Results for 'Proof-theoretic harmony'

998 found
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  1. Proof-Theoretic Semantics, a Problem with Negation and Prospects for Modality.Nils Kürbis - 2015 - 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 (...)
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  2. A Note on Harmony.Nissim Francez & Roy Dyckhoff - 2012 - Journal of Philosophical Logic 41 (3):613-628.
    In the proof-theoretic semantics approach to meaning, harmony , requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony , requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony : imposes the existence of certain transformations of derivations, known (...)
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  3. Against Harmony.Ian Rumfitt - forthcoming - In Bob Hale, Crispin Wright & Alexander Miller (eds.), The Blackwell Companion to the Philosophy of Language. Blackwell.
    Many prominent writers on the philosophy of logic, including Michael Dummett, Dag Prawitz, Neil Tennant, have held that the introduction and elimination rules of a logical connective must be ‘in harmony ’ if the connective is to possess a sense. This Harmony Thesis has been used to justify the choice of logic: in particular, supposed violations of it by the classical rules for negation have been the basis for arguments for switching from classical to intuitionistic logic. The Thesis (...)
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  4. Stable Harmony.Nils Kurbis - 2008 - In Peliš Michal (ed.), Logica Yearbook 2007.
    In this paper, I'll present a general way of "reading off" introduction/elimination rules from elimination/introduction rules, and define notions of harmony and stability on the basis of it.
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  5. Proof-Theoretic Semantics for Subsentential Phrases.Nissim Francez, Roy Dyckhoff & Gilad Ben-Avi - 2010 - Studia Logica 94 (3):381-401.
    The paper briefly surveys the sentential proof-theoretic semantics for fragment of English. Then, appealing to a version of Frege’s context-principle (specified to fit type-logical grammar), a method is presented for deriving proof-theoretic meanings for sub-sentential phrases, down to lexical units (words). The sentential meaning is decomposed according to the function-argument structure as determined by the type-logical grammar. In doing so, the paper presents a novel proof-theoretic interpretation of simple type, replacing Montague’s model-theoretic type (...)
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  6. A Proof-Theoretical View of Collective Rationality.Daniele Porello - 2013 - In Proceedings of the 23rd International Joint Conference of Artificial Intelligence (IJCAI 2013).
    The impossibility results in judgement aggregation show a clash between fair aggregation procedures and rational collective outcomes. In this paper, we are interested in analysing the notion of rational outcome by proposing a proof-theoretical understanding of collective rationality. In particular, we use the analysis of proofs and inferences provided by linear logic in order to define a fine-grained notion of group reasoning that allows for studying collective rationality with respect to a number of logics. We analyse the well-known paradoxes (...)
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  7.  32
    Proof-Theoretic Semantics and Inquisitive Logic.Will Stafford - 2021 - Journal of Philosophical Logic 50 (5):1199-1229.
    Prawitz conjectured that proof-theoretic validity offers a semantics for intuitionistic logic. This conjecture has recently been proven false by Piecha and Schroeder-Heister. This article resolves one of the questions left open by this recent result by showing the extensional alignment of proof-theoretic validity and general inquisitive logic. General inquisitive logic is a generalisation of inquisitive semantics, a uniform semantics for questions and assertions. The paper further defines a notion of quasi-proof-theoretic validity by restricting (...)-theoretic validity to allow double negation elimination for atomic formulas and proves the extensional alignment of quasi-proof-theoretic validity and inquisitive logic. (shrink)
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  8. On Proof-Theoretic Approaches to the Paradoxes: Problems of Undergeneration and Overgeneration in the Prawitz-Tennant Analysis.Seungrak Choi - 2019 - Dissertation, Korea University
    In this dissertation, we shall investigate whether Tennant's criterion for paradoxicality(TCP) can be a correct criterion for genuine paradoxes and whether the requirement of a normal derivation(RND) can be a proof-theoretic solution to the paradoxes. Tennant’s criterion has two types of counterexamples. The one is a case which raises the problem of overgeneration that TCP makes a paradoxical derivation non-paradoxical. The other is one which generates the problem of undergeneration that TCP renders a non-paradoxical derivation paradoxical. Chapter 2 (...)
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  9.  92
    On the Notion of Validity for the Bilateral Classical Logic.Ukyo Suzuki & Yoriyuki Yamagata - manuscript
    This paper considers Rumfitt’s bilateral classical logic (BCL), which is proposed to counter Dummett’s challenge to classical logic. First, agreeing with several authors, we argue that Rumfitt’s notion of harmony, used to justify logical rules by a purely proof theoretical manner, is not sufficient to justify coordination rules in BCL purely proof-theoretically. For the central part of this paper, we propose a notion of proof-theoretical validity similar to Prawitz for BCL and proves that BCL is sound (...)
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  10. Revisiting Dummett's Proof-Theoretic Justification Procedures.Hermógenes Oliveira - 2017 - In Pavel Arazim & Tomáš Lávička (eds.), The Logica Yearbook 2016. London: College Publications. pp. 141-155.
    Dummett’s justification procedures are revisited. They are used as background for the discussion of some conceptual and technical issues in proof-theoretic semantics, especially the role played by assumptions in proof-theoretic definitions of validity.
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  11.  80
    Sketch of a Proof-Theoretic Semantics for Necessity.Nils Kürbis - 2020 - In Nicola Olivetti, Rineke Verbrugge & Sara Negri (eds.), Advances in Modal Logic 13. Booklet of Short Papers. Helsinki: pp. 37-43.
    This paper considers proof-theoretic semantics for necessity within Dummett's and Prawitz's framework. Inspired by a system of Pfenning's and Davies's, the language of intuitionist logic is extended by a higher order operator which captures a notion of validity. A notion of relative necessary is defined in terms of it, which expresses a necessary connection between the assumptions and the conclusion of a deduction.
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  12. Metainferences From a Proof-Theoretic Perspective, and a Hierarchy of Validity Predicates.Rea Golan - forthcoming - Journal of Philosophical Logic 1:1-31.
    I explore, from a proof-theoretic perspective, the hierarchy of classical and paraconsistent logics introduced by Barrio, Pailos and Szmuc in. First, I provide sequent rules and axioms for all the logics in the hierarchy, for all inferential levels, and establish soundness and completeness results. Second, I show how to extend those systems with a corresponding hierarchy of validity predicates, each one of which is meant to capture “validity” at a different inferential level. Then, I point out two potential (...)
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  13. Some Comments on Ian Rumfitt’s Bilateralism.Nils Kürbis - 2016 - Journal of Philosophical Logic 45 (6):623-644.
    Ian Rumfitt has proposed systems of bilateral logic for primitive speech acts of assertion and denial, with the purpose of ‘exploring the possibility of specifying the classically intended senses for the connectives in terms of their deductive use’ : 810f). Rumfitt formalises two systems of bilateral logic and gives two arguments for their classical nature. I assess both arguments and conclude that only one system satisfies the meaning-theoretical requirements Rumfitt imposes in his arguments. I then formalise an intuitionist system of (...)
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  14. Strategy-Proof Judgment Aggregation.Franz Dietrich & Christian List - 2005 - Economics and Philosophy 23 (3):269-300.
    Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than (...)
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  15.  85
    Takeuti's Proof Theory in the Context of the Kyoto School.Andrew Arana - 2019 - Jahrbuch Für Philosophie Das Tetsugaku-Ronso 46:1-17.
    Gaisi Takeuti (1926–2017) is one of the most distinguished logicians in proof theory after Hilbert and Gentzen. He extensively extended Hilbert's program in the sense that he formulated Gentzen's sequent calculus, conjectured that cut-elimination holds for it (Takeuti's conjecture), and obtained several stunning results in the 1950–60s towards the solution of his conjecture. Though he has been known chiefly as a great mathematician, he wrote many papers in English and Japanese where he expressed his philosophical thoughts. In particular, he (...)
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  16. Some Concerns Regarding Ternary-Relation Semantics and Truth-Theoretic Semantics in General.Ross T. Brady - 2017 - IfCoLog Journal of Logics and Their Applications 4 (3):755--781.
    This paper deals with a collection of concerns that, over a period of time, led the author away from the Routley–Meyer semantics, and towards proof- theoretic approaches to relevant logics, and indeed to the weak relevant logic MC of meaning containment.
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  17. Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic.Matthias Baaz & Richard Zach - 2000 - In Peter G. Clote & Helmut Schwichtenberg (eds.), Computer Science Logic. 14th International Workshop, CSL 2000. Berlin: Springer. pp. 187– 201.
    Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Gödel logics by Avron. It is shown that the system is sound and (...)
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  18. On the Alleged Simplicity of Impure Proof.Andrew Arana - 2017 - In Roman Kossak & Philip Ording (eds.), Simplicity: Ideals of Practice in Mathematics and the Arts. pp. 207-226.
    Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical (...)
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  19. L'etica moderna. Dalla Riforma a Nietzsche.Sergio Cremaschi - 2007 - Roma RM, Italia: Carocci.
    This book tells the story of modern ethics, namely the story of a discourse that, after the Renaissance, went through a methodological revolution giving birth to Grotius’s and Pufendorf’s new science of natural law, leaving room for two centuries of explorations of the possible developments and implications of this new paradigm, up to the crisis of the Eighties of the eighteenth century, a crisis that carried a kind of mitosis, the act of birth of both basic paradigms of the two (...)
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  20. Il relativismo etico fra antropologia culturale e filosofia analitica.Sergio Volodia Marcello Cremaschi - 2007 - In I. Tolomio (ed.), Rileggere l'etica tra contingenza e principi. Padova, Italy: CLUEP. pp. 15-46.
    I intend to: a) clarify the origins and de facto meanings of the term relativism; b) reconstruct the reasons for the birth of the thesis named “cultural relativism”; d) reconstruct ethical implications of the above thesis; c) revisit the recent discussion between universalists and particularists in the light of the idea of cultural relativism.. -/- 1.Prescriptive Moral Relativism: “everybody is justified in acting in the way imposed by criteria accepted by the group he belongs to”. Universalism: there are at least (...)
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  21. Existential Inertia and the Aristotelian Proof.Joseph C. Schmid - 2021 - International Journal for Philosophy of Religion 89 (3):201-220.
    Edward Feser defends the ‘Aristotelian proof’ for the existence of God, which reasons that the only adequate explanation of the existence of change is in terms of an unchangeable, purely actual being. His argument, however, relies on the falsity of the Existential Inertia Thesis, according to which concrete objects tend to persist in existence without requiring an existential sustaining cause. In this article, I first characterize the dialectical context of Feser’s Aristotelian proof, paying special attention to EIT and (...)
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  22. A Simple Proof of Born’s Rule for Statistical Interpretation of Quantum Mechanics.Biswaranjan Dikshit - 2017 - Journal for Foundations and Applications of Physics 4 (1):24-30.
    The Born’s rule to interpret the square of wave function as the probability to get a specific value in measurement has been accepted as a postulate in foundations of quantum mechanics. Although there have been so many attempts at deriving this rule theoretically using different approaches such as frequency operator approach, many-world theory, Bayesian probability and envariance, literature shows that arguments in each of these methods are circular. In view of absence of a convincing theoretical proof, recently some researchers (...)
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  23. Beyond the Paralogisms: The Proofs of Immortality in the Lectures on Metaphysics.Corey W. Dyck - 2015 - In Robert Clewis (ed.), Reading Kant's Lectures. De Gruyter. pp. 115-134.
    Considered in light of the reader’s expectation of a thoroughgoing criticism of the pretensions of the rational psychologist, and of the wealth of discussions available in the broader 18th century context, which includes a variety of proofs that do not explicitly turn on the identification of the soul as a simple substance, Kant’s discussion of immortality in the Paralogisms falls lamentably short. However, outside of the Paralogisms (and the published works generally), Kant had much more to say about the arguments (...)
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  24.  44
    Bilateral Harmony.Nils Kürbis - manuscript
    This paper formulates a bilateral account of harmony, which is an alternative to the one proposed by Francez. It builds on an account of harmony for unilateral logic proposed by Kürbis and the observation that reading some of the rules for the connectives of bilateral logic bottom up gives the grounds and consequences of formulas with the opposite speech act. Thus the consequences of asserting a formula give grounds for denying it, namely if the opposite speech act is (...)
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  25. Questions About Proof Theory Vis-À-Vis Natural Language Semantics (2007).Anna Szabolcsi - manuscript
    Semantics plays a role in grammar in at least three guises. (A) Linguists seek to account for speakers‘ knowledge of what linguistic expressions mean. This goal is typically achieved by assigning a model theoretic interpretation2 in a compositional fashion. For example, No whale flies is true if and only if the intersection of the sets of whales and fliers is empty in the model. (B) Linguists seek to account for the ability of speakers to make various inferences based on (...)
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  26. Scientific Proof of the Natural Moral Law.Eric Brown - manuscript
    Introduction to the Scientific Proof of the Natural Moral Law This paper proves that Aquinas has a means of demonstrating and deriving both moral goodness and the natural moral law from human nature alone. Aquinas scientifically proves the existence of the natural moral law as the natural rule of human operations from human nature alone. The distinction between moral goodness and transcendental goodness is affirmed. This provides the intellectual tools to refute the G.E. Moore (Principles of Ethics) attack against (...)
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  27.  58
    On Graph-Theoretic Fibring of Logics.A. Sernadas, C. Sernadas, J. Rasga & M. Coniglio - 2009 - Journal of Logic and Computation 19 (6):1321-1357.
    A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as a multi-graph (m-graph) where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is a multi-graph (m-graph) where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of two deductive systems (...)
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  28.  83
    Takeuti's well-ordering proofs revisited.Andrew Arana & Ryota Akiyoshi - 2021 - Mita Philosophy Society 3 (146):83-110.
    Gaisi Takeuti extended Gentzen's work to higher-order case in 1950's–1960's and proved the consistency of impredicative subsystems of analysis. He has been chiefly known as a successor of Hilbert's school, but we pointed out in the previous paper that Takeuti's aimed to investigate the relationships between "minds" by carrying out his proof-theoretic project rather than proving the "reliability" of such impredicative subsystems of analysis. Moreover, as briefly explained there, his philosophical ideas can be traced back to Nishida's philosophy (...)
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  29. Simulation Models of the Evolution of Cooperation as Proofs of Logical Possibilities. How Useful Are They?Eckhart Arnold - 2013 - Etica E Politica 15 (2):101-138.
    This paper discusses critically what simulation models of the evolution ofcooperation can possibly prove by examining Axelrod’s “Evolution of Cooperation” and the modeling tradition it has inspired. Hardly any of the many simulation models of the evolution of cooperation in this tradition have been applicable empirically. Axelrod’s role model suggested a research design that seemingly allowed to draw general conclusions from simulation models even if the mechanisms that drive the simulation could not be identified empirically. But this research design was (...)
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  30.  31
    An Elementary, Pre-Formal, Proof of FLT: Why is X^N+y^N=Z^N Solvable Only for N≪3?Bhupinder Singh Anand - manuscript
    Andrew Wiles' analytic proof of Fermat's Last Theorem FLT, which appeals to geometrical properties of real and complex numbers, leaves two questions unanswered: (i) What technique might Fermat have used that led him to, even if only briefly, believe he had `a truly marvellous demonstration' of FLT? (ii) Why is x^n+y^n=z^n solvable only for n<3? In this inter-disciplinary perspective, we offer insight into, and answers to, both queries; yielding a pre-formal proof of why FLT can be treated as (...)
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  31.  20
    Études in Light and Harmony: An Interdisciplinary Workbook for Creative Discovery and Dialogue.Timothy M. Rogers - manuscript
    This workbook of "études" offers a collection of experimental texts for communal dialogue and discovery that crosses multiple academic disciplines, including: foundations of physics, metaphysics, theoretical biology, semiotics, cognitive science, linguistics, phenomenology, logic & mathematics, poetry and theology. Each étude probes limits, horizons and boundaries by implicitly bring into relation foundational issues that characterize different academic disciplines or systems of meaning formation. Some formal techniques are deployed the études. Most notable is the use of the “logic of three” to overcome (...)
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  32.  68
    Symmetry in Physics: Proportion and Harmony to the Term of Metalanguage.Ruth Castillo - 2018 - Dissertation, Universidad Central de Venezuela
    SYMMETRY IN PHYSICS: FROM PROPORTION AND HARMONY TO THE TERM OF METALENGUAJE -/- Ruth Castillo Universidad Central de Venezuela -/- The revolutionary changes in physics require a careful exploration of the way in which concepts depend on the theoretical structure in which they are immerse. A historical reconstruction allows us to show how the notion of symmetry evolves from the definition as proportion and harmony to its consideration within the language of contemporary physics, as a linguistic meta-theoretical requirement (...)
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  33. Epistemic Multilateral Logic.Luca Incurvati & Julian J. Schlöder - forthcoming - Review of Symbolic Logic:1-44.
    We present epistemic multilateral logic, a general logical framework for reasoning involving epistemic modality. Standard bilateral systems use propositional formulae marked with signs for assertion and rejection. Epistemic multilateral logic extends standard bilateral systems with a sign for the speech act of weak assertion (Incurvati and Schlöder 2019) and an operator for epistemic modality. We prove that epistemic multilateral logic is sound and complete with respect to the modal logic S5 modulo an appropriate translation. The logical framework developed provides the (...)
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  34.  37
    'Gramsci and Ancient Philosophy: Prelude to a Study' (Please Contact Me for Proofs).Phillip Sidney Horky - 2021 - In Emilio Zucchetti & Anna Maria Cimino (eds.), Antonio Gramsci and the Classics. London, UK: pp. 86-100.
    This chapter investigates the precise ways in which Antonio Gramsci engaged with ancient philosophy. A brief examination of the longest discussion in the Prison Notebooks of any ancient philosopher or text, Plato’s Republic (Q8, §22), raises many questions about Gramsci’s approach to ancient philosophy. These questions motivate an investigation into Gramsci’s surprisingly minimal discussion of ancient philosophy and philosophers, which is best explained in the light of his theoretical commitments to his distinctive species of historical materialism. Rather than responding to (...)
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  35. The Power of Naive Truth.Hartry Field - manuscript
    While non-classical theories of truth that take truth to be transparent have some obvious advantages over any classical theory that evidently must take it as non-transparent, several authors have recently argued that there's also a big disadvantage of non-classical theories as compared to their “external” classical counterparts: proof-theoretic strength. While conceding the relevance of this, the paper argues that there is a natural way to beef up extant internal theories so as to remove their proof-theoretic disadvantage. (...)
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  36. The Epistemic Significance of Valid Inference – A Model-Theoretic Approach.Constantin C. Brîncuș - 2015 - In Sorin Costreie & Mircea Dumitru (eds.), Meaning and Truth. Bucharest: PRO Universitaria Publishing. pp. 11-36.
    The problem analysed in this paper is whether we can gain knowledge by using valid inferences, and how we can explain this process from a model-theoretic perspective. According to the paradox of inference (Cohen & Nagel 1936/1998, 173), it is logically impossible for an inference to be both valid and its conclusion to possess novelty with respect to the premises. I argue in this paper that valid inference has an epistemic significance, i.e., it can be used by an agent (...)
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  37. On the Explanatory Power of Truth in Logic.Gila Sher - 2018 - Philosophical Issues 28 (1):348-373.
    Philosophers are divided on whether the proof- or truth-theoretic approach to logic is more fruitful. The paper demonstrates the considerable explanatory power of a truth-based approach to logic by showing that and how it can provide (i) an explanatory characterization —both semantic and proof-theoretical—of logical inference, (ii) an explanatory criterion for logical constants and operators, (iii) an explanatory account of logic’s role (function) in knowledge, as well as explanations of (iv) the characteristic features of logic —formality, strong (...)
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  38. On the Logical Origins of Quantum Mechanics Demonstrated By Using Clifford Algebra: A Proof That Quantum Interference Arises in a Clifford Algebraic Formulation of Quantum Mechanics.Elio Conte - 2011 - Electronic Journal of Theoretical Physics 8 (25):109-126.
    We review a rough scheme of quantum mechanics using the Clifford algebra. Following the steps previously published in a paper by another author [31], we demonstrate that quantum interference arises in a Clifford algebraic formulation of quantum mechanics. In 1932 J. von Neumann showed that projection operators and, in particular, quantum density matrices can be interpreted as logical statements. In accord with a previously obtained result by V. F Orlov , in this paper we invert von Neumann’s result. Instead of (...)
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  39. On Dummett’s Verificationist Justification Procedure.Wagner de Campos Sanz & Hermógenes Oliveira - 2016 - Synthese 193 (8):2539-2559.
    We examine the proof-theoretic verificationist justification procedure proposed by Dummett. After some scrutiny, two distinct interpretations with respect to bases are advanced: the independent and the dependent interpretation. We argue that both are unacceptable as a semantics for propositional intuitionistic logic.
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  40. How Fundamental is the Fundamental Assumption?Nils Kurbis - 2012 - Teorema: International Journal of Philosophy 2 (2):5-19.
    The fundamental assumption of Dummett’s and Prawitz’ proof-theoretic justification of deduction is that ‘if we have a valid argument for a complex statement, we can construct a valid argument for it which finishes with an application of one of the introduction rules governing its principal operator’. I argue that the assumption is flawed in this general version, but should be restricted, not to apply to arguments in general, but only to proofs. I also argue that Dummett’s and Prawitz’ (...)
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  41.  30
    On the Correspondence Between Nested Calculi and Semantic Systems for Intuitionistic Logics.Tim Lyon - 2021 - Journal of Logic and Computation 31 (1):213-265.
    This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated labelled calculi, (...)
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  42. What is Wrong with Classical Negation?Nils Kürbis - 2015 - Grazer Philosophische Studien 92 (1):51-86.
    The focus of this paper are Dummett's meaning-theoretical arguments against classical logic based on consideration about the meaning of negation. Using Dummettian principles, I shall outline three such arguments, of increasing strength, and show that they are unsuccessful by giving responses to each argument on behalf of the classical logician. What is crucial is that in responding to these arguments a classicist need not challenge any of the basic assumptions of Dummett's outlook on the theory of meaning. In particular, I (...)
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  43.  73
    On Deriving Nested Calculi for Intuitionistic Logics From Semantic Systems.Tim Lyon - 2020 - In Sergei Artemov & Anil Nerode (eds.), Logical Foundations of Computer Science. Cham: pp. 177-194.
    This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from (...)
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  44. Topics in Philosophical Logic.Jon Erling Litland - 2012 - Dissertation, Harvard
    In “Proof-Theoretic Justification of Logic”, building on work by Dummett and Prawitz, I show how to construct use-based meaning-theories for the logical constants. The assertability-conditional meaning-theory takes the meaning of the logical constants to be given by their introduction rules; the consequence-conditional meaning-theory takes the meaning of the logical constants to be given by their elimination rules. I then consider the question: given a set of introduction rules \, what are the strongest elimination rules that are validated by (...)
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  45. Pluralism and the Logical Basis of Metaphysics.N. Kurbis - 2007 - In Logica Yearbook.
    I argue for a kind of logical pluralism on the basis of a difficulty with defining the meaning of negation in the framework of Dummett's and Prawitz' proof-theoretic semantics.
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  46. Axiomatic Theories of Partial Ground I: The Base Theory.Johannes Korbmacher - 2018 - Journal of Philosophical Logic 47 (2):161-191.
    This is part one of a two-part paper, in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. This allows us to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we develop an axiomatization of the relation of partial ground over the truths of arithmetic and show that (...)
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  47. The Enduring Scandal of Deduction: Is Propositional Logic Really Uninformative?Marcello D'Agostino & Luciano Floridi - 2009 - 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 (...)
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  48. Curry’s Paradox and Ω -Inconsistency.Andrew Bacon - 2013 - Studia Logica 101 (1):1-9.
    In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which (...)
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  49. Aristotle's Syllogistic and Core Logic.Neil Tennant - 2014 - History and Philosophy of Logic 35 (2):120-147.
    I use the Corcoran–Smiley interpretation of Aristotle's syllogistic as my starting point for an examination of the syllogistic from the vantage point of modern proof theory. I aim to show that fresh logical insights are afforded by a proof-theoretically more systematic account of all four figures. First I regiment the syllogisms in the Gentzen–Prawitz system of natural deduction, using the universal and existential quantifiers of standard first-order logic, and the usual formalizations of Aristotle's sentence-forms. I explain how the (...)
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  50.  2
    Refining Labelled Systems for Modal and Constructive Logics with Applications.Tim Lyon - 2021 - Dissertation, Technischen Universität Wien
    This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated (...)
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