.
     
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  24. Gerard Allwein & J. Michael Dunn (1993). Kripke Models for Linear Logic. Journal of Symbolic Logic 58 (2):514-545.
    We present a Kripke model for Girard's Linear Logic (without exponentials) in a conservative fashion where the logical functors beyond the basic lattice operations may be added one by one without recourse to such things as negation. You can either have some logical functors or not as you choose. Commutatively and associatively are isolated in such a way that the base Kripke model is a model for noncommutative, nonassociative Linear Logic. We also extend the logic by adding a coimplication operator, (...)
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  25. Alan Ross Anderson, Nuel D. Belnap, J. Michael Dunn & D. M. Balme (1993). Appearance in the List Does Not Preclude a Future Review of the Book. Where They Are Known Prices Are Given in $ US or in£ UK. Allen, Colin and Hand, Michael, Logic Primer, Cambridge Massachusetts, USA, The MIT Press, 1992, Pp. 171,£ 11.75. [REVIEW] Mind 102:405.
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  26. J. Michael Dunn (1993). Star and Perp: Two Treatments of Negation. Philosophical Perspectives 7:331-357.
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  27. Alan Anderson, Belnap R., D. Nuel & J. Michael Dunn (1992). Entailment: The Logic of Relevance and Necessity, Vol. Ii. Princeton University Press.
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  28. J. Michael Dunn (1990). Relevant Predication 2: Intrinsic Properties and Internal Relations. Philosophical Studies 60 (3):177-206.
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  29. J. Michael Dunn (1990). Relevant Predication 3: Essential Properties. In J. Dunn & A. Gupta (eds.), Truth or Consequences. Kluwer. 77--95.
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  30. Carlos Giannoni, Robert Meyer, J. Michael Dunn, Peter Woodruff, James Garson, Kent Wilson, Dorothy Grover, Ruth Manor, Alasdair Urquhart & Garrel Pottinger (1990). Nuel Belnap: Doctoral Students. In J. Dunn & A. Gupta (eds.), Truth or Consequences. Kluwer.
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  31. J. Michael Dunn (1988). The Impossibility of Certain Higher-Order Non-Classical Logics with Extensionality. In D. F. Austin (ed.), Philosophical Analysis. Kluwer Academic Publishers. 261--279.
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  32. J. Michael Dunn (1987). Incompleteness of the Bibinary Semantics for R. Bulletin of the Section of Logic 16 (3):107-109.
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  33. J. Michael Dunn (1987). Relevant Predication 1: The Formal Theory. [REVIEW] Journal of Philosophical Logic 16 (4):347 - 381.
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  34. J. Michael Dunn & Geoffrey Hellman (1986). Dualling: A Critique of an Argument of Popper and Miller. British Journal for the Philosophy of Science 37 (2):220-223.
  35. J. Michael Dunn (1982). A Relational Representation of Quasi-Boolean Algebras. Notre Dame Journal of Formal Logic 23 (4):353-357.
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  36. Nuel D. Belnap, Anil Gupta & J. Michael Dunn (1980). A Consecutive Calculus for Positive Relevant Implication with Necessity. Journal of Philosophical Logic 9 (4):343-362.
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  37. J. Michael Dunn (1980). A Sieve for Entailments. Journal of Philosophical Logic 9 (1):41 - 57.
    The validity of an entailment has nothing to do with whether or not the components are true, false, necessary, or impossible; it has to do solely with whether or not there is a necessary connection between antecedent and consequent. Hence it is a mistake (we feel) to try to build a sieve which will “strain out” entailments from the set of material or strict “implications” present in some system of truth-functions, or of truth-functions with modality. Anderson and Belnap (1962, p. (...)
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  38. J. Michael Dunn (1980). Quantum Mathematics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:512 - 531.
    This paper explores the development of mathematics on a quantum logical base when mathematical postulates are taken as necessary truths. First it is shown that first-order Peano arithmetic formulated with quantum logic has the same theorems as classical first-order Peano arithmetic. Distribution for first-order arithmetical formulas is a theorem not of quantum logic but rather of arithmetic. Second, it is shown that distribution fails for second-order Peano arithmetic without extensionality. Third, it is shown that distribution holds for second-order Peano arithmetic (...)
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  39. Nuel D. Belnap Jr, Anil Gupta & J. Michael Dunn (1980). A Consecutive Calculus for Positive Relevant Implication with Necessity. Journal of Philosophical Logic 9 (4):343 - 362.
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  40. J. Michael Dunn (1979). A Theorem in 3-Valued Model Theory with Connections to Number Theory, Type Theory, and Relevant Logic. Studia Logica 38 (2):149 - 169.
    Given classical (2 valued) structures and and a homomorphism h of onto , it is shown how to construct a (non-degenerate) 3-valued counterpart of . Classical sentences that are true in are non-false in . Applications to number theory and type theory (with axiom of infinity) produce finite 3-valued models in which all classically true sentences of these theories are non-false. Connections to relevant logic give absolute consistency proofs for versions of these theories formulated in relevant logic (the proof for (...)
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  41. J. Michael Dunn (1979). Relevant Robinson's Arithmetic. Studia Logica 38 (4):407 - 418.
    In this paper two different formulations of Robinson's arithmetic based on relevant logic are examined. The formulation based on the natural numbers (including zero) is shown to collapse into classical Robinson's arithmetic, whereas the one based on the positive integers (excluding zero) is shown not to similarly collapse. Relations of these two formulations to R. K. Meyer's system R# of relevant Peano arithmetic are examined, and some remarks are made about the role of constant functions (e.g., multiplication by zero) in (...)
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  42. J. Michael Dunn (1979). ${\Rm R}$-Mingle and Beneath. Extensions of the Routley-Meyer Semantics for ${\Rm R}$. Notre Dame Journal of Formal Logic 20 (2):369-376.
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  43. Robert K. Meyer, Richard Routley & J. Michael Dunn (1979). Curry's Paradox. Analysis 39 (3):124 - 128.
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  44. J. Michael Dunn (1978). Review: Hugues LeBlanc, Truth-Value Semantics. [REVIEW] Journal of Symbolic Logic 43 (2):376-377.
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  45. J. Michael Dunn (1976). A Kripke-Style Semantics for R-Mingle Using a Binary Accessibility Relation. Studia Logica 35 (2):163 - 172.
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  46. J. Michael Dunn (1976). Intuitive Semantics for First-Degree Entailments and 'Coupled Trees'. Philosophical Studies 29 (3):149-168.
  47. J. Michael Dunn (1976). Quantification and RM. Studia Logica 35 (3):315 - 322.
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  48. J. Michael Dunn (1975). Axiomatizing Belnap's Conditional Assertion. Journal of Philosophical Logic 4 (4):383 - 397.
  49. Robert K. Meyer, J. Michael Dunn & Hugues Leblanc (1974). Completeness of Relevant Quantification Theories. Notre Dame Journal of Formal Logic 15 (1):97-121.
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  50. J. Michael Dunn (1973). A Truth Value Semantics for Modal Logic. In Hugues Leblanc (ed.), Truth, Syntax and Modality. Amsterdam,North-Holland. 87--100.
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