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

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  1. Srećko Kovač (2012). Modal Collapse in Gödel's Ontological Proof. In Miroslaw Szatkowski (ed.), Ontological Proofs Today. Ontos Verlag. 50--323.score: 25.0
    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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  2. Massimo Pigliucci & Maarten Boudry (2013). Prove It! The Burden of Proof Game in Science Vs. Pseudoscience Disputes. Philosophia 42 (2):487-502.score: 24.0
    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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  3. Peter Murphy (ed.) (2003). Evidence, Proof, and Facts: A Book of Sources. New York ;Oxford University Press.score: 24.0
    This book is a collection of materials concerned not only with the law of evidence, but also with the logical and rhetorical aspects of proof; the epistemology of evidence as a basis for the proof of disputed facts; and scientific aspects of the subject. The editor also raises issues such as the philosophical basis for the use of evidence.
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  4. Luca Moretti (2014). The Dogmatist, Moore's Proof and Transmission Failure. Analysis 74 (3):382-389.score: 24.0
    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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  5. Imran Aijaz, Jonathan McKeown-Green & Aness Webster (2013). Burdens of Proof and the Case for Unevenness. Argumentation 27 (3):259-282.score: 24.0
    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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  6. Michael Detlefsen (ed.) (1992). Proof, Logic, and Formalization. Routledge.score: 24.0
    Proof, Logic and Formalization addresses the various problems associated with finding a philosophically satisfying account of mathematical proof. It brings together many of the most notable figures currently writing on this issue in an attempt to explain why it is that mathematical proof is given prominence over other forms of mathematical justification. The difficulties that arise in accounts of proof range from the rightful role of logical inference and formalization to questions concerning the place of experience (...)
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  7. 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.score: 24.0
    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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  8. Gregor Damschen (2011). Questioning Gödel's Ontological Proof: Is Truth Positive? European Journal for Philosophy of Religion 3 (1):161-169.score: 24.0
    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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  9. Greg Restall (2009). Truth Values and Proof Theory. Studia Logica 92 (2):241 - 264.score: 24.0
    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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  10. Nissim Francez & Roy Dyckhoff (2010). Proof-Theoretic Semantics for a Natural Language Fragment. Linguistics and Philosophy 33 (6):447-477.score: 24.0
    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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  11. A. S. Troelstra (2000). Basic Proof Theory. Cambridge University Press.score: 24.0
    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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  12. Nils Kürbis (forthcoming). Proof-Theoretic Semantics, a Problem with Negation and Prospects for Modality. Journal of Philosophical Logic:1-15.score: 24.0
    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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  13. Florian Steinberger (2013). On the Equivalence Conjecture for Proof-Theoretic Harmony. Notre Dame Journal of Formal Logic 54 (1):79-86.score: 24.0
    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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  14. Jörgen Sjögren (2010). A Note on the Relation Between Formal and Informal Proof. Acta Analytica 25 (4):447-458.score: 24.0
    Using Carnap’s concept explication, we propose a theory of concept formation in mathematics. This theory is then applied to the problem of how to understand the relation between the concepts formal proof (deduction) and informal, mathematical proof.
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  15. H. Wansing (ed.) (1996). Proof Theory of Modal Logic. Kluwer.score: 24.0
    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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  16. Jeffrey Bub (2010). Von Neumann's 'No Hidden Variables' Proof: A Re-Appraisal. [REVIEW] Foundations of Physics 40 (9-10):1333-1340.score: 24.0
    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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  17. Michèle Friend (2010). Confronting Ideals of Proof with the Ways of Proving of the Research Mathematician. Studia Logica 96 (2):273-288.score: 24.0
    In this paper, we discuss the prevailing view amongst philosophers and many mathematicians concerning mathematical proof. Following Cellucci, we call the prevailing view the “axiomatic conception” of proof. The conception includes the ideas that: a proof is finite, it proceeds from axioms and it is the final word on the matter of the conclusion. This received view can be traced back to Frege, Hilbert and Gentzen, amongst others, and is prevalent in both mathematical text books and logic (...)
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  18. Luca Tranchini (2012). Truth From a Proof-Theoretic Perspective. Topoi 31 (1):47-57.score: 24.0
    Validity, the central concept of the so-called ‘proof-theoretic semantics’ is described as correctly applying to the arguments that denote proofs. In terms of validity, I propose an anti-realist characterization of the notions of truth and correct assertion, at the core of which is the idea that valid arguments may fail to be recognized as such. The proposed account is compared with Dummett’s and Prawitz’s views on the matter.
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  19. Donald C. Benson (1999). The Moment of Proof: Mathematical Epiphanies. Oxford University Press.score: 24.0
    When Archimedes, while bathing, suddenly hit upon the principle of buoyancy, he ran wildly through the streets of Syracuse, stark naked, crying "eureka!" In The Moment of Proof, Donald Benson attempts to convey to general readers the feeling of eureka--the joy of discovery--that mathematicians feel when they first encounter an elegant proof. This is not an introduction to mathematics so much as an introduction to the pleasures of mathematical thinking. And indeed the delights of this book are many (...)
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  20. Peter Schroeder-Heister (2012). Proof-Theoretic Semantics, Self-Contradiction, and the Format of Deductive Reasoning. Topoi 31 (1):77-85.score: 24.0
    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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  21. James Franklin (1996). Proof in Mathematics. Quakers Hill Press.score: 24.0
    A textbook on proof in mathematics, inspired by an Aristotelian point of view on mathematics and proof. It explains how to prove statements in mathematics, from evident premises. It deals with the proof of "all" statements, "some" statements, multiple quantifiers and mathematical induction.
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  22. Enrico Moriconi (2012). Steps Towards a Proof-Theoretical Semantics. Topoi 31 (1):67-75.score: 24.0
    The aim of this paper is to reconsider several proposals that have been put forward in order to develop a Proof-Theoretical Semantics, from the by now classical neo-verificationist approach provided by D. Prawitz and M. Dummett in the Seventies, to an alternative, more recent approach mainly due to the work of P. Schroeder-Heister and L. Hallnäs, based on clausal definitions. Some other intermediate proposals are very briefly sketched. Particular attention will be given to the role played by the so-called (...)
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  23. Ryo Takemura (2013). Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization. Studia Logica 101 (1):157-191.score: 24.0
    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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  24. Marc Aiguier & Delphine Longuet (2010). Some General Results About Proof Normalization. Logica Universalis 4 (1):1-29.score: 24.0
    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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  25. Julien Boyer & Gabriel Sandu (2012). Between Proof and Truth. Synthese 187 (3):821-832.score: 24.0
    We consider two versions of truth as grounded in verification procedures: Dummett's notion of proof as an effective way to establish the truth of a statement and Hintikka's GTS notion of truth as given by the existence of a winning strategy for the game associated with a statement. Hintikka has argued that the two notions should be effective and that one should thus restrict one's attention to recursive winning strategies. In the context of arithmetic, we show that the two (...)
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  26. Samuel R. Buss (ed.) (1998). Handbook of Proof Theory. Elsevier.score: 24.0
    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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  27. Petr Cintula & Carles Noguera (2013). The Proof by Cases Property and its Variants in Structural Consequence Relations. Studia Logica 101 (4):713-747.score: 24.0
    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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  28. Justin Khoo (2013). A Note on Gibbard's Proof. Philosophical Studies 166 (1):153-164.score: 24.0
    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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  29. David J. Pym (2004). Reductive Logic and Proof-Search: Proof Theory, Semantics, and Control. Oxford University Press.score: 24.0
    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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  30. Henk van den Belt & Bart Gremmen (2002). Between Precautionary Principle and “Sound Science”: Distributing the Burdens of Proof. [REVIEW] Journal of Agricultural and Environmental Ethics 15 (1):103-122.score: 24.0
    Opponents of biotechnology ofteninvoke the Precautionary Principle to advancetheir cause, whereas biotech enthusiasts preferto appeal to ``sound science.'' Publicauthorities are still groping for a usefuldefinition. A crucial issue in this debate isthe distribution of the burden of proof amongthe parties favoring and opposing certaintechnological developments. Indeed, the debateon the significance and scope of thePrecautionary Principle can be fruitfullyre-framed as a debate on the proper division ofburdens of proof. In this article, we attemptto arrive at a more refined way (...)
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  31. Peter Aczel, Harold Simmons & S. S. Wainer (eds.) (1992). Proof Theory: A Selection of Papers From the Leeds Proof Theory Programme, 1990. Cambridge University Press.score: 24.0
    This work is derived from the SERC "Logic for IT" Summer School Conference on Proof Theory held at Leeds University. The contributions come from acknowledged experts and comprise expository and research articles which form an invaluable introduction to proof theory aimed at both mathematicians and computer scientists.
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  32. Paolo Maffezioli & Alberto Naibo (forthcoming). Proof Theory of Epistemic Logic of Programs. Logic and Logical Philosophy.score: 24.0
    A combination of epistemic logic and dynamic logic of programs is presented. Although rich enough to formalize some simple game-theoretic scenarios, its axiomatization is problematic as it leads to the paradoxical conclusion that agents are omniscient. A cut-free labelled Gentzen-style proof system is then introduced where knowledge and action, as well as their combinations, are formulated as rules of inference, rather than axioms. This provides a logical framework for reasoning about games in a modular and systematic way, and to (...)
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  33. Juha Räikkä (1997). Burden of Proof Rules in Social Criticism. Argumentation 11 (4):463-477.score: 24.0
    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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  34. Nissim Francez (2013). Bilateralism in Proof-Theoretic Semantics. Journal of Philosophical Logic (2-3):1-21.score: 24.0
    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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  35. Sara Negri (2011). Proof Analysis: A Contribution to Hilbert's Last Problem. Cambridge University Press.score: 24.0
    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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  36. V. Michele Abrusci & Elena Maringelli (1998). A New Correctness Criterion for Cyclic Proof Nets. Journal of Logic, Language and Information 7 (4):449-459.score: 24.0
    We define proof nets for cyclic multiplicative linear logic as edge bi-coloured graphs. Our characterization is purely graph theoretical and works without further complication for proof nets with cuts, which are usually harder to handle in the non-commutative case. This also provides a new characterization of the proof nets for the Lambek calculus (with the empty sequence) which simply are a restriction on the formulas to be considered (which are asked to be intuitionistic).
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  37. Irving H. Anellis (2012). Jean van Heijenoort's Contributions to Proof Theory and Its History. Logica Universalis 6 (3-4):411-458.score: 24.0
    Jean van Heijenoort was best known for his editorial work in the history of mathematical logic. I survey his contributions to model-theoretic proof theory, and in particular to the falsifiability tree method. This work of van Heijenoort’s is not widely known, and much of it remains unpublished. A complete list of van Heijenoort’s unpublished writings on tableaux methods and related work in proof theory is appended.
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  38. Despina A. Stylianou, Maria L. Blanton & Eric J. Knuth (eds.) (2009). Teaching and Learning Proof Across the Grades: A K-16 Perspective. Routledge.score: 24.0
    Collectively these essays inform educators and researchers at different grade levels about the teaching and learning of proof at each level and, thus, help ...
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  39. C. F. M. Vermeulen (2000). Text Structure and Proof Structure. Journal of Logic, Language and Information 9 (3):273-311.score: 24.0
    This paper is concerned with the structure of texts in which aproof is presented. Some parts of such a text are assumptions, otherparts are conclusions. We show how the structural organisation of thetext into assumptions and conclusions helps to check the validity of theproof. Then we go on to use the structural information for theformulation of proof rules, i.e., rules for the (re-)construction ofproof texts. The running example is intuitionistic propositional logicwith connectives , and. We give new proofs of (...)
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  40. Wendy MacCaull (1998). Relational Semantics and a Relational Proof System for Full Lambek Calculus. Journal of Symbolic Logic 63 (2):623-637.score: 24.0
    In this paper we give relational semantics and an accompanying relational proof theory for full Lambek calculus (a sequent calculus which we denote by FL). We start with the Kripke semantics for FL as discussed in [11] and develop a second Kripke-style semantics, RelKripke semantics, as a bridge to relational semantics. The RelKripke semantics consists of a set with two distinguished elements, two ternary relations and a list of conditions on the relations. It is accompanied by a Kripke-style valuation (...)
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  41. N. Raja (2005). A Negation-Free Proof of Cantor's Theorem. Notre Dame Journal of Formal Logic 46 (2):231-233.score: 24.0
    We construct a novel proof of Cantor's theorem in set theory.
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  42. Peter Schroeder-Heister (forthcoming). The Calculus of Higher-Level Rules, Propositional Quantification, and the Foundational Approach to Proof-Theoretic Harmony. Studia Logica:1-32.score: 24.0
    We present our calculus of higher-level rules, extended with propositional quantification within rules. This makes it possible to present general schemas for introduction and elimination rules for arbitrary propositional operators and to define what it means that introductions and eliminations are in harmony with each other. This definition does not presuppose any logical system, but is formulated in terms of rules themselves. We therefore speak of a foundational (rather than reductive) account of proof-theoretic harmony. With every set of introduction (...)
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  43. M. W. Bunder & R. M. Rizkalla (2009). Proof-Finding Algorithms for Classical and Subclassical Propositional Logics. Notre Dame Journal of Formal Logic 50 (3):261-273.score: 24.0
    The formulas-as-types isomorphism tells us that every proof and theorem, in the intuitionistic implicational logic $H_\rightarrow$, corresponds to a lambda term or combinator and its type. The algorithms of Bunder very efficiently find a lambda term inhabitant, if any, of any given type of $H_\rightarrow$ and of many of its subsystems. In most cases the search procedure has a simple bound based roughly on the length of the formula involved. Computer implementations of some of these procedures were done in (...)
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  44. Yuping Shen & Xishun Zhao (2013). Proof Systems for Planning Under Cautious Semantics. Minds and Machines 23 (1):5-45.score: 24.0
    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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  45. Floris Bex & Bart Verheij (2013). Legal Stories and the Process of Proof. Artificial Intelligence and Law 21 (3):253-278.score: 24.0
    In this paper, we continue our research on a hybrid narrative-argumentative approach to evidential reasoning in the law by showing the interaction between factual reasoning (providing a proof for ‘what happened’ in a case) and legal reasoning (making a decision based on the proof). First we extend the hybrid theory by making the connection with reasoning towards legal consequences. We then emphasise the role of legal stories (as opposed to the factual stories of the hybrid theory). Legal stories (...)
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  46. Philipp Gerhardy (2008). Proof Mining in Topological Dynamics. Notre Dame Journal of Formal Logic 49 (4):431-446.score: 24.0
    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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  47. Dale Jacquette (2008). Mathematical Proof and Discovery Reductio Ad Absurdum. Informal Logic 28 (3):242-261.score: 24.0
    The uses and interpretation of reductio ad absurdum argumentation in mathematical proof and discovery are examined, illustrated with elementary and progressively sophisticated examples, and explained. Against Arthur Schopenhauer’s objections, reductio reasoning is defended as a method of uncovering new mathematical truths, and not merely of confirming independently grasped mathematical intuitions. The application of reductio argument is contrasted with purely mechanical brute algorithmic inferences as an art requiring skill and intelligent intervention in the choice of hypotheses and attribution of contradictions (...)
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  48. H. Kushida & M. Okada (2007). A Proof–Theoretic Study of the Correspondence of Hybrid Logic and Classical Logic. Journal of Logic, Language and Information 16 (1):35-61.score: 24.0
    In this paper, we show the equivalence between the provability of a proof system of basic hybrid logic and that of translated formulas of the classical predicate logic with equality and explicit substitution by a purely proof–theoretic method. Then we show the equivalence of two groups of proof systems of hybrid logic: the group of labelled deduction systems and the group of modal logic-based systems.
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  49. Anthony Peressini (2003). Proof, Reliability, and Mathematical Knowledge. Theoria 69 (3):211-232.score: 24.0
    With respect to the confirmation of mathematical propositions, proof possesses an epistemological authority unmatched by other means of confirmation. This paper is an investigation into why this is the case. I make use of an analysis drawn from an early reliability perspective on knowledge to help make sense of mathematical proofs singular epistemological status.
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  50. Thomas Piecha, Wagner de Campos Sanz & Peter Schroeder-Heister (forthcoming). Failure of Completeness in Proof-Theoretic Semantics. Journal of Philosophical Logic:1-15.score: 24.0
    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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