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

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  1. Massimo Pigliucci & Maarten Boudry (2013). Prove It! The Burden of Proof Game in Science Vs. Pseudoscience Disputes. Philosophia 42 (2):487-502.
    The concept of burden of proof is used in a wide range of discourses, from philosophy to law, science, skepticism, and even in everyday reasoning. This paper provides an analysis of the proper deployment of burden of proof, focusing in particular on skeptical discussions of pseudoscience and the paranormal, where burden of proof assignments are most poignant and relatively clear-cut. We argue that burden of proof is often misapplied or used as a mere rhetorical gambit, with (...)
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  2. Courtney Fugate (2014). The Highest Good and Kant's Proof(s) of God's Existence. History of Philosophy Quarterly 31 (2).
    This paper explains a way of understanding Kant's proof of God's existence in the Critique of Practical Reason that has hitherto gone unnoticed and argues that this interpretation possesses several advantages over its rivals. By first looking at examples where Kant indicates the role that faith plays in moral life and then reconstructing the proof of the second Critique with this in view, I argue that, for Kant, we must adopt a certain conception of the highest good, and (...)
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  3.  70
    Kevin Morris & Consuelo Preti (2015). How to Read Moore's "Proof of an External World". Journal for the History of Analytical Philosophy 4 (1).
    We develop a reading of Moore’s “Proof of an External World” that emphasizes the connections between this paper and Moore’s earlier concerns and strategies. Our reading has the benefit of explaining why the claims that Moore advances in “Proof of an External World” would have been of interest to him, and avoids attributing to him arguments that are either trivial or wildly unsuccessful. Part of the evidence for our view comes from unpublished drafts which, we believe, contain important (...)
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  4.  44
    A. S. Troelstra (2000). Basic Proof Theory. Cambridge University Press.
    This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in (...)
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  5.  18
    Michael Detlefsen (2008). Proof: Its Nature and Significance. In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America 1.
    I focus on three preoccupations of recent writings on proof. -/- I. The role and possible effects of empirical reasoning in mathematics. Do recent developments (specifically, the computer-assisted proof of the 4CT) point to something essentially new as regards the need for and/or effects of using broadly empirical and inductive reasoning in mathematics? In particular, should we see such things as the computer-assisted proof of the 4CT as pointing to the existence of mathematical truths of which we (...)
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  6. Christian Buth, Nonexistence of Gods: An Inductive Proof.
    I prove the nonexistence of gods. The proof is based on three axioms: Ockham’s razor (OR), religiosity is endogenous in humans, and, there are no miracles. The OR is formulated operationally, to remove improper postulates, such that it yields not only a plausible argument but truth. The validity of the second and the third axiom is established empirically by inductive reasoning relying on a thorough analysis of the psychiatric literature and skeptical publications. With these axioms I prove that gods (...)
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  7. Luca Moretti (2014). The Dogmatist, Moore's Proof and Transmission Failure. Analysis 74 (3):382-389.
    According to Jim Pryor’s dogmatism, if you have an experience as if P, you acquire immediate prima facie justification for believing P. Pryor contends that dogmatism validates Moore’s infamous proof of a material world. Against Pryor, I argue that if dogmatism is true, Moore’s proof turns out to be non-transmissive of justification according to one of the senses of non-transmissivity defined by Crispin Wright. This type of non-transmissivity doesn’t deprive dogmatism of its apparent antisceptical bite.
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  8.  9
    Laura Silva-Castañeda (2012). A Forest of Evidence: Third-Party Certification and Multiple Forms of Proof—a Case Study of Oil Palm Plantations in Indonesia. [REVIEW] Agriculture and Human Values 29 (3):361-370.
    In recent years, new forms of transnational regulation have emerged, filling the void created by the failure of governments and international institutions to effectively regulate transnational corporations. Among the variety of initiatives addressing social and environmental problems, a growing number of certification systems have appeared in various sectors, particularly agrifood. Most initiatives rely on independent third-party certification to verify compliance with a standard, as it is seen as the most credible route for certification. The effects of third-party audits, however, still (...)
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  9.  61
    Nissim Francez & Roy Dyckhoff (2010). Proof-Theoretic Semantics for a Natural Language Fragment. Linguistics and Philosophy 33 (6):447-477.
    The paper presents a proof-theoretic semantics (PTS) for a fragment of natural language, providing an alternative to the traditional model-theoretic (Montagovian) semantics (MTS), whereby meanings are truth-condition (in arbitrary models). Instead, meanings are taken as derivability-conditions in a dedicated natural-deduction (ND) proof-system. This semantics is effective (algorithmically decidable), adhering to the meaning as use paradigm, not suffering from several of the criticisms formulated by philosophers of language against MTS as a theory of meaning. In particular, Dummett’s manifestation argument (...)
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  10.  25
    John Corcoran (1971). Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value. Journal of Structural Learning 3 (2):1-16.
    1971. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value, Journal of Structural Learning 3, #2, 1–16. REPRINTED 1976. Structural Learning II Issues and Approaches, ed. J. Scandura, Gordon & Breach Science Publishers, New York, MR56#15263. -/- This is the second of a series of three articles dealing with application of linguistics and logic to the study of mathematical reasoning, especially in the setting of a concern for improvement (...)
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  11.  13
    Sara Negri (2011). Proof Analysis: A Contribution to Hilbert's Last Problem. Cambridge University Press.
    Machine generated contents note: Prologue: Hilbert's Last Problem; 1. Introduction; Part I. Proof Systems Based on Natural Deduction: 2. Rules of proof: natural deduction; 3. Axiomatic systems; 4. Order and lattice theory; 5. Theories with existence axioms; Part II. Proof Systems Based on Sequent Calculus: 6. Rules of proof: sequent calculus; 7. Linear order; Part III. Proof Systems for Geometric Theories: 8. Geometric theories; 9. Classical and intuitionistic axiomatics; 10. Proof analysis in elementary geometry; (...)
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  12.  22
    Samuel R. Buss (ed.) (1998). Handbook of Proof Theory. Elsevier.
    This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory (...)
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  13.  19
    Thomas Piecha, Wagner de Campos Sanz & Peter Schroeder-Heister (2015). Failure of Completeness in Proof-Theoretic Semantics. Journal of Philosophical Logic 44 (3):321-335.
    Several proof-theoretic notions of validity have been proposed in the literature, for which completeness of intuitionistic logic has been conjectured. We define validity for intuitionistic propositional logic in a way which is common to many of these notions, emphasizing that an appropriate notion of validity must be closed under substitution. In this definition we consider atomic systems whose rules are not only production rules, but may include rules that allow one to discharge assumptions. Our central result shows that Harrop’s (...)
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  14. Tim Dare & Justine Kingsbury (2008). Putting the Burden of Proof in Its Place: When Are Differential Allocations Legitimate? Southern Journal of Philosophy 46 (4):503-518.
    To have the burden of proof is to be rationally required to argue for or provide evidence for your position. To have a heavier burden than an opponent is to be rationally required to provide better evidence or better arguments than they are required to provide. Many commentators suggest that differential or uneven distribution of the burden of proof is ubiquitous. In reasoned discourse, the idea goes, it is almost always the case that one party must prove the (...)
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  15.  26
    Ryo Takemura (2013). Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization. Studia Logica 101 (1):157-191.
    Proof-theoretical notions and techniques, developed on the basis of sentential/symbolic representations of formal proofs, are applied to Euler diagrams. A translation of an Euler diagrammatic system into a natural deduction system is given, and the soundness and faithfulness of the translation are proved. Some consequences of the translation are discussed in view of the notion of free ride, which is mainly discussed in the literature of cognitive science as an account of inferential efficacy of diagrams. The translation enables us (...)
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  16.  10
    Catherine Elizabeth Kendig (forthcoming). What is Proof of Concept Research and How Does It Generate Epistemic and Ethical Categories for Future Scientific Practice? Science and Engineering Ethics:1-19.
    Proof of concept” is a phrase frequently used in descriptions of research sought in program announcements, in experimental studies, and in the marketing of new technologies. It is often coupled with either a short definition or none at all, its meaning assumed to be fully understood. This is problematic. As a phrase with potential implications for research and technology, its assumed meaning requires some analysis to avoid it becoming a descriptive category that refers to all things scientifically exciting. I (...)
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  17. Nils Kürbis (2015). Proof-Theoretic Semantics, a Problem with Negation and Prospects for Modality. Journal of Philosophical Logic 44 (6):713-727.
    This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett’s and Dag Prawitz’ philosophical motivations and give precise characterisations of the crucial notions of harmony and stability, placed in the context of proving normalisation results in systems of natural deduction. I point out a problem for defining the meaning of negation in this framework and prospects for an account of the meanings (...)
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  18. Imran Aijaz, Jonathan McKeown-Green & Aness Webster (2013). Burdens of Proof and the Case for Unevenness. Argumentation 27 (3):259-282.
    How is the burden of proof to be distributed among individuals who are involved in resolving a particular issue? Under what conditions should the burden of proof be distributed unevenly? We distinguish attitudinal from dialectical burdens and argue that these questions should be answered differently, depending on which is in play. One has an attitudinal burden with respect to some proposition when one is required to possess sufficient evidence for it. One has a dialectical burden with respect to (...)
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  19.  20
    Justin Khoo (2013). A Note on Gibbard's Proof. Philosophical Studies 166 (1):153-164.
    A proof by Allan Gibbard (Ifs: Conditionals, beliefs, decision, chance, time. Reidel, Dordrecht, 1981) seems to demonstrate that if indicative conditionals have truth conditions, they cannot be stronger than material implication. Angelika Kratzer's theory that conditionals do not denote two-place operators purports to escape this result [see Kratzer (Chic Linguist Soc 22(2):1–15, 1986, 2012)]. In this note, I raise some trouble for Kratzer’s proposed method of escape and then show that her semantics avoids this consequence of Gibbard’s proof (...)
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  20.  14
    Petr Cintula & Carles Noguera (2013). The Proof by Cases Property and its Variants in Structural Consequence Relations. Studia Logica 101 (4):713-747.
    This paper is a contribution to the study of the rôle of disjunction inAlgebraic Logic. Several kinds of (generalized) disjunctions, usually defined using a suitable variant of the proof by cases property, were introduced and extensively studied in the literature mainly in the context of finitary logics. The goals of this paper are to extend these results to all logics, to systematize the multitude of notions of disjunction (both those already considered in the literature and those introduced in this (...)
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  21.  13
    Nissim Francez (2013). Bilateralism in Proof-Theoretic Semantics. Journal of Philosophical Logic (2-3):1-21.
    The paper suggests a revision of the notion of harmony, a major necessary condition in proof-theoretic semantics for a natural-deduction proof-system to qualify as meaning conferring, when moving to a bilateral proof-system. The latter considers both forces of assertion and denial as primitive, and is applied here to positive logics, lacking negation altogether. It is suggested that in addition to the balance between (positive) introduction and elimination rules traditionally imposed by harmony, a balance should be imposed also (...)
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  22.  54
    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 (...)
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  23.  29
    Peter Schroeder-Heister (2012). Proof-Theoretic Semantics, Self-Contradiction, and the Format of Deductive Reasoning. Topoi 31 (1):77-85.
    From the point of view of proof-theoretic semantics, it is argued that the sequent calculus with introduction rules on the assertion and on the assumption side represents deductive reasoning more appropriately than natural deduction. In taking consequence to be conceptually prior to truth, it can cope with non-well-founded phenomena such as contradictory reasoning. The fact that, in its typed variant, the sequent calculus has an explicit and separable substitution schema in form of the cut rule, is seen as a (...)
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  24.  94
    Jeffrey Bub (2010). Von Neumann's 'No Hidden Variables' Proof: A Re-Appraisal. [REVIEW] Foundations of Physics 40 (9-10):1333-1340.
    Since the analysis by John Bell in 1965, the consensus in the literature is that von Neumann’s ‘no hidden variables’ proof fails to exclude any significant class of hidden variables. Bell raised the question whether it could be shown that any hidden variable theory would have to be nonlocal, and in this sense ‘like Bohm’s theory.’ His seminal result provides a positive answer to the question. I argue that Bell’s analysis misconstrues von Neumann’s argument. What von Neumann proved was (...)
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  25.  61
    Alexander Paseau (2015). Knowledge of Mathematics Without Proof. British Journal for the Philosophy of Science 66 (4):775-799.
    Mathematicians do not claim to know a proposition unless they think they possess a proof of it. For all their confidence in the truth of a proposition with weighty non-deductive support, they maintain that, strictly speaking, the proposition remains unknown until such time as someone has proved it. This article challenges this conception of knowledge, which is quasi-universal within mathematics. We present four arguments to the effect that non-deductive evidence can yield knowledge of a mathematical proposition. We also show (...)
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  26.  3
    Dov M. Gabbay (2000). Goal-Directed Proof Theory. Kluwer Academic.
    Goal Directed Proof Theory presents a uniform and coherent methodology for automated deduction in non-classical logics, the relevance of which to computer science is now widely acknowledged. The methodology is based on goal-directed provability. It is a generalization of the logic programming style of deduction, and it is particularly favourable for proof search. The methodology is applied for the first time in a uniform way to a wide range of non-classical systems, covering intuitionistic, intermediate, modal and (...)
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  27.  22
    Ulrike Hahn & Mike Oaksford (2007). The Burden of Proof and Its Role in Argumentation. Argumentation 21 (1):39-61.
    The notion of “the burden of proof” plays an important role in real-world argumentation contexts, in particular in law. It has also been given a central role in normative accounts of argumentation, and has been used to explain a range of classic argumentation fallacies. We argue that in law the goal is to make practical decisions whereas in critical discussion the goal is frequently simply to increase or decrease degree of belief in a proposition. In the (...)
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  28.  7
    Douglas N. Walton (2007). Metadialogues for Resolving Burden of Proof Disputes. Argumentation 21 (3):291-316.
    In this paper, a solution to the problem of analyzing burden of proof in argumentation is developed by building on the pioneering work of Erik C. W. Krabbe on metadialogues. Three classic cases of burden of proof disputes are analyzed, showing how metadialogue theory can solve the problems they pose. The solution is based on five dialectical requirements: (1) global burden of proof needs to be set at the confrontation stage of a dialogue, (2) there need to (...)
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  29. Tyler Burge (1998). Computer Proof, Apriori Knowledge, and Other Minds. Noûs 32 (S12):1-37.
  30.  7
    John Corcoran (1971). Discourse Grammars and the Structure of Mathematical Reasoning III: Two Theories of Proof,. Journal of Structural Learning 3 (3):1-24.
    ABSTRACT This part of the series has a dual purpose. In the first place we will discuss two kinds of theories of proof. The first kind will be called a theory of linear proof. The second has been called a theory of suppositional proof. The term "natural deduction" has often and correctly been used to refer to the second kind of theory, but I shall not do so here because many of the theories so-called are not of (...)
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  31.  6
    San-min Wang & Petr Cintula (2008). Logics with Disjunction and Proof by Cases. Archive for Mathematical Logic 47 (5):435-446.
    This paper is a contribution to the general study of consequence relations which contain (definable) connective of “disjunction”. Our work is centered around the “proof by cases property”, we present several of its equivalent definitions, and show some interesting applications, namely in constructing axiomatic systems for intersections of logics and recognizing weakly implicative fuzzy logics among the weakly implicative ones.
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  32. Fabrizio Macagno (2010). Dialectical and Heuristic Arguments: Presumptions and Burden of Proof. In C. Tindale & C. Reed (eds.), Dialectics, Dialogue and Argumentation: An Examination of Douglas Walton's Theories of Reasoning and Argument. College Publications 45-57.
    Presumption is a complex concept in law, affecting the dialogue setting. However, it is not clear how presumptions work in everyday argumentation, in which the concept of “plausible argumentation” seems to encompass all kinds of inferences. By analyzing the legal notion of presumption, it appears that this type of reasoning combines argument schemes with reasoning from ignorance. Presumptive reasoning can be considered a particular form of reasoning, which needs positive or negative evidence to carry a probative weight on the conclusion. (...)
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  33.  60
    Michael Detlefsen & Mark Luker (1980). The Four-Color Theorem and Mathematical Proof. Journal of Philosophy 77 (12):803-820.
    I criticize a recent paper by Thomas Tymoczko in which he attributes fundamental philosophical significance and novelty to the lately-published computer-assisted proof of the four color theorem (4CT). Using reasoning precisely analogous to that employed by Tymoczko, I argue that much of traditional mathematical proof must be seen as resting on what Tymoczko must take as being "empirical" evidence. The new proof of the 4CT, with its use of what Tymoczko calls "empirical" evidence is therefore not so (...)
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  34.  8
    Yuping Shen & Xishun Zhao (2013). Proof Systems for Planning Under Cautious Semantics. Minds and Machines 23 (1):5-45.
    Planning with incomplete knowledge becomes a very active research area since late 1990s. Many logical formalisms introduce sensing actions and conditional plans to address the problem. The action language $\mathcal{A}_{K}$ invented by Son and Baral is a well-known framework for this purpose. In this paper, we propose so-called cautious and weakly cautious semantics for $\mathcal{A}_{K}$ , in order to allow an agent to generate and execute reliable plans in safety-critical environments. Intuitively speaking, cautious and weakly cautious semantics enable the agent (...)
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  35.  24
    H. Wansing (ed.) (1996). Proof Theory of Modal Logic. Kluwer.
    Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.
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  36.  96
    Gregor Damschen (2011). Questioning Gödel's Ontological Proof: Is Truth Positive? European Journal for Philosophy of Religion 3 (1):161-169.
    In his "Ontological proof", Kurt Gödel introduces the notion of a second-order value property, the positive property P. The second axiom of the proof states that for any property φ: If φ is positive, its negation is not positive, and vice versa. I put forward that this concept of positiveness leads into a paradox when we apply it to the following self-reflexive sentences: (A) The truth value of A is not positive; (B) The truth value of B is (...)
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  37.  5
    Julian J. Koplin & Michael J. Selgelid (2015). Burden of Proof in Bioethics. Bioethics 29 (9):597-603.
    A common strategy in bioethics is to posit a prima facie case in favour of one policy, and to then claim that the burden of proof falls on those with opposing views. If the burden of proof is not met, it is claimed, then the policy in question should be accepted. This article illustrates, and critically evaluates, examples of this strategy in debates about the sale of organs by living donors, human enhancement, and the precautionary principle. We highlight (...)
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  38.  33
    Srećko Kovač (2012). Modal Collapse in Gödel's Ontological Proof. In Miroslaw Szatkowski (ed.), Ontological Proofs Today. Ontos Verlag 50--323.
    After introductory reminder of and comments on Gödel’s ontological proof, we discuss the collapse of modalities, which is provable in Gödel’s ontological system GO. We argue that Gödel’s texts confirm modal collapse as intended consequence of his ontological system. Further, we aim to show that modal collapse properly fits into Gödel’s philosophical views, especially into his ontology of separation and union of force and fact, as well as into his cosmological theory of the nonobjectivity of the lapse of time. (...)
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  39.  12
    Philipp Gerhardy (2008). Proof Mining in Topological Dynamics. Notre Dame Journal of Formal Logic 49 (4):431-446.
    A famous theorem by van der Waerden states the following: Given any finite coloring of the integers, one color contains arbitrarily long arithmetic progressions. Equivalently, for every q,k, there is an N = N(q,k) such that for every q-coloring of an interval of length N one color contains a progression of length k. An obvious question is what is the growth rate of N = N(q,k). Some proofs, like van der Waerden's combinatorial argument, answer this question directly, while the topological (...)
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  40.  8
    Jan Krajíček (2008). An Exponential Lower Bound for a Constraint Propagation Proof System Based on Ordered Binary Decision Diagrams. Journal of Symbolic Logic 73 (1):227-237.
    We prove an exponential lower bound on the size of proofs in the proof system operating with ordered binary decision diagrams introduced by Atserias, Kolaitis and Vardi [2]. In fact, the lower bound applies to semantic derivations operating with sets defined by OBDDs. We do not assume any particular format of proofs or ordering of variables, the hard formulas are in CNF. We utilize (somewhat indirectly) feasible interpolation. We define a proof system combining resolution and the OBDD (...) system. (shrink)
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  41.  1
    Masahiro Hamano (2004). Softness of MALL Proof-Structures and a Correctness Criterion with Mix. Archive for Mathematical Logic 43 (6):751-794.
    We show that every MALL proof-structure [9] satisfies the property of softness, originally a categorical notion introduced by Joyal. Furthermore, we show that the notion of hereditary softness precisely captures Girard’s algebraic restriction of the technical condition on proof-structures. Relying on this characterization, we prove a MALL+Mix sequentialization theorem by a proof-theoretical method, using Girard’s notion of jump. Our MALL+Mix correctness criterion subsumes the Danos/Fleury-Retoré criterion [6] for MLL+Mix.
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  42.  2
    Stefano Baratella & Andrea Masini (2004). An Approach to Infinitary Temporal Proof Theory. Archive for Mathematical Logic 43 (8):965-990.
    Aim of this work is to investigate from a proof-theoretic viewpoint a propositional and a predicate sequent calculus with an ω–type schema of inference that naturally interpret the propositional and the predicate until–free fragments of Linear Time Logic LTL respectively. The two calculi are based on a natural extension of ordinary sequents and of standard modal rules. We examine the pure propositional case (no extralogical axioms), the propositional and the first order predicate cases (both with a possibly infinite set (...)
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  43.  76
    Carlo Penco & Daniele Porello (2010). Sense and Proof. In M. D'agostino, G. Giorello, F. Laudisa, T. Pievani & C. Sinigaglia (eds.), New Essays in Logic and Philosophy of Science,. College Publicationss
    In this paper we give some formal examples of ideas developed by Penco in two papers on the tension inside Frege's notion of sense (see Penco 2003). The paper attempts to compose the tension between semantic and cognitive aspects of sense, through the idea of sense as proof or procedure – not as an alternative to the idea of sense as truth condition, but as complementary to it (as it happens sometimes in the old tradition of procedural semantics).
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  44.  10
    Pierluigi Minari (2007). Analytic Proof Systems for Λ-Calculus: The Elimination of Transitivity, and Why It Matters. [REVIEW] Archive for Mathematical Logic 46 (5-6):385-424.
    We introduce new proof systems G[β] and G ext[β], which are equivalent to the standard equational calculi of λβ- and λβη- conversion, and which may be qualified as ‘analytic’ because it is possible to establish, by purely proof-theoretical methods, that in both of them the transitivity rule admits effective elimination. This key feature, besides its intrinsic conceptual significance, turns out to provide a common logical background to new and comparatively simple demonstrations—rooted in nice proof-theoretical properties of transitivity-free (...)
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  45.  13
    Reinhard Kahle (2015). What is a Proof? Axiomathes 25 (1):79-91.
    In this programmatic paper we renew the well-known question “What is a proof?”. Starting from the challenge of the mathematical community by computer assisted theorem provers we discuss in the first part how the experiences from examinations of proofs can help to sharpen the question. In the second part we have a look to the new challenge given by “big proofs”.
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  46.  9
    Nissim Francez (2015). On a Distinction of Two Facets of Meaning and its Role in Proof-Theoretic Semantics. Logica Universalis 9 (1):121-127.
    I show that in the context of proof-theoretic semantics, Dummett’s distinction between the assertoric meaning of a sentence and its ingredient sense can be seen as a distinction between two proof-theoretic meanings of a sentence: 1.Meaning as a conclusion of an introduction rule in a meaning-conferring natural-deduction proof system. 2.Meaning as a premise of an introduction rule in a meaning-conferring natural-deduction proof system. The effect of this distinction on compositionality of proof-theoretic meaning is discussed.
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  47.  14
    Juha Räikkä (1997). Burden of Proof Rules in Social Criticism. Argumentation 11 (4):463-477.
    The article discusses burden of proof rules in social criticism. By social criticism I mean an argumentative situation in which an opponent publicly argues against certain social practices; the examples I consider are discrimination on the basis of species and discrimination on the basis of one's nationality. I argue that burden of proof rules assumed by those who defend discrimination are somewhat dubious. In social criticism, there are no shared values which would uncontroversially determine what is the reasonable (...)
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  48.  32
    Florian Steinberger (2013). On the Equivalence Conjecture for Proof-Theoretic Harmony. Notre Dame Journal of Formal Logic 54 (1):79-86.
    The requirement of proof-theoretic harmony has played a pivotal role in a number of debates in the philosophy of logic. Different authors have attempted to precisify the notion in different ways. Among these, three proposals have been prominent in the literature: harmony–as–conservative extension, harmony–as–leveling procedure, and Tennant’s harmony–as–deductive equilibrium. In this paper I propose to clarify the logical relationships between these accounts. In particular, I demonstrate that what I call the equivalence conjecture —that these three notions essentially come to (...)
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  49.  13
    David J. Pym (2004). Reductive Logic and Proof-Search: Proof Theory, Semantics, and Control. Oxford University Press.
    This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search including proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences.
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  50.  53
    Marc Aiguier & Delphine Longuet (2010). Some General Results About Proof Normalization. Logica Universalis 4 (1):1-29.
    In this paper, we provide a general setting under which results of normalization of proof trees such as, for instance, the logicality result in equational reasoning and the cut-elimination property in sequent or natural deduction calculi, can be unified and generalized. This is achieved by giving simple conditions which are sufficient to ensure that such normalization results hold, and which can be automatically checked since they are syntactical. These conditions are based on basic properties of elementary combinations of inference (...)
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