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Journal of Symbolic Logic 56 (3):1094-1096 (1991)

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  1. General Proof Theory: Introduction.Thomas Piecha & Peter Schroeder-Heister - 2019 - Studia Logica 107 (1):1-5.
    This special issue on general proof theory collects papers resulting from the conference on general proof theory held in November 2015 in Tübingen.
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  • Conjunction and Contradiction.Achille C. Varzi - 2004 - In Graham Priest, J. C. Beall & Bradley Armour-Garb (eds.), The Law of Non-Contradiction: New Philosophical Essays. Clarendon Press. pp. 93–110.
    There are two ways of understanding the notion of a contradiction: as a conjunction of a statement and its negation, or as a pair of statements one of which is the negation of the other. Correspondingly, there are two ways of understanding the Law of Non-Contradiction (LNC), i.e., the law that says that no contradictions can be true. In this paper I offer some arguments to the effect that on the first (collective) reading LNC is non-negotiable, but on the second (...)
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  • Natural Deduction for First-Order Hybrid Logic.Torben BraÜner - 2005 - Journal of Logic, Language and Information 14 (2):173-198.
    This is a companion paper to Braüner where a natural deduction system for propositional hybrid logic is given. In the present paper we generalize the system to the first-order case. Our natural deduction system for first-order hybrid logic can be extended with additional inference rules corresponding to conditions on the accessibility relations and the quantifier domains expressed by so-called geometric theories. We prove soundness and completeness and we prove a normalisation theorem. Moreover, we give an axiom system first-order hybrid logic.
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  • A Generalized Syllogistic Inference System Based on Inclusion and Exclusion Relations.Koji Mineshima, Mitsuhiro Okada & Ryo Takemura - 2012 - Studia Logica 100 (4):753-785.
    We introduce a simple inference system based on two primitive relations between terms, namely, inclusion and exclusion relations. We present a normalization theorem, and then provide a characterization of the structure of normal proofs. Based on this, inferences in a syllogistic fragment of natural language are reconstructed within our system. We also show that our system can be embedded into a fragment of propositional minimal logic.
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  • Implicit Epistemic Aspects of Constructive Logic.Göran Sundholm - 1997 - Journal of Logic, Language and Information 6 (2):191-212.
    In the present paper I wish to regard constructivelogic as a self-contained system for the treatment ofepistemological issues; the explanations of theconstructivist logical notions are cast in anepistemological mold already from the outset. Thediscussion offered here intends to make explicit thisimplicit epistemic character of constructivism.Particular attention will be given to the intendedinterpretation laid down by Heyting. This interpretation, especially as refined in the type-theoretical work of Per Martin-Löf, puts thesystem on par with the early efforts of Frege andWhitehead-Russell. This quite (...)
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  • Knowledge of Proofs.Peter Pagin - 1994 - Topoi 13 (2):93-100.
    If proofs are nothing more than truth makers, then there is no force in the standard argument against classical logic (there is no guarantee that there is either a proof forA or a proof fornot A). The standard intuitionistic conception of a mathematical proof is stronger: there are epistemic constraints on proofs. But the idea that proofs must be recognizable as such by us, with our actual capacities, is incompatible with the standard intuitionistic explanations of the meanings of the logical (...)
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  • Definite Descriptions in Intuitionist Positive Free Logic.Nils Kürbis - 2020 - Logic and Logical Philosophy 30:1.
    This paper presents rules of inference for a binary quantifier I for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. I binds one variable and forms a formula from two formulas. Ix[F, G] means ‘The F is G’. The system is shown to have desirable proof-theoretic properties: it is proved that deductions in it can be brought into normal form. The discussion is rounded up by comparisons between the approach to the formalisation of definite descriptions recommended (...)
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  • 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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  • 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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  • Bilateralism: Negations, Implications and Some Observations and Problems About Hypotheses.Nils Kürbis - 2017 - In Thomas Piecha & Jean Fichot (eds.), Beyond Logic. Proceedings of the Conference held in Cerisy-la-Salle, 22-27 May 2017. Tübingen, Germany:
    This short paper has two loosely connected parts. In the first part, I discuss the difference between classical and intuitionist logic in relation to different the role of hypotheses play in each logic. Harmony is normally understood as a relation between two ways of manipulating formulas in systems of natural deduction: their introduction and elimination. I argue, however, that there is at least a third way of manipulating formulas, namely the discharge of assumption, and that the difference between classical and (...)
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  • 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 applied to (...)
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  • Normalisation for Bilateral Classical Logic with Some Philosophical Remarks.Nils Kürbis - 2021 - Journal of Applied Logics 2 (8):531-556.
    Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk, for which, unlike for tonk, there are reduction steps for the removal of maximal formulas arising from introducing and eliminating formulas with those connectives as main operators. Adding either of them to bilateral classical logic results in an incoherent system. One way around this problem is (...)
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  • Normalisation and Subformula Property for a System of Classical Logic with Tarski’s Rule.Nils Kürbis - forthcoming - Archive for Mathematical Logic:1-25.
    This paper considers a formalisation of classical logic using general introduction rules and general elimination rules. It proposes a definition of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system, and gives reduction procedures for them. It is then shown that deductions in the system convert into normal form, i.e. deductions that contain neither maximal formulas nor maximal segments, and that deductions in normal form satisfy the subformula property. Tarski’s Rule is treated as a general introduction rule for implication. (...)
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  • Why Intuitionistic Relevant Logic Cannot Be a Core Logic.Joseph Vidal-Rosset - 2017 - Notre Dame Journal of Formal Logic 58 (2):241-248.
    At the end of the 1980s, Tennant invented a logical system that he called “intuitionistic relevant logic”. Now he calls this same system “Core logic.” In Section 1, by reference to the rules of natural deduction for $\mathbf{IR}$, I explain why $\mathbf{IR}$ is a relevant logic in a subtle way. Sections 2, 3, and 4 give three reasons to assert that $\mathbf{IR}$ cannot be a core logic.
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  • Truth-Value Semantics and Functional Extensions for Classical Logic of Partial Terms Based on Equality.F. Parlamento - 2014 - Notre Dame Journal of Formal Logic 55 (3):383-395.
    We develop a bottom-up approach to truth-value semantics for classical logic of partial terms based on equality and apply it to prove the conservativity of the addition of partial description and selection functions, independently of any strictness assumption.
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  • Truth Table Logic, with a Survey of Embeddability Results.Neil Tennant - 1989 - Notre Dame Journal of Formal Logic 30 (3):459-484.
    Kalrnaric. We set out a system T, consisting of normal proofs constructed by means of elegantly symmetrical introduction and elimination rules. In the system T there are two requirements, called ( ) and ()), on applications of discharge rules. T is sound and complete for Kalmaric arguments. ( ) requires nonvacuous discharge of assumptions; ()) requires that the assumption discharged be the sole one available of highest degree. We then consider a 'Duhemian' extension T*, obtained simply by dropping the requirement (...)
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  • Sheffer’s Stroke: A Study in Proof-Theoretic Harmony.Stephen Read - 1999 - Danish Yearbook of Philosophy 34 (1):7-23.
    In order to explicate Gentzen’s famous remark that the introduction-rules for logical constants give their meaning, the elimination-rules being simply consequences of the meaning so given, we develop natural deduction rules for Sheffer’s stroke, alternative denial. The first system turns out to lack Double Negation. Strengthening the introduction-rules by allowing the introduction of Sheffer’s stroke into a disjunctive context produces a complete system of classical logic, one which preserves the harmony between the rules which Gentzen wanted: all indirect proof reduces (...)
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  • Intuitionistic N-Graphs.M. Quispe-Cruz, A. G. de Oliveira, R. J. G. B. de Queiroz & V. de Paiva - 2014 - Logic Journal of the IGPL 22 (2):274-285.
    The geometric system of deduction called N-Graphs was introduced by de Oliveira in 2001. The proofs in this system are represented by means of digraphs and, while its derivations are mostly based on Gentzen's sequent calculus, the system gets its inspiration from geometrically based systems, such as the Kneales' tables of development, Statman's proofs-as-graphs, Buss' logical flow graphs, and Girard's proof-nets. Given that all these geometric systems appeal to the classical symmetry between premises and conclusions, providing an intuitionistic version of (...)
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  • The Stories of Logic and Information.Johan van Benthem, Maricarmen Martinez, David Israel & John Perry - unknown
    Information is a notion of wide use and great intuitive appeal, and hence, not surprisingly, different formal paradigms claim part of it, from Shannon channel theory to Kolmogorov complexity. Information is also a widely used term in logic, but a similar diversity repeats itself: there are several competing logical accounts of this notion, ranging from semantic to syntactic. In this chapter, we will discuss three major logical accounts of information.
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  • Logical Consequence for Nominalists.Marcus Rossberg & Daniel Cohnitz - 2009 - Theoria : An International Journal for Theory, History and Fundations of Science 24 (2):147-168.
    It is often claimed that nominalistic programmes to reconstruct mathematics fail, since they will at some point involve the notion of logical consequence which is unavailable to the nominalist. In this paper we use an idea of Goodman and Quine to develop a nominalistically acceptable explication of logical consequence.
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  • Speaking with Shadows: A Study of Neo‐Logicism.Fraser MacBride - 2003 - British Journal for the Philosophy of Science 54 (1):103-163.
    According to the species of neo-logicism advanced by Hale and Wright, mathematical knowledge is essentially logical knowledge. Their view is found to be best understood as a set of related though independent theses: (1) neo-fregeanism-a general conception of the relation between language and reality; (2) the method of abstraction-a particular method for introducing concepts into language; (3) the scope of logic-second-order logic is logic. The criticisms of Boolos, Dummett, Field and Quine (amongst others) of these theses are explicated and assessed. (...)
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  • Quine's Argument From Despair.Sander Verhaegh - 2014 - British Journal for the History of Philosophy 22 (1):150-173.
    Quine's argument for a naturalized epistemology is routinely perceived as an argument from despair: traditional epistemology must be abandoned because all attempts to deduce our scientific theories from sense experience have failed. In this paper, I will show that this picture is historically inaccurate and that Quine's argument against first philosophy is considerably stronger and subtler than the standard conception suggests. For Quine, the first philosopher's quest for foundations is inherently incoherent; the very idea of a self-sufficient sense datum language (...)
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  • Proof Theory and Meaning.B. G. Sundholm - unknown
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  • A Century of Inference: 1837-1936.B. G. Sundholm - unknown
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  • Proof-Theoretical Semantics and Fregean Identity Criteria for Propositions.B. G. Sundholm - 1994 - The Monist 77 (3):294-314.
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  • Semantics and the Justification of Deductive Inference.Ebba Gullberg & Sten Lindström - 2007 - Hommage À Wlodek: Philosophical Papers Dedicated to Wlodek Rabinowicz.
    Is it possible to give a justification of our own practice of deductive inference? The purpose of this paper is to explain what such a justification might consist in and what its purpose could be. On the conception that we are going to pursue, to give a justification for a deductive practice means to explain in terms of an intuitively satisfactory notion of validity why the inferences that conform to the practice coincide with the valid ones. That is, a justification (...)
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  • 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 modal force, generality, (...)
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  • Simple Decision Procedure for S5 in Standard Cut-Free Sequent Calculus.Andrzej Indrzejczak - 2016 - Bulletin of the Section of Logic 45 (2).
    In the paper a decision procedure for S5 is presented which uses a cut-free sequent calculus with additional rules allowing a reduction to normal modal forms. It utilizes the fact that in S5 every formula is equivalent to some 1-degree formula, i.e. a modally-flat formula with modal functors having only boolean formulas in its scope. In contrast to many sequent calculi for S5 the presented system does not introduce any extra devices. Thus it is a standard version of SC but (...)
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  • A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation.Nils Kürbis - 2019 - Bulletin of the Section of Logic 48 (2):81-97.
    This paper presents a way of formalising definite descriptions with a binary quantifier ι, where ιx[F, G] is read as ‘The F is G’. Introduction and elimination rules for ι in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ιx[F, G] are given, and it is shown that deductions in the system can be brought into normal form.
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  • 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 the meanings of (...)
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  • Proof-Theoretic Reconstruction of Generalized Quantifiers.Nissim Francez & Gilad Ben-Avi - 2015 - Journal of Semantics 32 (3):313-371.
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  • Pragmatic and Dialogic Interpretations of Bi-Intuitionism. Part I.Gianluigi Bellin, Massimiliano Carrara, Daniele Chiffi & Alessandro Menti - 2014 - Logic and Logical Philosophy.
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  • A Type-Theoretical Approach for Ontologies: The Case of Roles.Patrick Barlatier & Richard Dapoigny - 2012 - Applied Ontology 7 (3):311-356.
    In the domain of ontology design as well as in Knowledge Representation, modeling universals is a challenging problem.Most approaches that have addressed this problem rely on Description Logics (DLs) but many difficulties remain, due to under-constrained representation which reduces the inferences that can be drawn and further causes problems in expressiveness. In mathematical logic and program checking, type theories have proved to be appealing but, so far they have not been applied in the formalization of ontologies. To bridge this gap, (...)
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  • Weak Assertion.Luca Incurvati & Julian J. Schlöder - 2019 - Philosophical Quarterly 69 (277):741-770.
    We present an inferentialist account of the epistemic modal operator might. Our starting point is the bilateralist programme. A bilateralist explains the operator not in terms of the speech act of rejection ; we explain the operator might in terms of weak assertion, a speech act whose existence we argue for on the basis of linguistic evidence. We show that our account of might provides a solution to certain well-known puzzles about the semantics of modal vocabulary whilst retaining classical logic. (...)
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  • 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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  • Validity Concepts in Proof-Theoretic Semantics.Peter Schroeder-Heister - 2006 - Synthese 148 (3):525-571.
    The standard approach to what I call “proof-theoretic semantics”, which is mainly due to Dummett and Prawitz, attempts to give a semantics of proofs by defining what counts as a valid proof. After a discussion of the general aims of proof-theoretic semantics, this paper investigates in detail various notions of proof-theoretic validity and offers certain improvements of the definitions given by Prawitz. Particular emphasis is placed on the relationship between semantic validity concepts and validity concepts used in normalization theory. It (...)
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  • Intuitionistic epistemic logic.Sergei Artemov & Tudor Protopopescu - 2016 - Review of Symbolic Logic 9 (2):266-298.
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  • Wilfried Sieg. Hilbert's Programs and Beyond. Oxford: Oxford University Press, 2013. ISBN 978-0-19-537222-9 ; 978-0-19-970715-7 . Pp. Xii + 439†. [REVIEW]Oran Magal - 2014 - Philosophia Mathematica 22 (3):417-423.
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  • Classical Logic Without Bivalence.Tor Sandqvist - 2009 - Analysis 69 (2):211-218.
    Semantic justifications of the classical rules of logical inference typically make use of a notion of bivalent truth, understood as a property guaranteed to attach to a sentence or its negation regardless of the prospects for speakers to determine it as so doing. For want of a convincing alternative account of classical logic, some philosophers suspicious of such recognition-transcending bivalence have seen no choice but to declare classical deduction unwarranted and settle for a weaker system; intuitionistic logic in particular, buttressed (...)
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  • Replacing Modus Ponens With One-Premiss Rules.Lloyd Humberstone - 2008 - Logic Journal of the IGPL 16 (5):431-451.
    After some motivating remarks in Section 1, in Section 2 we show how to replace an axiomatic basis for any one of a broad range of sentential logics having finitely many axiom schemes and Modus Ponens as the sole proper rule, by a basis with the same axiom schemes and finitely many one-premiss rules. Section 3 mentions some questions arising from this replacement procedure , explores another such procedure, and discusses some aspects of the consequence relations associated with the different (...)
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  • Existence and Identity in Free Logic: A Problem for Inferentialism?Neil Tennant - 2007 - Mind 116 (464):1055-1078.
    Peter Milne (2007) poses two challenges to the inferential theorist of meaning. This study responds to both. First, it argues that the method of natural deduction idealizes the essential details of correct informal deductive reasoning. Secondly, it explains how rules of inference in free logic can determine unique senses for the existential quantifier and the identity predicate. The final part of the investigation brings out an underlying order in a basic family of free logics.
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  • A Brief History of Natural Deduction.Francis Jeffry Pelletier - 1999 - History and Philosophy of Logic 20 (1):1-31.
    Natural deduction is the type of logic most familiar to current philosophers, and indeed is all that many modern philosophers know about logic. Yet natural deduction is a fairly recent innovation in logic, dating from Gentzen and Ja?kowski in 1934. This article traces the development of natural deduction from the view that these founders embraced to the widespread acceptance of the method in the 1960s. I focus especially on the different choices made by writers of elementary textbooks?the standard conduits of (...)
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  • Label-Free Modular Systems for Classical and Intuitionistic Modal Logics.Sonia Marin & Lutz Straßburger - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10. CSLI Publications. pp. 387-406.
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  • Hegel's Dialectics as a Semantic Theory: An Analytic Reading.Francesco Berto - 2007 - European Journal of Philosophy 15 (1):19–39.
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  • Inference and Compulsion.Cesare Cozzo - 2014 - In E. Moriconi (ed.), Second Pisa Colloquium in Logic,Language and Epistemology. ETS. pp. 162-180.
    What is an inference? Logicians and philosophers have proposed various conceptions of inference. I shall first highlight seven features that contribute to distinguish these conceptions. I shall then compare three conceptions to see which of them best explains the special force that compels us to accept the conclusion of an inference, if we accept its premises.
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  • What is Inferentialism?Jaroslav Peregrin - unknown
    Inferentialism is the conviction that to be meaningful in the distinctively human way, or to have a 'conceptual content', is to be governed by a certain kind of inferential rules. The term was coined by Robert Brandom as a label for his theory of language; however, it is also naturally applicable (and is growing increasingly common) within the philosophy of logic.
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  • Categorical Harmony and Path Induction.Patrick Walsh - 2017 - Review of Symbolic Logic 10 (2):301-321.
    This paper responds to recent work in the philosophy of Homotopy Type Theory by James Ladyman and Stuart Presnell. They consider one of the rules for identity, path induction, and justify it along ‘pre-mathematical’ lines. I give an alternate justification based on the philosophical framework of inferentialism. Accordingly, I construct a notion of harmony that allows the inferentialist to say when a connective or concept is meaning-bearing and this conception unifies most of the prominent conceptions of harmony through category theory. (...)
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  • Tonking a Theory of Content: An Inferentialist Rejoinder.Jon Cogburn - 2004 - Logic and Logical Philosophy 13:31-55.
    If correct, Christopher Peacocke’s [20] “manifestationism without verificationism,” would explode the dichotomy between realism and inferentialism in the contemporary philosophy of language. I first explicate Peacocke’s theory, defending it from a criticism of Neil Tennant’s. This involves devising a recursive definition for grasp of logical contents along the lines Peacocke suggests. Unfortunately though, the generalized account reveals the Achilles’ heel of the whole theory. By inventing a new logical operator with the introduction rule for the existential quantifier and the elimination (...)
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  • Nelson's paraconsistent logics.Seiki Akama - 1999 - Logic and Logical Philosophy 7:101.
    David Nelson’s constructive logics with strong negation may beviewed as alternative paraconsistent logic. These logics have been developedbefore da Costa’s works. We address some philosophical aspects of Nelson’slogics and give technical results concerning Kripke models and tableau calculi. We also suggest possible applications of paraconsistent constructivelogics.
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  • A Meta-Logic of Inference Rules: Syntax.Alex Citkin - 2015 - Logic and Logical Philosophy 24 (3).
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