Search results for 'deduction' (try it on Scholar)

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  1.  9
    Historicizing Deduction (2004). Malachi Hacohen Historicizing Deduction: Scientific Method, Critical Debate, and the Historian. In Friedrich Stadler (ed.), Induction and Deduction in the Sciences. Springer 11--17.
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  2. Dennis Schulting (2014). Kant's Deduction From Apperception: A Reply to My Critics. Studi Kantiani 27:95-115.
    In my reply to the respective critiques by Corey Dyck, Marcel Quarfood and Andrew Stephenson of my book Kant’s Deduction and Apperception: Explaining the Categories (Palgrave 2012), I go over some of the main planks of my interpretation of the first step of the B-Deduction. In response to Dyck, I explain that there are several reasons why I believe that the deduction of the categories must indeed be seen as a logical derivation from the unity of apperception, (...)
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  3. Norihiro Kamide & Motohiko Mouri (2007). Natural Deduction Systems for Some Non-Commutative Logics. Logic and Logical Philosophy 16 (2-3):105-146.
    Varieties of natural deduction systems are introduced for Wansing’s paraconsistent non-commutative substructural logic, called a constructive sequential propositional logic (COSPL), and its fragments. Normalization, strong normalization and Church-Rosser theorems are proved for these systems. These results include some new results on full Lambek logic (FL) and its fragments, because FL is a fragment of COSPL.
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  4. John Corcoran (1974). Aristotle's Natural Deduction System. In Ancient Logic and its Modern Interpretations. Boston,Reidel 85--131.
    This presentation of Aristotle's natural deduction system supplements earlier presentations and gives more historical evidence. Some fine-tunings resulted from conversations with Timothy Smiley, Charles Kahn, Josiah Gould, John Kearns,John Glanvillle, and William Parry.The criticism of Aristotle's theory of propositions found at the end of this 1974 presentation was retracted in Corcoran's 2009 HPL article "Aristotle's demonstrative logic".
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  5. Mark Jago (2013). The Content of Deduction. Journal of Philosophical Logic 42 (2):317-334.
    For deductive reasoning to be justified, it must be guaranteed to preserve truth from premises to conclusion; and for it to be useful to us, it must be capable of informing us of something. How can we capture this notion of information content, whilst respecting the fact that the content of the premises, if true, already secures the truth of the conclusion? This is the problem I address here. I begin by considering and rejecting several accounts of informational content. I (...)
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  6. Danny Frederick (2014). Deduction and Novelty Again. The Reasoner 8 (5):51-52.
    It is commonly claimed that the conclusion of a valid deductive argument is contained in its premises and says nothing new. In 'Deduction and Novelty,' in The Reasoner 5 (4), pp. 56-57, I refuted that claim. In The Reasoner, 8 (3), pp. 24-25, David McBride criticised my refutation. I show that McBride’s arguments are unsound.
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  7.  30
    Nikolaos Galatos & Hiroakira Ono (2006). Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics Over FL. Studia Logica 83 (1-3):279 - 308.
    Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.
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  8. Anil Gomes (2014). Kant on Perception: Naive Realism, Non-Conceptualism, and the B-Deduction. Philosophical Quarterly 64 (254):1-19.
    According to non-conceptualist interpretations, Kant held that the application of concepts is not necessary for perceptual experience. Some have motivated non-conceptualism by noting the affinities between Kant's account of perception and contemporary relational theories of perception. In this paper I argue (i) that non-conceptualism cannot provide an account of the Transcendental Deduction and thus ought to be rejected; and (ii) that this has no bearing on the issue of whether Kant endorsed a relational account of perceptual experience.
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  9. Maria Lasonen-Aarnio (2008). Single Premise Deduction and Risk. Philosophical Studies 141 (2):157 - 173.
    It is tempting to think that multi premise closure creates a special class of paradoxes having to do with the accumulation of risks, and that these paradoxes could be escaped by rejecting the principle, while still retaining single premise closure. I argue that single premise deduction is also susceptible to risks. I show that what I take to be the strongest argument for rejecting multi premise closure is also an argument for rejecting single premise closure. Because of the symmetry (...)
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  10. Curtis Sommerlatte (forthcoming). Empirical Cognition in the Transcendental Deduction: Kant’s Starting Point and His Humean Problem. Kantian Review.
    In this paper, I argue that in the sense of greatest epistemological concern for Kant, empirical cognition is “rational sensory discrimination”: the identification or differentiation of sensory objects from each other, occurring through a capacity to become aware of and express judgments. With this account of empirical cognition, I show how the transcendental deduction of the first Critique is most plausibly read as having as its fundamental assumption the thesis that we have empirical cognition, and I provide evidence that (...)
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  11.  42
    Raul Hakli & Sara Negri (2012). Does the Deduction Theorem Fail for Modal Logic? Synthese 187 (3):849-867.
    Various sources in the literature claim that the deduction theorem does not hold for normal modal or epistemic logic, whereas others present versions of the deduction theorem for several normal modal systems. It is shown here that the apparent problem arises from an objectionable notion of derivability from assumptions in an axiomatic system. When a traditional Hilbert-type system of axiomatic logic is generalized into a system for derivations from assumptions, the necessitation rule has to be modified in a (...)
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  12. Ian Proops (2003). Kant's Legal Metaphor and the Nature of a Deduction. Journal of the History of Philosophy 41 (2):209-229.
    This essay partly builds on and partly criticizes a striking idea of Dieter Henrich. Henrich argues that Kant's distinction in the first Critique between the question of fact (quid facti) and the question of law (quid juris) provides clues to the argumentative structure of a philosophical "Deduction". Henrich suggests that the unity of apperception plays a role analogous to a legal factum. By contrast, I argue, first, that the question of fact in the first Critique is settled by the (...)
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  13.  84
    Justin B. Shaddock (2015). Kant’s Transcendental Idealism and His Transcendental Deduction. Kantian Review 20 (2):265-288.
    I argue for a novel, non-subjectivist interpretation of Kant’s transcendental idealism. Kant’s idealism is often interpreted as specifying how we must experience objects or how objects must appear to us. I argue to the contrary by appealing to Kant’s Transcendental Deduction. Kant’s Deduction is the proof that the categories are not merely subjectively necessary conditions we need for our cognition, but objectively valid conditions necessary for objects to be appearances. My interpretation centres on two claims. First, Kant’s method (...)
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  14. Moritz Cordes & Friedrich Reinmuth, A Speech Act Calculus. A Pragmatised Natural Deduction Calculus and its Meta-Theory.
    Building on the work of Peter Hinst and Geo Siegwart, we develop a pragmatised natural deduction calculus, i.e. a natural deduction calculus that incorporates illocutionary operators at the formal level, and prove its adequacy. In contrast to other linear calculi of natural deduction, derivations in this calculus are sequences of object-language sentences which do not require graphical or other means of commentary in order to keep track of assumptions or to indicate subproofs. (Translation of our German paper (...)
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  15.  54
    Jeffrey Goodman & Daniel Flage (2012). On 'Deduction' and the Inductive/Deductive Distinction. Studies in Logic 5 (3).
    The definitions of ‘deduction’ found in virtually every introductory logic textbook would encourage us to believe that the inductive/deductive distinction is a distinction among kinds of arguments and that the extension of ‘deduction’ is a determinate class of arguments. In this paper, we argue that that this approach is mistaken. Specifically, we defend the claim that typical definitions of ‘deduction’ operative in attempts to get at the induction/deduction distinction are either too narrow or insufficiently precise. We (...)
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  16.  20
    Allen P. Hazen & Francis Jeffry Pelletier (2014). Gentzen and Jaśkowski Natural Deduction: Fundamentally Similar but Importantly Different. Studia Logica 102 (6):1103-1142.
    Gentzen’s and Jaśkowski’s formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen’s formulation more straightforwardly lends itself both to a normalization theorem and to a theory of “meaning” for connectives . The present paper investigates cases where Jaskowski’s formulation seems better suited. These cases range from the phenomenology and epistemology of proof construction to the ways to incorporate novel logical connectives into the language. We close with a demonstration of this latter aspect (...)
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  17. Nathan Bauer (2010). Kant's Subjective Deduction. British Journal for the History of Philosophy 18 (3):433-460.
    In the transcendental deduction, the central argument of the Critique of Pure Reason, Kant seeks to secure the objective validity of our basic categories of thought. He distinguishes objective and subjective sides of this argument. The latter side, the subjective deduction, is normally understood as an investigation of our cognitive faculties. It is identified with Kant’s account of a threefold synthesis involved in our cognition of objects of experience, and it is said to precede and ground Kant’s proof (...)
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  18. Susan Haack (1976). The Justification of Deduction. Mind 85 (337):112-119.
    It is often taken for granted by writers who propose--and, for that matter, by writers who oppose--'justifications' of inductions, that deduction either does not need, or can readily be provided with, justification. The purpose of this paper is to argue that, contrary to this common opinion, problems analogous to those which, notoriously, arise in the attempt to justify induction, also arise in the attempt to justify deduction.
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  19. Huajie Liu (2006). Instability, Modus Ponens and Uncertainty of Deduction. Frontiers of Philosophy in China 1 (4):658-674.
    Considering the instability of nonlinear dynamics, the deductive inference rule Modus ponens itself is not enough to guarantee the validity of reasoning sequences in the real physical world, and similar results cannot necessarily be obtained from similar causes. Some kind of stability hypothesis should be added in order to draw meaningful conclusions. Hence, the uncertainty of deductive inference appears to be like that of inductive inference, and the asymmetry between deduction and induction becomes unrecognizable such as to undermine the (...)
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  20.  43
    Torben BraÜner (2005). Natural Deduction for First-Order Hybrid Logic. Journal of Logic, Language and Information 14 (2):173-198.
    This is a companion paper to Braüner where a natural deduction system for propositional hybrid logic is given. In the present paper we generalize the system to the first-order case. Our natural deduction system for first-order hybrid logic can be extended with additional inference rules corresponding to conditions on the accessibility relations and the quantifier domains expressed by so-called geometric theories. We prove soundness and completeness and we prove a normalisation theorem. Moreover, we give an axiom system first-order (...)
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  21. Marcello D'Agostino & Luciano Floridi (2009). The Enduring Scandal of Deduction. Synthese 167 (2):271 - 315.
    Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means of growing (...)
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  22. Melissa McBay Merritt (2010). Kant on the Transcendental Deduction of Space and Time: An Essay on the Philosophical Resources of the Transcendental Aesthetic. Kantian Review 14 (2):1-37.
    I take up Kant's remarks about a " transcendental deduction" of the "concepts of space and time". I argue for the need to make a clearer assessment of the philosophical resources of the Aesthetic in order to account for this transcendental deduction. Special attention needs to be given to the fact that the central task of the Aesthetic is simply the "exposition" of these concepts. The Metaphysical Exposition reflects upon facts about our usage to reveal our commitment to (...)
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  23. Anil Gomes (2010). Is Kant's Transcendental Deduction of the Categories Fit for Purpose? Kantian Review 15 (2):118-137.
    James Van Cleve has argued that Kant’s Transcendental Deduction of the categories shows, at most, that we must apply the categories to experience. And this falls short of Kant’s aim, which is to show that they must so apply. In this discussion I argue that once we have noted the differences between the first and second editions of the Deduction, this objection is less telling. But Van Cleve’s objection can help illuminate the structure of the B Deduction, (...)
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  24.  16
    Roberto Horácio de Sá Pereira (forthcoming). A Nonconceptualist Reading of the B-Deduction. Philosophical Studies:1-18.
    In this paper, I propose a new nonconceptual reading of the B-Deduction. As Hanna correctly remarks :399–415, 2011: 405), the word “cognition” has in both editions of the first Critique a wide sense, meaning nonconceptual cognition, and a narrow meaning, in Kant’s own words “an objective perception”. To be sure, Kant assumes the first meaning to account for why the Deduction is unavoidable. And if we take this meaning as a premise of the B-Deduction, then there is (...)
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  25.  36
    Gary Hatfield (2003). What Were Kant's Aims in the Deduction? Philosophical Topics 31 (1/2):165-198.
    This article argues that many (often Anglophone) interpreters of the Deduction have mistakenly identified Kant's aim as vindicating ordinary knowledge of objects and as refuting Hume's (alleged) skepticism about such knowledge. Instead, the article contends that Kant's aims were primarily negative. His primary mission (in the Deduction) was not to justify application of the categories to experience, but to show that any use beyond the domain of experience could not be justified. To do this, he needed to show (...)
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  26.  21
    Torben Braüner (2004). Two Natural Deduction Systems for Hybrid Logic: A Comparison. [REVIEW] Journal of Logic, Language and Information 13 (1):1-23.
    In this paper two different natural deduction systems forhybrid logic are compared and contrasted.One of the systems was originally given by the author of the presentpaper whereasthe other system under consideration is a modifiedversion of a natural deductionsystem given by Jerry Seligman.We give translations in both directions between the systems,and moreover, we devise a set of reduction rules forthe latter system bytranslation of already known reduction rules for the former system.
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  27.  11
    Steven Tester (2016). Mental Powers and the Soul in Kant’s Subjective Deduction and the Second Paralogism. Canadian Journal of Philosophy 46 (3):426-452.
    Kant’s claim in the Subjective Deduction that we have multiple fundamental mental powers appears to be susceptible to some a priori metaphysical arguments made against multiple fundamental mental powers by Christian Wolff who held that these powers would violate the unity of thought and entail that the soul is an extended composite. I argue, however, that in the Second Paralogism and his lectures on metaphysics, Kant provides arguments that overcome these objections by showing that it is possible that a (...)
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  28. William P. Bechtel (1994). Natural Deduction in Connectionist Systems. Synthese 101 (3):433-463.
    The relation between logic and thought has long been controversial, but has recently influenced theorizing about the nature of mental processes in cognitive science. One prominent tradition argues that to explain the systematicity of thought we must posit syntactically structured representations inside the cognitive system which can be operated upon by structure sensitive rules similar to those employed in systems of natural deduction. I have argued elsewhere that the systematicity of human thought might better be explained as resulting from (...)
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  29.  82
    John Corcoran (1974). Remarks on Stoic Deduction. In Ancient Logic and its Modern Interpretations. Boston,Reidel 169--181.
    This paper raises obvious questions undermining any residual confidence in Mates work and revealing our embarrassing ignorance of true nature of Stoic deduction. It was inspired by the challenging exploratory work of JOSIAH GOULD.
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  30.  21
    Nissim Francez (2014). Harmony in Multiple-Conclusion Natural-Deduction. Logica Universalis 8 (2):215-259.
    The paper studies the extension of harmony and stability, major themes in proof-theoretic semantics, from single-conclusion natural-deduction systems to multiple -conclusions natural-deduction, independently of classical logic. An extension of the method of obtaining harmoniously-induced general elimination rules from given introduction rules is suggested, taking into account sub-structurality. Finally, the reductions and expansions of the multiple -conclusions natural-deduction representation of classical logic are formulated.
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  31.  52
    John Corcoran (2014). “Truth-Preserving and Consequence-Preserving Deduction Rules”,. Bulletin of Symbolic Logic 20:130-1.
    A truth-preservation fallacy is using the concept of truth-preservation where some other concept is needed. For example, in certain contexts saying that consequences can be deduced from premises using truth-preserving deduction rules is a fallacy if it suggests that all truth-preserving rules are consequence-preserving. The arithmetic additive-associativity rule that yields 6 = (3 + (2 + 1)) from 6 = ((3 + 2) + 1) is truth-preserving but not consequence-preserving. As noted in James Gasser’s dissertation, Leibniz has been criticized (...)
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  32.  5
    J. G. Raftery (2011). Contextual Deduction Theorems. Studia Logica 99 (1-3):279-319.
    Logics that do not have a deduction-detachment theorem (briefly, a DDT) may still possess a contextual DDT —a syntactic notion introduced here for arbitrary deductive systems, along with a local variant. Substructural logics without sentential constants are natural witnesses to these phenomena. In the presence of a contextual DDT, we can still upgrade many weak completeness results to strong ones, e.g., the finite model property implies the strong finite model property. It turns out that a finitary system has a (...)
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  33.  79
    Corey W. Dyck (2008). The Subjective Deduction and the Search for a Fundamental Force. Kant-Studien 99 (2):152-179.
    In this paper, I claim that Kant’s subjective deduction in the first edition of the KrV is to be understood in terms of an investigation of the fundamental force(s) (Grundkraft) of the soul, an investigation essential to Wolffian psychology and much debated throughout Germany in the second half of the 1700’s. I argue that the subjective deduction is indeed presented by means of the exposition of the three-fold syntheses but only insofar as these syntheses are employed as pointers (...)
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  34.  73
    Manuel Sánchez Rodríguez (2013). The Conclusion of the Deduction of Taste in the Dialectic of Aesthetic Power of Judgment in Kant. Trans/Form/Ação 36 (2):45-62.
    In this paper, it is argued that only in the section on dialectic in the Critique of Judgment does Kant reach a definitive and conclusive version of deduction, after discovering the concept of the supersensible. In the section on the deduction of pure aesthetic judgments, Kant does not satisfactorily explain the critical distinction between the sensible nature of humanity and the supersensible nature of human reason presupposed in the concept of universal communicability. While the concept of the supersensible (...)
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  35.  4
    Francesca Poggiolesi (2016). Natural Deduction Calculi and Sequent Calculi for Counterfactual Logics. Studia Logica 104 (5):1003-1036.
    In this paper we present labelled sequent calculi and labelled natural deduction calculi for the counterfactual logics CK + {ID, MP}. As for the sequent calculi we prove, in a semantic manner, that the cut-rule is admissible. As for the natural deduction calculi we prove, in a purely syntactic way, the normalization theorem. Finally, we demonstrate that both calculi are sound and complete with respect to Nute semantics [12] and that the natural deduction calculi can be effectively (...)
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  36.  71
    Marcello D'Agostino & Luciano Floridi (2009). The Enduring Scandal of Deduction: Is Propositional Logic Really Uninformative? Synthese 167 (2):271 - 315.
    Deductive inference is usually regarded as being "tautological" or "analytical": the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means of growing (...)
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  37.  22
    Cassiano Terra Rodrigues (2011). The Method of Scientific Discovery in Peirce's Philosophy: Deduction, Induction, and Abduction. [REVIEW] Logica Universalis 5 (1):127-164.
    In this paper we will show Peirce’s distinction between deduction, induction and abduction. The aim of the paper is to show how Peirce changed his views on the subject, from an understanding of deduction, induction and hypotheses as types of reasoning to understanding them as stages of inquiry very tightly connected. In order to get a better understanding of Peirce’s originality on this, we show Peirce’s distinctions between qualitative and quantitative induction and between theorematical and corollarial deduction, (...)
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  38.  39
    Thomas Land (2015). Nonconceptualist Readings of Kant and the Transcendental Deduction. Kantian Review 20 (1):25-51.
    I give an argument against nonconceptualist readings of Kants claim that intuitions and concepts constitute two distinct kinds of representation than is assumed by proponents of nonconceptualist readings. I present such an interpretation and outline the alternative reading of the Deduction that results.
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  39.  25
    Gal Yehezkel (2016). The New Riddle of Induction and the New Riddle of Deduction. Acta Analytica 31 (1):31-41.
    Many believe that Goodman’s new riddle of induction proves the impossibility of a purely syntactical theory of confirmation. After discussing and rejecting Jackson’s solution to Goodman’s paradox, I formulate the “new riddle of deduction,” in analogy to the new riddle of induction. Since it is generally agreed that deductive validity can be defined syntactically, the new riddle of induction equally does not show that inductive validity cannot be defined syntactically. I further rely on the analogy between induction and (...) in order to explain why some predicates, such as “grue,” are unprojectible. (shrink)
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  40.  5
    Karel Chvalovský & Petr Cintula (2012). Note on Deduction Theorems in Contraction‐Free Logics. Mathematical Logic Quarterly 58 (3):236-243.
    This paper provides a finer analysis of the well-known form of the Local Deduction Theorem in contraction-free logics . An infinite hierarchy of its natural strengthenings is introduced and studied. The main results are the separation of its initial four members and the subsequent collapse of the hierarchy.
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  41.  8
    J. Von Plato (2003). Translations From Natural Deduction to Sequent Calculus. Mathematical Logic Quarterly 49 (5):435.
    Gentzen's “Untersuchungen” [1] gave a translation from natural deduction to sequent calculus with the property that normal derivations may translate into derivations with cuts. Prawitz in [8] gave a translation that instead produced cut-free derivations. It is shown that by writing all elimination rules in the manner of disjunction elimination, with an arbitrary consequence, an isomorphic translation between normal derivations and cut-free derivations is achieved. The standard elimination rules do not permit a full normal form, which explains the cuts (...)
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  42.  45
    Jonathan Payne (2015). Natural Deduction for Modal Logic with a Backtracking Operator. Journal of Philosophical Logic 44 (3):237-258.
    Harold Hodes in [1] introduces an extension of first-order modal logic featuring a backtracking operator, and provides a possible worlds semantics, according to which the operator is a kind of device for ‘world travel’; he does not provide a proof theory. In this paper, I provide a natural deduction system for modal logic featuring this operator, and argue that the system can be motivated in terms of a reading of the backtracking operator whereby it serves to indicate modal scope. (...)
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  43.  7
    Andrew Stephenson (2014). A Deduction From Apperception? Studi Kantiani 27:77-86.
    I discuss three elements of Dennis Schulting’s new book on the transcendental deduction of the pure concepts of the understanding, or categories. First, that Schulting gives a detailed account of the role of each individual category. Second, Schulting’s insistence that the categories nevertheless apply ‘en bloc’. Third, Schulting’s defence of Kant’s so-called reciprocity thesis that subjective unity of consciousness and objectivity in the sense of cognition’s objective purport are necessary conditions for the possibility of one another. I endorse these (...)
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  44.  14
    Hans Lycke (2009). Fitch-Style Natural Deduction for Modal Paralogics. Logique Et Analyse 207:193-218.
    In this paper, I will present a Fitch–style natural deduction proof theory for modal paralogics (modal logics with gaps and/or gluts for negation). Besides the standard classical subproofs, the presented proof theory also contains modal subproofs, which express what would follow from a hypothesis, in case it would be true in some arbitrary world.
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  45.  9
    Tin Perkov (2016). Natural Deduction for Modal Logic of Judgment Aggregation. Journal of Logic, Language and Information 25 (3-4):335-354.
    We can formalize judgments as logical formulas. Judgment aggregation deals with judgments of several agents, which need to be aggregated to a collective judgment. There are several logical formalizations of judgment aggregation. This paper focuses on a modal formalization which nicely expresses classical properties of judgment aggregation rules and famous results of social choice theory, like Arrow’s impossibility theorem. A natural deduction system for modal logic of judgment aggregation is presented in this paper. The system is sound and complete. (...)
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  46. Bruno G. Bara & Monica Bucciarelli (2000). Deduction and Induction: Reasoning Through Mental Models. [REVIEW] Mind and Society 1 (1):95-107.
    In this paper we deal with two types of reasoning: induction, and deduction First, we present a unified computational model of deductive reasoning through models, where deduction occurs in five phases: Construction, Integration, Conclusion, Falsification, and Response. Second, we make an attempt, to analyze induction through the same phases. Our aim is an explorative evaluation of the mental processes possibly shared by deductive and inductive reasoning.
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  47.  11
    Félix Bou, Josep Maria Font & José Luis García Lapresta (2004). On Weakening the Deduction Theorem and Strengthening Modus Ponens. Mathematical Logic Quarterly 50 (3):303-324.
    This paper studies, with techniques ofAlgebraic Logic, the effects of putting a bound on the cardinality of the set of side formulas in the Deduction Theorem, viewed as a Gentzen-style rule, and of adding additional assumptions inside the formulas present in Modus Ponens, viewed as a Hilbert-style rule. As a result, a denumerable collection of new Gentzen systems and two new sentential logics have been isolated. These logics are weaker than the positive implicative logic. We have determined their algebraic (...)
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  48.  21
    Richard Zach (2016). Natural Deduction for the Sheffer Stroke and Peirce’s Arrow. Journal of Philosophical Logic 45 (2):183-197.
    Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions (...)
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  49.  7
    Ernst Zimmermann (2010). Full Lambek Calculus in Natural Deduction. Mathematical Logic Quarterly 56 (1):85-88.
    A formulation of Full Lambek Calculus in the framework of natural deduction is given.
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  50.  9
    Carlo Cellucci (1995). On Quine's Approach to Natural Deduction'. In Paolo Leonardi & Marco Santambrogio (eds.), On Quine: New Essays. Cambridge University Press 314--335.
    This article examines Quine's original proposal for a natural deduction calculus including an existential specification rule, it argues that it introduces a new paradigm of natural deduction alternative to Gentzen's but has some substantial defects. As an alternative the article puts forward a system of sequent natural deduction.
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