109 found
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  1. Jc Beall & Greg Restall (2005). Logical Pluralism. Oxford University Press.
    Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...)
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  2.  47
    Greg Restall (2000). An Introduction to Substructural Logics. Routledge.
    This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. _An Introduction to Substrucural Logics_ is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both (...)
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  3.  66
    Greg Restall (2013). Assertion, Denial and Non-Classical Theories. In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer 81--99.
    In this paper I urge friends of truth-value gaps and truth-value gluts – proponents of paracomplete and paraconsistent logics – to consider theories not merely as sets of sentences, but as pairs of sets of sentences, or what I call ‘bitheories,’ which keep track not only of what holds according to the theory, but also what fails to hold according to the theory. I explain the connection between bitheories, sequents, and the speech acts of assertion and denial. I illustrate the (...)
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  4. Jc Beall & Greg Restall (2000). Logical Pluralism. Australasian Journal of Philosophy 78 (4):475 – 493.
    Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...)
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  5. 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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  6. Greg Restall (1996). Truthmakers, Entailment and Necessity. Australasian Journal of Philosophy 74 (2):331 – 340.
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  7. Daniel Nolan, Greg Restall & Caroline West (2005). Moral Fictionalism Versus the Rest. Australasian Journal of Philosophy 83 (3):307 – 330.
    In this paper we introduce a distinct metaethical position, fictionalism about morality. We clarify and defend the position, showing that it is a way to save the 'moral phenomena' while agreeing that there is no genuine objective prescriptivity to be described by moral terms. In particular, we distinguish moral fictionalism from moral quasi-realism, and we show that fictionalism possesses the virtues of quasi-realism about morality, but avoids its vices.
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  8.  10
    Greg Restall (2016). On Priest on Nonmonotonic and Inductive Logic. Thought: A Journal of Philosophy 5 (2):119-124.
    Graham Priest defends the use of a nonmonotonic logic, LPm, in his analysis of reasoning in the face of true contradictions, such as those arising from the paradoxes of self-reference. In the course of defending this choice of logic in the face of the criticism that this logic is not truth preserving, Priest argued that requirement is too much to ask: since LPm is a nonmonotonic logic, it necessarily fails to preserve truth. In this article, I show that this assumption (...)
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  9.  53
    Greg Restall (2005). Multiple Conclusions. In Petr Hájek, Luis Valdés-Villanueva & Dag Westerståhl (eds.), Logic, Methodology and Philosophy of Science. College Publications
    Our topic is the notion of logical consequence: the link between premises and conclusions, the glue that holds together deductively valid argument. How can we understand this relation between premises and conclusions? It seems that any account begs questions. Painting with very broad brushtrokes, we can sketch the landscape of disagreement like this: “Realists” prefer an analysis of logical consequence in terms of the preservation of truth [29]. “Anti-realists” take this to be unhelpful and o:er alternative analyses. Some, like Dummett, (...)
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  10.  85
    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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  11. Greg Restall (1997). Ways Things Can't Be. Notre Dame Journal of Formal Logic 38 (4):583-596.
    Paraconsistent logics are often semantically motivated by considering "impossible worlds." Lewis, in "Logic for equivocators," has shown how we can understand paraconsistent logics by attributing equivocation of meanings to inconsistent believers. In this paper I show that we can understand paraconsistent logics without attributing such equivocation. Impossible worlds are simply sets of possible worlds, and inconsistent believers (inconsistently) believe that things are like each of the worlds in the set. I show that this account gives a sound and complete semantics (...)
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  12. Greg Restall (2002). Carnap's Tolerance, Meaning, and Logical Pluralism. Journal of Philosophy 99 (8):426 - 443.
    In this paper, I distinguish different kinds of pluralism about logical consequence. In particular, I distinguish the pluralism about logic arising from Carnap’s Principle of Tolerance from a pluralism which maintains that there are different, equally “good” logical consequence relations on the one language. I will argue that this second form of pluralism does more justice to the contemporary state of logical theory and practice than does Carnap’s more moderate pluralism.
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  13.  54
    Greg Restall (2012). A Cut-Free Sequent System for Two-Dimensional Modal Logic, and Why It Matters. Annals of Pure and Applied Logic 163 (11):1611-1623.
    The two-dimensional modal logic of Davies and Humberstone [3] is an important aid to our understanding the relationship between actuality, necessity and a priori knowability. I show how a cut-free hypersequent calculus for 2D modal logic not only captures the logic precisely, but may be used to address issues in the epistemology and metaphysics of our modal concepts. I will explain how the use of our concepts motivates the inference rules of the sequent calculus, and then show that the completeness (...)
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  14.  66
    Greg Restall (2009). Not Every Truth Can Be Known (at Least, Not All at Once). In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press 339--354.
    According to the “knowability thesis,” every truth is knowable. Fitch’s paradox refutes the knowability thesis by showing that if we are not omniscient, then not only are some truths not known, but there are some truths that are not knowable. In this paper, I propose a weakening of the knowability thesis (which I call the “conjunctive knowability thesis”) to the e:ect that for every truth p there is a collection of truths such that (i) each of them is knowable and (...)
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  15.  27
    Greg Restall (2014). Pluralism and Proofs. Erkenntnis 79 (S2):279-291.
    Beall and Restall’s Logical Pluralism (2006) characterises pluralism about logical consequence in terms of the different ways cases can be selected in the analysis of logical consequence as preservation of truth over a class of cases. This is not the only way to understand or to motivate pluralism about logical consequence. Here, I will examine pluralism about logical consequence in terms of different standards of proof. We will focus on sequent derivations for classical logic, imposing two different restrictions on classical (...)
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  16.  91
    Greg Restall (2005). Łukasiewicz, Supervaluations and the Future. Logic and Philosophy of Science 3:1-10.
    A B S T R AC T: In this paper I consider an interpretation of future contingents which motivates a unification of a Łukasiewicz-style logic with the more classical supervaluational semantics. This in turn motivates a new non-classical logic modelling what is “made true by history up until now. ” I give a simple Hilbert-style proof theory, and a soundness and completeness argument for the proof theory with respect to the intended models.
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  17.  20
    Greg Restall (1999). Negation in Relevant Logics (How I Stopped Worrying and Learned to Love the Routley Star). In Dov M. Gabbay & Heinrich Wansing (eds.), What is Negation? Kluwer Academic Publishers 53-76.
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  18.  45
    JC Beall & Greg Restall, Logical Consequence.
    A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises. But in what sense do conclusions follow from premises? What is it for a conclusion to be a consequence of premises? Those questions, in many respects, are at the heart of logic (as a philosophical discipline). Consider the following argument: 1. If we charge high fees for university, only the rich will enroll. We charge high fees for university. Therefore, only the rich (...)
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  19. Michael Dunn & Greg Restall (2002). Relevance Logic. In D. Gabbay & F. Guenthner (eds.), Handbook of Philosophical Logic. Kluwer
     
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  20.  21
    Greg Restall (2014). Normal Proofs, Cut Free Derivations and Structural Rules. Studia Logica 102 (6):1143-1166.
    Different natural deduction proof systems for intuitionistic and classical logic —and related logical systems—differ in fundamental properties while sharing significant family resemblances. These differences become quite stark when it comes to the structural rules of contraction and weakening. In this paper, I show how Gentzen and Jaśkowski’s natural deduction systems differ in fine structure. I also motivate directed proof nets as another natural deduction system which shares some of the design features of Genzen and Jaśkowski’s systems, but which differs again (...)
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  21.  25
    Greg Restall (1993). How to Be Really Contraction Free. Studia Logica 52 (3):381 - 391.
    A logic is said to becontraction free if the rule fromA (A B) toA B is not truth preserving. It is well known that a logic has to be contraction free for it to support a non-trivial naïve theory of sets or of truth. What is not so well known is that if there isanother contracting implication expressible in the language, the logic still cannot support such a naïve theory. A logic is said to berobustly contraction free if there is (...)
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  22.  61
    Greg Restall (2009). Truth Values and Proof Theory. Studia Logica 92 (2):241 - 264.
    I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.
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  23.  66
    Greg Restall, Relevant and Substructural Logics.
    This essay is structured around the bifurcation between proofs and models: The first section discusses Proof Theory of relevant and substructural logics, and the second covers the Model Theory of these logics. This order is a natural one for a history of relevant and substructural logics, because much of the initial work — especially in the Anderson–Belnap tradition of relevant logics — started by developing proof theory. The model theory of relevant logic came some time later. As we will see, (...)
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  24.  74
    Greg Restall (2004). One Way to Face Facts. Philosophical Quarterly 54 (216):420–426.
    Stephen Neale presents, in Facing Facts (Oxford: Clarendon Press, 2001), one convenient package containing his reasoned complaints against theories of facts and non-extensional connectives. The slingshot is a powerful argument (or better, it is a powerful family of arguments) which constrains theories of facts, propositions and non-extensional connectives by showing that some of these theories are rendered trivial. This book is the best place to find the state of the art on the slingshot and its implications for logic, language and (...)
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  25. JC Beall & Greg Restall, Defending Logical Pluralism.
    We are pluralists about logical consequence [1]. We hold that there is more than one sense in which arguments may be deductively valid, that these senses are equally good, and equally deserving of the name deductive validity. Our pluralism starts with our analysis of consequence. This analysis of consequence is not idiosyncratic. We agree with Richard Jeffrey, and with many other philosophers of logic about how logical consequence is to be defined. To quote Jeffrey.
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  26.  25
    Susan Rogerson & Greg Restall (2004). Routes to Triviality. Journal of Philosophical Logic 33 (4):421-436.
    It is known that a number of inference principles can be used to trivialise the axioms of naïve comprehension - the axioms underlying the naïve theory of sets. In this paper we systematise and extend these known results, to provide a number of general classes of axioms responsible for trivialising naïve comprehension.
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  27. Tim Bayne & Greg Restall (2009). A Participatory Model of the Atonement. In Yujin Nagasawa & Erik J. Wielenberg (eds.), New Waves in Philosophy of Religion. Palgrave Macmillan 150.
    In this paper we develop a participatory model of the Christian doctrine of the atonement, according to which the atonement involves participating in the death and resurrection of Christ. In part one we argue that current models of the atonement—exemplary, penal, substitutionary and merit models—are unsatisfactory. The central problem with these models is that they assume a purely deontic conception of sin and, as a result, they fail to address sin as a relational and ontological problem. In part two we (...)
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  28.  61
    Greg Restall (2010). On T and U, and What They Can Do. Analysis 70 (4):673 - 676.
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  29.  41
    Greg Restall (1998). Displaying and Deciding Substructural Logics 1: Logics with Contraposition. Journal of Philosophical Logic 27 (2):179-216.
    Many logics in the relevant family can be given a proof theory in the style of Belnap's display logic. However, as originally given, the proof theory is essentially more expressive than the logics they seek to model. In this paper, we consider a modified proof theory which more closely models relevant logics. In addition, we use this proof theory to show decidability for a large range of substructural logics.
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  30.  46
    Greg Restall (1997). Paraconsistent logics! Bulletin of the Section of Logic 26 (3):156-163.
    In this note I respond to Hartley Slater's argument 12 to the e ect that there is no such thing as paraconsistent logic. Slater's argument trades on the notion of contradictoriness in the attempt to show that the negation of paraconsistent logics is merely a subcontrary forming operator and not one which forms contradictories. I will show that Slater's argument fails, for two distinct reasons. Firstly, the argument does not consider the position of non-dialethic paraconsistency which rejects the possible truth (...)
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  31. Daniel Nolan, Greg Restall & Caroline West, Moral Fictionalism.
    What would morality have to be like in order to answer to our everyday moral concepts'? What are we committed to when we make moral claims such as "female infibulation is wrong"; or "we ought give money to famine relief"; or "we have a duty to not to harm others", and when we go on to argue about these sorts of claims'? It has seemed to many — and it seems plausible to us — that when we assert and argue (...)
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  32.  68
    Greg Restall (1996). Information Flow and Relevant Logics. In Jerry Seligman & Dag Westerståhl (eds.), Logic, Language and Computation. Csli Publications, Stanford 1--463.
  33. Greg Restall & Gillian Kay Russell (eds.) (2012). New Waves in Philosophical Logic. Palgrave Macmillan.
    Machine generated contents note: -- Series Editors' PrefaceAcknowledgementsNotes on ContributorsHow Things Are Elsewhere; W. Schwarz Information Change and First-Order Dynamic Logic; B.Kooi Interpreting and Applying Proof Theories for Modal Logic; F.Poggiolesi & G.Restall The Logic(s) of Modal Knowledge; D.Cohnitz On Probabilistically Closed Languages; H.Leitgeb Dogmatism, Probability and Logical Uncertainty; B.Weatherson & D.Jehle Skepticism about Reasoning; S.Roush, K.Allen & I.HerbertLessons in Philosophy of Logic from Medieval Obligations; C.D.Novaes How to Rule Out Things with Words: Strong Paraconsistency and the Algebra of Exclusion; (...)
     
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  34.  25
    Greg Restall (1993). Simplified Semantics for Relevant Logics (and Some of Their Rivals). Journal of Philosophical Logic 22 (5):481 - 511.
    This paper continues the work of Priest and Sylvan in Simplified Semantics for Basic Relevant Logics, a paper on the simplified semantics of relevant logics, such as B⁺ and B. We show that the simplified semantics can also be used for a large number of extensions of the positive base logic B⁺, and then add the dualising '*' operator to model negation. This semantics is then used to give conservative extension results for Boolean negation.
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  35.  28
    Greg Restall (2010). What Are We to Accept, and What Are We to Reject, While Saving Truth From Paradox? [REVIEW] Philosophical Studies 147 (3):433 - 443.
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  36.  15
    Greg Restall (1992). A Note on Naive Set Theory in ${Rm LP}$. Notre Dame Journal of Formal Logic 33 (3):422-432.
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  37. Graham Priest & Greg Restall, Envelopes and Indifference.
    Consider this situation: Here are two envelopes. You have one of them. Each envelope contains some quantity of money, which can be of any positive real magnitude. One contains twice the amount of money that the other contains, but you do not know which one. You can keep the money in your envelope, whose numerical value you do not know at this stage, or you can exchange envelopes and have the money in the other. You wish to maximise your money. (...)
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  38.  50
    Greg Restall (1995). Four-Valued Semantics for Relevant Logics (and Some of Their Rivals). Journal of Philosophical Logic 24 (2):139 - 160.
    This paper gives an outline of three different approaches to the four-valued semantics for relevant logics (and other non-classical logics in their vicinity). The first approach borrows from the 'Australian Plan' semantics, which uses a unary operator '⋆' for the evaluation of negation. This approach can model anything that the two-valued account can, but at the cost of relying on insights from the Australian Plan. The second approach is natural, well motivated, independent of the Australian Plan, and it provides a (...)
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  39.  15
    Greg Restall (1992). Arithmetic and Truth in Lukasiewicz's Infinitely Valued Logic. Logique Et Analyse 139 (140):303-312.
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  40.  26
    Greg Restall, Logics, Situations and Channels.
    The notion of that information is relative to a context is important in many different ways. The idea that the context is small — that is, not necessarily a consistent and complete possible world — plays a role not only in situation theory, but it is also an enlightening perspective from which to view other areas, such as modal logics, relevant logics, categorial grammar and much more. In this article we will consider these areas, and focus then on one further (...)
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  41. Greg Restall (2000). An Introduction to Substructural Logics. Routledge.
    This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. _An Introduction to Substrucural Logics_ is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both (...)
     
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  42. Greg Restall (2005). Logic: An Introduction. Routledge.
    Propositional logic -- Propositions and arguments -- Connectives and argument forms -- Truth tables -- Trees -- Vagueness and bivalence -- Conditionality -- Natural deduction -- Predicate logic -- Predicates, names, and quantifiers -- Models for predicate logic -- Trees for predicate logic -- Identity and functions -- Definite descriptions -- Some things do not exist -- What is a predicate? -- What is logic?
     
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  43.  13
    Greg Restall (1992). Modalities in Substructural Logics. Logique Et Analyse 35:303-321.
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  44. Greg Restall (2006). Laws of Non-Contradiction, Laws of the Excluded Middle, and Logics. In Graham Priest, J. C. Beall & Bradley Armour-Garb (eds.), The Law of Non-Contradiction: New Philosophical Essays. Clarendon Press
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  45.  83
    Greg Restall (2004). Logical Pluralism and the Preservation of Warrant. In S. Rahman (ed.), Logic, Epistemology, and the Unity of Science. Dordrecht, Kluwer 163--173.
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  46.  87
    Sam Butchart, Toby Handfield & Greg Restall (2009). Teaching Philosophy, Logic and Critical Thinking Using Peer Instruction. Teaching Philosophy (1):1-40.
    Peer Instruction (or PI for short) is a simple and effective technique you can use to make lectures more interactive, more engaging, and more effective learning experiences.
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  47.  55
    Greg Restall (forthcoming). Substructural Logics. Stanford Encyclopedia of Philosophy.
    summary of work in relevant in the Anderson– tradition.]; Mares Troestra, Anne, 1992, Lectures on , CSLI Publications [A quick, easy-to.
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  48.  82
    Greg Restall (2000). Modelling Truthmaking. Logique Et Analyse 43 (169-170):211-230.
    According to one tradition in realist philosophy, 'truthmaking' amounts to necessitation. That is, an object x is a truthmaker for the claim A if x exists, and the existence of x necessitates the truth of A. I argued in my paper "Truthmakers, Entailment and Necessity" [14], that if we wish to use this account of truthmaking, we ought understand the entailment connective "=>" in such a claim as a relevant entailment, in the tradition of Anderson and Belnap and their co-workers (...)
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  49.  57
    Greg Restall (2007). Curry's Revenge: The Costs of Non-Classical Solutions to the Paradoxes of Self-Reference. In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox. Oxford University Press
    The paradoxes of self-reference are genuinely paradoxical. The liar paradox, Russell’s paradox and their cousins pose enormous difficulties to anyone who seeks to give a comprehensive theory of semantics, or of sets, or of any other domain which allows a modicum of self-reference and a modest number of logical principles. One approach to the paradoxes of self-reference takes these paradoxes as motivating a non-classical theory of logical consequence. Similar logical principles are used in each of the paradoxical inferences. If one (...)
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  50.  38
    Greg Restall (2005). Constant Domain Quantified Modal Logics Without Boolean Negation. Australasian Journal of Logic 3 (1):45-62.
    This paper provides a sound and complete axiomatisation for constant domain modal logics without Boolean negation. This is a simpler case of the difficult problem of providing a sound and complete axiomatisation for constant-domain quantified relevant logics, which can be seen as a kind of modal logic with a two-place modal operator, the relevant conditional. The completeness proof is adapted from a proof for classical modal predicate logic , but with an important twist, to do with the absence of Boolean (...)
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