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  1. added 2014-11-27
    Heinrich Wansing & Graham Priest (forthcoming). External Curries. Journal of Philosophical Logic:1-19.
    Curry’s paradox is well known. The original version employed a conditional connective, and is not forthcoming if the conditional does not satisfy contraction. A newer version uses a validity predicate, instead of a conditional, and is not forthcoming if validity does not satisfy structural contraction. But there is a variation of the paradox which uses “external validity” (that is, essentially, preservation of theoremhood). And since external validity contracts, one might expect the appropriate version of the Curry paradox to be inescapable. (...)
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  2. added 2014-11-26
    Wesley H. Holliday (2013). Response to Egré and Xu. In Johan van Benthem Fenrong Liu (ed.), Logic Across the University: Foundations and Applications. College Publications. 39-46.
    In this note, I respond to comments by Paul Egré and Xu Zhaoqing on my “Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism” (Journal of Philosophical Logic).
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  3. added 2014-11-25
    John-Michael Kuczynski, Mathematics as the Science of Pure Structure.
    A brief but rigorous description of the logical structure of mathematical truth.
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  4. added 2014-11-25
    Nino B. Cocchiarella (forthcoming). Two Views of the Logic of Plurals and a Reduction of One to the Other. Studia Logica:1-24.
    There are different views of the logic of plurals that are now in circulation, two of which we will compare in this paper. One of these is based on a two-place relation of being among, as in ‘Peter is among the juveniles arrested’. This approach seems to be the one that is discussed the most in philosophical journals today. The other is based on Bertrand Russell’s early notion of a class as many, by which is meant not a class as (...)
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  5. added 2014-11-25
    Juan Manuel Cornejo (forthcoming). The Semi Heyting–Brouwer Logic. Studia Logica:1-23.
    In this paper we introduce a logic that we name semi Heyting–Brouwer logic, \({\mathcal{SHB}}\) , in such a way that the variety of double semi-Heyting algebras is its algebraic counterpart. We prove that, up to equivalences by translations, the Heyting–Brouwer logic \({\mathcal{HB}}\) is an axiomatic extension of \({\mathcal{SHB}}\) and that the propositional calculi of intuitionistic logic \({\mathcal{I}}\) and semi-intuitionistic logic \({\mathcal{SI}}\) turn out to be fragments of \({\mathcal{SHB}}\).
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  6. added 2014-11-24
    Arthur Sullivan (forthcoming). What Do Deviant Logians Show About the Epistemology of Logic? Acta Analytica:1-13.
    What I will call “the deviant logician objection” [DLO] is one line of attack against the common and compelling tenet that our justification for logical truths is grounded in our understanding of their constituent concepts. This objection seeks to undermine the possibility of any deep constitutive connection, in the epistemology of logic (and also beyond), between understanding and justification. I will consider varieties of the deviant logician objection developed by Horwich (2000, 2006) and by Williamson (2006, 2008). My thesis is (...)
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  7. added 2014-11-22
    Jonas Frey (forthcoming). Triposes, Q-Toposes and Toposes. Annals of Pure and Applied Logic.
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  8. added 2014-11-19
    N. C. A. Da Costa & C. De Ronde (2014). Non-Reflexive Logical Foundation for Quantum Mechanics. Foundations of Physics 44 (12):1369-1380.
    On the one hand, non-reflexive logics are logics in which the principle of identity does not hold in general. On the other hand, quantum mechanics has difficulties regarding the interpretation of ‘particles’ and their identity, also known in the literature as ‘the problem of indistinguishable particles’. In this article, we will argue that non-reflexive logics can be a useful tool to account for such quantum indistinguishability. In particular, we will provide a particular non-reflexive logic that can help us to analyze (...)
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  9. added 2014-11-16
    Yitzhak Melamed (forthcoming). Gersonides and Spinoza on God’s Knowledge of Universals and Particulars. In Gad Freudenthal, David Wirmer & Ofer Elior (eds.), Gersonides Through the Ages.
  10. added 2014-11-16
    Xiaoping Chen (2006). Zi Ran Yan Yi Luo Ji Dao Lun. Zhongshan da Xue Chu Ban She.
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  11. added 2014-11-14
    Ole Hjortland (2014). Verbal Disputes in Logic: Against Minimalism for Logical Connectives. Logique Et Analyse 227:463-486.
    Logic, Logical connectives, Verbal disputes, Proof theory, Non-classical logic.
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  12. added 2014-11-13
    Jean-Yves Beziau (forthcoming). Preface: Scope of Logic Theorems In Memoriam Adolf Lindenbaum. Logica Universalis:1-2.
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  13. added 2014-11-12
    Leila Amgoud, Philippe Besnard & Srdjan Vesic (2014). Equivalence in Logic-Based Argumentation. Journal of Applied Non-Classical Logics 24 (3):181-208.
    This paper investigates when two abstract logic-based argumentation systems are equivalent. It defines various equivalence criteria, investigates the links between them, and identifies cases where two systems are equivalent with respect to each of the proposed criteria. In particular, it shows that under some reasonable conditions on the logic underlying an argumentation system, the latter has an equivalent finite subsystem, called core. This core constitutes a threshold under which arguments of the system have not yet attained their final status and (...)
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  14. added 2014-11-12
    Lloyd Humberstone (2014). Prior's OIC Nonconservativity Example Revisited. Journal of Applied Non-Classical Logics 24 (3):209-235.
    In his 1964 note, ‘Two Additions to Positive Implication’, A. N. Prior showed that standard axioms governing conjunction yield a nonconservative extension of the pure implicational intermediate logic OIC (order implicational calculus) of R. A. Bull. Here, after reviewing the situation with the aid of an adapted form of the Kripke semantics for intuitionistic and intermediate logics, we proceed to illuminate this example by transposing it to the setting of modal logic, and then relate it to the propositional logic of (...)
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  15. added 2014-11-12
    Hadja Faiza Khellaf-Haned & Salem Benferhat (2014). Quantitative Possibility Theory: Logical- and Graphical-Based Representations. Journal of Applied Non-Classical Logics 24 (3):236-261.
    In the framework of quantitative possibility theory, two representation modes were developed: logical-based representation in terms of quantitative possibilistic bases and graphical-based representation in terms of product-based possibilistic networks. This paper deals with logical and graphical representations of uncertain information using a quantitative possibility theory framework. We first provide a deep analysis of the relationships between these two forms of representational frameworks. Then, in the logical setting, we develop syntactic relations between penalty logic and quantitative possibilistic logic. These translations are (...)
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  16. added 2014-11-12
    Janardan Misra & Suman Roy (2014). A Decidable Timeout-Based Extension of Linear Temporal Logic. Journal of Applied Non-Classical Logics 24 (3):262-291.
    We develop a timeout extension of propositional linear temporal logic (which we call ToLTL) to specify timing properties of timeout-based models of real-time systems. A timeout is used to model the execution of an action marking the end of a delay. With a view to expressing such timeout constraints, ToLTL uses a dynamic variable to abstract the timeout behaviour in addition to a variable which captures the global clock and some static timing variables which record time instances when discrete events (...)
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  17. added 2014-11-11
    Geoff Georgi (forthcoming). Logic for Languages Containing Referentially Promiscuous Expressions. Journal of Philosophical Logic:1-23.
    Some expressions of English, like the demonstratives ‘this’ and ‘that’, are referentially promiscuous: distinct free occurrences of them in the same sentence can differ in content relative to the same context. One lesson of referentially promiscuous expressions is that basic logical properties like validity and logical truth obtain or fail to obtain only relative to a context. This approach to logic can be developed in just as rigorous a manner as David Kaplan’s classic logic of demonstratives. The result is a (...)
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  18. added 2014-11-09
    V. Yu Shavrukov & Albert Visser (2014). Uniform Density in Lindenbaum Algebras. Notre Dame Journal of Formal Logic 55 (4):569-582.
    In this paper we prove that the preordering $\lesssim $ of provable implication over any recursively enumerable theory $T$ containing a modicum of arithmetic is uniformly dense. This means that we can find a recursive extensional density function $F$ for $\lesssim $. A recursive function $F$ is a density function if it computes, for $A$ and $B$ with $A\lnsim B$, an element $C$ such that $A\lnsim C\lnsim B$. The function is extensional if it preserves $T$-provable equivalence. Secondly, we prove a (...)
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  19. added 2014-11-09
    Grigor Sargsyan (2014). An Inner Model Proof of the Strong Partition Property for $Delta^{2}_{1}$. Notre Dame Journal of Formal Logic 55 (4):563-568.
    Assuming $V=L(\mathbb{R})+AD$, using methods from inner model theory, we give a new proof of the strong partition property for ${\sim}{ \delta }^{2}_{1}$. The result was originally proved by Kechris et al.
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  20. added 2014-11-09
    Arthur W. Apter (2014). Inaccessible Cardinals, Failures of GCH, and Level-by-Level Equivalence. Notre Dame Journal of Formal Logic 55 (4):431-444.
    We construct models for the level-by-level equivalence between strong compactness and supercompactness containing failures of the Generalized Continuum Hypothesis (GCH) at inaccessible cardinals. In one of these models, no cardinal is supercompact up to an inaccessible cardinal, and for every inaccessible cardinal $\delta $, $2^{\delta }\gt \delta ^{++}$. In another of these models, no cardinal is supercompact up to an inaccessible cardinal, and the only inaccessible cardinals at which GCH holds are also measurable. These results extend and generalize earlier work (...)
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  21. added 2014-11-09
    Ioannis Souldatos (2014). Notes on Cardinals That Are Characterizable by a Complete (Scott) Sentence. Notre Dame Journal of Formal Logic 55 (4):533-551.
    This is the first part of a study on cardinals that are characterizable by Scott sentences. Building on previous work of Hjorth, Malitz, and Baumgartner, we study which cardinals are characterizable by a Scott sentence $\phi$, in the sense that $\phi$ characterizes $\kappa$, if $\phi$ has a model of size $\kappa$ but no models of size $\kappa^{+}$. We show that the set of cardinals that are characterized by a Scott sentence is closed under successors, countable unions, and countable products (see (...)
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  22. added 2014-11-09
    Pieter A. M. Seuren (2014). The Cognitive Ontogenesis of Predicate Logic. Notre Dame Journal of Formal Logic 55 (4):499-532.
    Since Aristotle and the Stoa, there has been a clash, worsened by modern predicate logic, between logically defined operator meanings and natural intuitions. Pragmatics has tried to neutralize the clash by an appeal to the Gricean conversational maxims. The present study argues that the pragmatic attempt has been unsuccessful. The “softness” of the Gricean explanation fails to do justice to the robustness of the intuitions concerned, leaving the relation between the principles evoked and the observed facts opaque. Moreover, there are (...)
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  23. added 2014-11-09
    William Craig (2014). Peter van Inwagen, Substitutional Quantification, and Ontological Commitment. Notre Dame Journal of Formal Logic 55 (4):553-561.
    Peter van Inwagen has long claimed that he doesn’t understand substitutional quantification and that the notion is, in fact, meaningless. Van Inwagen identifies the source of his bewilderment as an inability to understand the proposition expressed by a simple sentence like “($\Sigma x$) ($x$ is a dog),” where “$\Sigma$” is the existential quantifier understood substitutionally. I should think that the proposition expressed by this sentence is the same as that expressed by “($\exists x$) ($x$ is a dog).” So what’s the (...)
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  24. added 2014-11-09
    Tero Tulenheimo (2014). Classical Negation and Game-Theoretical Semantics. Notre Dame Journal of Formal Logic 55 (4):469-498.
    Typical applications of Hintikka’s game-theoretical semantics (GTS) give rise to semantic attributes—truth, falsity—expressible in the $\Sigma^{1}_{1}$-fragment of second-order logic. Actually a much more general notion of semantic attribute is motivated by strategic considerations. When identifying such a generalization, the notion of classical negation plays a crucial role. We study two languages, $L_{1}$ and $L_{2}$, in both of which two negation signs are available: $\rightharpoondown $ and $\sim$. The latter is the usual GTS negation which transposes the players’ roles, while the (...)
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  25. added 2014-11-08
    Susanne Bobzien (2014). Higher-Order Vagueness and Numbers of Distinct Modalities. Disputatio (39):131-137.
    This paper shows that the following common assumption is false: that in modal-logical representations of higher-order vagueness, for there to be borderline cases to borderline cases ad infinitum, the number of possible distinct modalities in a modal system must be infinite. (Open access journal).
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  26. added 2014-11-07
    John Corcoran & Hassan Masoud (forthcoming). Existential Import Today: New Metatheorems; Historical, Philosophical, and Pedagogical Misconceptions. History and Philosophy of Logic:1-23.
    Contrary to common misconceptions, today’s logic is not devoid of existential import: the universalized conditional "Ax [S(x) ® P(x)] implies its corresponding existentialized conjunction Ex [S(x) & P(x)], not in all cases, but in some. We characterize the proexamples by proving the Existential-Import Equivalence: "Ax [S(x) ® P(x)] implies Ex [S(x) & P(x)] iff Ex S(x) is logically true. -/- The antecedent S(x) of the universalized conditional alone determines whether the universalized conditional has existential import, i.e., whether it implies its (...)
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  27. added 2014-11-07
    Cesare Cozzo (2011). Discussion. In Carlo Cellucci, Emily Grosholz & Emiliano Ippoliti (eds.), Logic and Knowledge. Cambridge Scholars. 101-7.
    Is a rational dispute over the validity of a fundamental logical law possible? In his lecture ‘Logics and Metalogics’, Timothy Williamson criticizes Dummett’s approach to this problem and maintains that a semantic theory does not provide a way of settling disputes over the validity of fundamental logical laws. I argue that Dummett’s view is different from the view criticized by Williamson. Dummett does not think that a semantic theory alone can settle a dispute over the validity of a fundamental logical (...)
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  28. added 2014-11-06
    David Ripley (forthcoming). Anything Goes. Topoi.
    This paper consider Prior's connective Tonk from a particular bilateralist perspective. I show that there is a natural perspective from which we can see Tonk and its ilk as perfectly well-defined pieces of vocabulary; there is no need for restrictions to bar things like Tonk.
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  29. added 2014-11-06
    Rohan French & David Ripley (forthcoming). Contractions of Noncontractive Consequence Relations. Review of Symbolic Logic.
    Some theorists have developed formal approaches to truth that depend on counterexamples to the structural rules of contraction. Here, we study such approaches, with an eye to helping them respond to a certain kind of objection. We define a contractive relative of each noncontractive relation, for use in responding to the objection in question, and we explore one example: the contractive relative of multiplicative-additive affine logic with transparent truth, or MAALT. -/- .
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  30. added 2014-11-05
    John Corcoran (2007). 2007. Notes on the Founding of Logics and Metalogic: Aristotle, Boole, and Tarski. Eds. C. Martínez Et Al. Current Topics in Logic and Analytic Philosophy / Temas Actuales de Lógica y Filosofía Analítica. Imprenta Univeridade Santiago de Compostela. In C. Martínez (ed.), Current Topics in Logic and Analytic Philosophy /. 145-178.
  31. added 2014-10-29
    Jamin Asay (forthcoming). Epistemicism and the Liar. Synthese:1-21.
    One well known approach to the soritical paradoxes is epistemicism, the view that propositions involving vague notions have definite truth values, though it is impossible in principle to know what they are. Recently, Paul Horwich has extended this approach to the liar paradox, arguing that the liar proposition has a truth value, though it is impossible to know which one it is. The main virtue of the epistemicist approach is that it need not reject classical logic, and in particular the (...)
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  32. added 2014-10-29
    Daniele Porello & Nicolas Troquard (2014). A Resource-Sensitive Logic of Agency. In Ios Press (ed.), Proceedings of the 21st European Conference on Artificial Intelligence (ECAI'14), Prague, Czech Republic. 2014. 723-728.
    We study a fragment of Intuitionistic Linear Logic combined with non-normal modal operators. Focusing on the minimal modal logic, we provide a Gentzen-style sequent calculus as well as a semantics in terms of Kripke resource models. We show that the proof theory is sound and complete with respect to the class of minimal Kripke resource models. We also show that the sequent calculus allows cut elimination. We put the logical framework to use by instantiating it as a logic of agency. (...)
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  33. added 2014-10-29
    Daniele Porello (2013). A Proof-Theoretical View of Collective Rationality. In Proceedings of the 23rd International Joint Conference of Artificial Intelligence (IJCAI 2013).
    The impossibility results in judgement aggregation show a clash between fair aggregation procedures and rational collective outcomes. In this paper, we are interested in analysing the notion of rational outcome by proposing a proof-theoretical understanding of collective rationality. In particular, we use the analysis of proofs and inferences provided by linear logic in order to define a fine-grained notion of group reasoning that allows for studying collective rationality with respect to a number of logics. We analyse the well-known paradoxes in (...)
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  34. added 2014-10-28
    John Corcoran (1999). Information-Theoretic Logic and Transformation-Theoretic Logic,. In R. A. M. M. (ed.), Fragments in Science,. World Scientific Publishing Company,. 25-35.
  35. added 2014-10-22
    John Corcoran (forthcoming). Tarski’s Convention T: Condition Beta. SOUTH AMERICAN JOURNAL OF LOGIC 1 (1).
    Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In Tarski’s preferred usage, it is part of the meaning (...)
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  36. added 2014-10-22
    Roberto Festa (1999). Bayesian Confirmation. In M. C. Galavotti & A. Pagnini (eds.), Experience, Reality, and Scientific Explanation. Kluwer. 55–87.
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  37. added 2014-10-21
    Cesare Cozzo (forthcoming). Necessity of Thought. In Heinrich Wansing (ed.), Dag Prawitz on Proofs and Meaning. Springer. 115-36.
    The concept of “necessity of thought” plays a central role in Dag Prawitz’s essay “Logical Consequence from a Constructivist Point of View” (Prawitz 2005). The theme is later developed in various articles devoted to the notion of valid inference (Prawitz, 2009, forthcoming a, forthcoming b). In section 1 I explain how the notion of necessity of thought emerges from Prawitz’s analysis of logical consequence. I try to expound Prawitz’s views concerning the necessity of thought in sections 2, 3 and 4. (...)
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  38. added 2014-10-18
    Hartry Field, Harvey Lederman & Tore Fjetland Øgaard (forthcoming). Prospects for a Naive Theory of Classes. Notre Dame Journal of Formal Logic.
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  39. added 2014-10-17
    David Ellerman, Partitions and Objective Indefiniteness.
    Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically dual (...)
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  40. added 2014-10-16
    David Ellerman, Four Ways From Universal to Particular: How Chomsky's Language-Acquisition Faculty is Not Selectionist.
    Following the development of the selectionist theory of the immune system, there was an attempt to characterize many biological mechanisms as being "selectionist" as juxtaposed to "instructionist." But this broad definition would group Darwinian evolution, the immune system, embryonic development, and Chomsky's language-acquisition mechanism as all being "selectionist." Yet Chomsky's mechanism (and embryonic development) are significantly different from the selectionist mechanisms of biological evolution or the immune system. Surprisingly, there is a very abstract way using two dual mathematical logics to (...)
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  41. added 2014-10-16
    David Ellerman (forthcoming). On Concrete Universals: A Modern Treatment Using Category Theory. AL-MUKHATABAT.
    Today it would be considered "bad Platonic metaphysics" to think that among all the concrete instances of a property there could be a universal instance so that all instances had the property by virtue of participating in that concrete universal. Yet there is a mathematical theory, category theory, dating from the mid-20th century that shows how to precisely model concrete universals within the "Platonic Heaven" of mathematics. This paper, written for the philosophical logician, develops this category-theoretic treatment of concrete universals (...)
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  42. added 2014-10-16
    David Ellerman (2014). An Introduction to Partition Logic. Logic Journal of the Igpl 22 (1):94-125.
    Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the idea arises of a dual (...)
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  43. added 2014-10-16
    Fred Johnson (1991). Suppositional Reasoning. In Frans H. Van Eemeren (ed.), Proceedings of the Second International Conference on Argumentation 1990. 281-287.
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  44. added 2014-10-15
    Fred Johnson (1976). A Three-Valued Interpretation for a Relevance Logic. The Relevance Logic Newsletter 1 (3):123-128.
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  45. added 2014-10-11
    Fred Johnson & Peter Woodruff (2002). Categorical Consequence for Paraconsistent Logic. In Walter Carnielli (ed.), Paraconsistency:the logical way to the inconsistent. 141-150.
    Consequence rleations over sets of "judgments" are defined by using "overdetermined" as well as "underdetermined" valuations. Some of these relations are shown to be categorical. And generalized soundness and completeness results are given for both multiple and single conclusion consequence relations.
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  46. added 2014-10-08
    Patrick Todd (forthcoming). Future Contingents Are All False! On Behalf of a Russellian Open Future. Mind.
    There is a familiar debate between Russell and Strawson concerning bivalence and ‘the present King of France’. According to the Strawsonian view, ‘The present King of France is bald’ is neither true nor false, whereas, on the Russellian view, that proposition is simply false. In this paper, I develop what I take to be a crucial (and unnoticed) connection between this debate and a different domain where bivalence has been at stake: future contingents. On the familiar ‘Aristotelian’ view, future contingent (...)
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  47. added 2014-10-08
    Elia Zardini (forthcoming). The Opacity of Truth. Topoi:1-18.
    The paper offers a critical examination of a prominent, “quasi-deflationist” argument advanced in the contemporary debate on the semantic paradoxes against non-naive and non-transparent theories of truth. The argument claims that truth unrestrictedly fulfils certain expressive functions, and that its so doing requires the unrestricted validity of naivety and transparency principles. The paper criticises the quasi-deflationist argument by considering some kinds of cases in which transparency and naivety arguably fail. In some such cases truth still fulfils the relevant expressive functions (...)
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  48. added 2014-09-30
    Allard Tamminga (2014). Correspondence Analysis for Strong Three-Valued Logic. Logical Investigations 20:255-268.
    I apply Kooi and Tamminga's (2012) idea of correspondence analysis for many-valued logics to strong three-valued logic (K3). First, I characterize each possible single entry in the truth-table of a unary or a binary truth-functional operator that could be added to K3 by a basic inference scheme. Second, I define a class of natural deduction systems on the basis of these characterizing basic inference schemes and a natural deduction system for K3. Third, I show that each of the resulting natural (...)
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  49. added 2014-09-23
    Gregory Wheeler (2014). Defeat Reconsidered and Repaired. The Reasoner 8 (2):15-15.
  50. added 2014-09-22
    Kazumi Inoue (2014). Dialectical Contradictions and Classical Formal Logic. International Studies in the Philosophy of Science 28 (2):113-132.
    A dialectical contradiction can be appropriately described within the framework of classical formal logic. It is in harmony with the law of noncontradiction. According to our definition, two theories make up a dialectical contradiction if each of them is consistent and their union is inconsistent. It can happen that each of these two theories has an intended model. Plenty of examples are to be found in the history of science.
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