92 found
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Jon Michael Dunn
PhD: University of Pittsburgh; Last affiliation: Indiana University, Bloomington
  1. Intuitive Semantics for First-Degree Entailments and 'Coupled Trees'.J. Michael Dunn - 1976 - Philosophical Studies 29 (3):149-168.
  2. Entailment: The Logic of Relevance and Necessity, Vol. II.Alan Ross Anderson, Nuel D. Belnap & J. Michael Dunn - 1992 - Princeton University Press.
  3. On the Ternary Relation and Conditionality.Jc Beall, Ross T. Brady, J. Michael Dunn, A. P. Hazen, Edwin D. Mares, Robert K. Meyer, Graham Priest, Greg Restall, David Ripley, John Slaney & Richard Sylvan - 2012 - 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.  56
    Algebraic Methods in Philosophical Logic.J. Michael Dunn - 2001 - Oxford, England: Oxford University Press.
    This comprehensive text shows how various notions of logic can be viewed as notions of universal algebra providing more advanced concepts for those who have an introductory knowledge of algebraic logic, as well as those wishing to delve into more theoretical aspects.
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  5. Curry’s Paradox.Robert K. Meyer, Richard Routley & J. Michael Dunn - 1979 - Analysis 39 (3):124 - 128.
  6.  71
    Partiality and its Dual.J. Michael Dunn - 2000 - Studia Logica 66 (1):5-40.
    This paper explores allowing truth value assignments to be undetermined or "partial" and overdetermined or "inconsistent", 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 relevant entailments, Priest's "Logic of Paradox", and the first-degree fragment of the Dunn-McCall system "R-mingle". None of these systems have nested implications, and I investigate (...)
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  7. Star and Perp: Two Treatments of Negation.J. Michael Dunn - 1993 - Philosophical Perspectives 7:331-357.
  8. Relevant Predication 2: Intrinsic Properties and Internal Relations.J. Michael Dunn - 1990 - Philosophical Studies 60 (3):177-206.
  9. Algebraic Methods in Philosophical Logic.J. Michael Dunn & Gary M. Hardegree - 2005 - Studia Logica 79 (2):305-306.
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  10.  3
    Generalized Galois Logics: Relational Semantics of Nonclassical Logical Calculi.Katalin Bimbó & J. Michael Dunn - 2008 - Center for the Study of Language and Inf.
    Nonclassical logics have played an increasing role in recent years in disciplines ranging from mathematics and computer science to linguistics and philosophy. _Generalized Galois Logics_ develops a uniform framework of relational semantics to mediate between logical calculi and their semantics through algebra. This volume addresses normal modal logics such as K and S5, and substructural logics, including relevance logics, linear logic, and Lambek calculi. The authors also treat less-familiar and new logical systems with equal deftness.
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  11. The Substitution Interpretation of the Quantifiers.J. Michael Dunn & Nuel D. Belnap - 1968 - Noûs 2 (2):177-185.
  12. Algebraic Methods in Philosophical Logic.J. Michael Dunn & Gary M. Hardegree - 2003 - Bulletin of Symbolic Logic 9 (2):231-234.
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  13.  74
    Positive Modal Logic.J. Michael Dunn - 1995 - 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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  14.  38
    Algebraic Completeness Results for R-Mingle and its Extensions.J. Michael Dunn - 1970 - Journal of Symbolic Logic 35 (1):1-13.
  15.  83
    Relevant Predication 1: The Formal Theory. [REVIEW]J. Michael Dunn - 1987 - Journal of Philosophical Logic 16 (4):347-381.
  16.  68
    Negation in the Context of Gaggle Theory.J. Michael Dunn & Chunlai Zhou - 2005 - 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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  17. The Trilaticce of Constructive Truth Values.Yaroslav Shramko, J. Michael Dunn & Tatsutoshi Takenaka - 2001 - Journal of Logic and Computation 11 (1):761--788.
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  18. Kripke Models for Linear Logic.Gerard Allwein & J. Michael Dunn - 1993 - 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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  19.  1
    Entailment: The Logic of Relevance and Necessity, Vol. 1.Alan Ross Anderson, Nuel D. Belnap, Jr & J. Michael Dunn (eds.) - 1975 - Princeton, NJ, USA: Princeton University Press.
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  20.  74
    Canonical Extensions and Relational Completeness of Some Substructural Logics.J. Michael Dunn, Mai Gehrke & Alessandra Palmigiano - 2005 - 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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  21.  36
    Completeness of Relevant Quantification Theories.Robert K. Meyer, J. Michael Dunn & Hugues Leblanc - 1974 - Notre Dame Journal of Formal Logic 15 (1):97-121.
  22.  79
    A Kripke-Style Semantics for R-Mingle Using a Binary Accessibility Relation.J. Michael Dunn - 1976 - Studia Logica 35 (2):163 - 172.
  23.  27
    E, R, and Γ.Robert K. Meyer & J. Michael Dunn - 1969 - Journal of Symbolic Logic 34 (3):460-474.
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  24.  44
    Relevant Predication 3: Essential Properties.J. Michael Dunn - 1990 - In J. Dunn & A. Gupta (eds.), Truth or Consequences. Kluwer Academic Publishers. pp. 77--95.
  25.  25
    New Consecution Calculi for R→T.Katalin Bimbó & J. Michael Dunn - 2012 - 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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  26.  33
    A Modification of Parry's Analytic Implication.J. Michael Dunn - 1972 - Notre Dame Journal of Formal Logic 13 (2):195-205.
  27. Contradictory Information: Too Much of a Good Thing. [REVIEW]J. Michael Dunn - 2010 - 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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  28.  21
    On the Decidability of Implicational Ticket Entailment.Katalin Bimbó & J. Michael Dunn - 2013 - 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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  29.  28
    Algebraic Completeness Results for Dummett's LC and Its Extensions.J. Michael Dunn & Robert K. Meyer - 1971 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 17 (1):225-230.
  30.  10
    Contradictory Information: Better Than Nothing? The Paradox of the Two Firefighters.J. Michael Dunn & Nicholas M. Kiefer - 2019 - In Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency. Springer Verlag. pp. 231-247.
    Prominent philosophers have argued that contradictions contain either too much or too little information to be useful. We dispute this with what we call the “Paradox of the Two Firefighters.” Suppose you are awakened in your hotel room by a fire alarm. You open the door. You see three possible ways out: left, right, straight ahead. You see two firefighters. One says there is exactly one safe route and it is to your left. The other says there is exactly one (...)
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  31.  2
    Entailment: The Logic of Relevance and Necessity Vol. 2.Alan Ross Anderson, Nuel D. Belnap & J. Michael Dunn (eds.) - 1992 - Princeton, NJ, USA: Princeton University Press.
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  32.  47
    A Theorem in 3-Valued Model Theory with Connections to Number Theory, Type Theory, and Relevant Logic.J. Michael Dunn - 1979 - 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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  33.  16
    A Truth Value Semantics for Modal Logic.J. Michael Dunn - 1973 - In Hugues Leblanc (ed.), Journal of Symbolic Logic. Amsterdam: North-Holland. pp. 87--100.
  34. Dualling: A Critique of an Argument of Popper and Miller.J. Michael Dunn & Geoffrey Hellman - 1986 - British Journal for the Philosophy of Science 37 (2):220-223.
  35.  28
    E, R, and $Gamma$.Robert K. Meyer & J. Michael Dunn - 1969 - Journal of Symbolic Logic 34 (3):460-474.
  36.  14
    Truth-Value Semantics.J. Michael Dunn - 1978 - Journal of Symbolic Logic 43 (2):376-377.
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  37.  16
    Generalized Onrno Negation.J. Michael Dunn - 1996 - In H. Wansing (ed.), Negation: A Notion in Focus. W. De Gruyter. pp. 7--3.
  38.  38
    Four-Valued Logic.Katalin Bimbó & J. Michael Dunn - 2001 - 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 and its residuals can be added to the sequent calculus straightforwardly. We extend a simplified version of the earlier semantics for this system (...)
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  39.  79
    Quantum Logic as Motivated by Quantum Computing.J. Michael Dunn, Tobias J. Hagge, Lawrence S. Moss & Zhenghan Wang - 2005 - Journal of Symbolic Logic 70 (2):353 - 359.
  40.  59
    Symmetric Generalized Galois Logics.Katalin Bimbó & J. Michael Dunn - 2009 - 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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  41.  40
    Relevant Robinson's Arithmetic.J. Michael Dunn - 1979 - 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. Relevance Logics and Relation Algebras.Katalin Bimbó, J. Michael Dunn & Roger D. Maddux - 2009 - 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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  43.  43
    A Relational Representation of Quasi-Boolean Algebras.J. Michael Dunn - 1982 - Notre Dame Journal of Formal Logic 23 (4):353-357.
  44.  17
    The Impossibility of Certain Higher-Order Non-Classical Logics with Extensionality.J. Michael Dunn - 1988 - In D. F. Austin (ed.), Philosophical Analysis. Kluwer Academic Publishers. pp. 261--279.
  45.  26
    Quantification and RM.J. Michael Dunn - 1976 - Studia Logica 35 (3):315 - 322.
  46.  23
    A Guide to the Floridi Keys: Luciano Floridi: The Philosophy of Information. Oxford: Oxford University Press, 2011, Xx+405pp, £37.50 HB.J. Michael Dunn - 2013 - Metascience 22 (1):93-98.
  47. Conditional Assertion and Restricted Quantification: Abstracts of Comments.J. Michael Dunn - 1970 - Noûs 4 (1):13.
  48.  44
    A Sieve for Entailments.J. Michael Dunn - 1980 - 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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  49.  77
    Quantum Mathematics.J. Michael Dunn - 1980 - 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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  50.  2
    Entailment, Vol. Ii: The Logic of Relevance and Necessity.J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson - 2017 - Princeton University Press.
    In spite of a powerful tradition, more than two thousand years old, that in a valid argument the premises must be relevant to the conclusion, twentieth-century logicians neglected the concept of relevance until the publication of Volume I of this monumental work. Since that time relevance logic has achieved an important place in the field of philosophy: Volume II of Entailment brings to a conclusion a powerful and authoritative presentation of the subject by most of the top people working in (...)
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