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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 the meanings of (...)
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  • General-Elimination Harmony and the Meaning of the Logical Constants.Stephen Read - 2010 - Journal of Philosophical Logic 39 (5):557-576.
    Inferentialism claims that expressions are meaningful by virtue of rules governing their use. In particular, logical expressions are autonomous if given meaning by their introduction-rules, rules specifying the grounds for assertion of propositions containing them. If the elimination-rules do no more, and no less, than is justified by the introduction-rules, the rules satisfy what Prawitz, following Lorenzen, called an inversion principle. This connection between rules leads to a general form of elimination-rule, and when the rules have this form, they may (...)
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  • Hopeful Monsters: A Note on Multiple Conclusions.Bogdan Dicher - 2020 - Erkenntnis 85 (1):77-98.
    Arguments, the story goes, have one or more premises and only one conclusion. A contentious generalisation allows arguments with several disjunctively connected conclusions. Contentious as this generalisation may be, I will argue nevertheless that it is justified. My main claim is that multiple conclusions are epiphenomena of the logical connectives: some connectives determine, in a certain sense, multiple-conclusion derivations. Therefore, such derivations are completely natural and can safely be used in proof-theoretic semantics.
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  • The Calculus of Higher-Level Rules, Propositional Quantification, and the Foundational Approach to Proof-Theoretic Harmony.Peter Schroeder-Heister - 2014 - Studia Logica 102 (6):1185-1216.
    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 account of proof-theoretic harmony. With every set of introduction rules a canonical elimination (...)
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  • A Logic Inspired by Natural Language: Quantifiers As Subnectors.Nissim Francez - 2014 - Journal of Philosophical Logic 43 (6):1153-1172.
    Inspired by the grammar of natural language, the paper presents a variant of first-order logic, in which quantifiers are not sentential operators, but are used as subnectors . A quantified term formed by a subnector is an argument of a predicate. The logic is defined by means of a meaning-conferring natural-deduction proof-system, according to the proof-theoretic semantics program. The harmony of the I/E-rules is shown. The paper then presents a translation, called the Frege translation, from the defined logic to standard (...)
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  • Bilateralism in Proof-Theoretic Semantics.Nissim Francez - 2013 - Journal of Philosophical Logic (2-3):1-21.
    The paper suggests a revision of the notion of harmony, a major necessary condition in proof-theoretic semantics for a natural-deduction proof-system to qualify as meaning conferring, when moving to a bilateral proof-system. The latter considers both forces of assertion and denial as primitive, and is applied here to positive logics, lacking negation altogether. It is suggested that in addition to the balance between (positive) introduction and elimination rules traditionally imposed by harmony, a balance should be imposed also on: (i) negative (...)
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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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  • 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 deals with (...)
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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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  • More Reflections on Consequence.Julien Murzi & Massimiliano Carrara - 2014 - Logique Et Analyse 57 (227):223-258.
    This special issue collects together nine new essays on logical consequence :the relation obtaining between the premises and the conclusion of a logically valid argument. The present paper is a partial, and opinionated,introduction to the contemporary debate on the topic. We focus on two influential accounts of consequence, the model-theoretic and the proof-theoretic, and on the seeming platitude that valid arguments necessarilypreserve truth. We briefly discuss the main objections these accounts face, as well as Hartry Field’s contention that such objections (...)
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  • Sentence Connectives in Formal Logic.Lloyd Humberstone - forthcoming - Stanford Encyclopedia of Philosophy.
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  • Bilateralism in Proof-Theoretic Semantics.Nissim Francez - 2014 - Journal of Philosophical Logic 43 (2-3):239-259.
    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 introduction and elimination rules traditionally imposed by harmony, a balance should be imposed also on: negative introduction and (...)
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  • Proof-Theoretic Semantics for a Natural Language Fragment.Nissim Francez & Roy Dyckhoff - 2010 - Linguistics and Philosophy 33 (6):447-477.
    The paper presents a proof-theoretic semantics (PTS) for a fragment of natural language, providing an alternative to the traditional model-theoretic (Montagovian) semantics (MTS), whereby meanings are truth-condition (in arbitrary models). Instead, meanings are taken as derivability-conditions in a dedicated natural-deduction (ND) proof-system. This semantics is effective (algorithmically decidable), adhering to the meaning as use paradigm, not suffering from several of the criticisms formulated by philosophers of language against MTS as a theory of meaning. In particular, Dummett’s manifestation argument does not (...)
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  • Harmonic Inferentialism and the Logic of Identity.Stephen Read - 2016 - Review of Symbolic Logic 9 (2):408-420.
    Inferentialism claims that the rules for the use of an expression express its meaning without any need to invoke meanings or denotations for them. Logical inferentialism endorses inferentialism specically for the logical constants. Harmonic inferentialism, as the term is introduced here, usually but not necessarily a subbranch of logical inferentialism, follows Gentzen in proposing that it is the introduction-rules whch give expressions their meaning and the elimination-rules should accord harmoniously with the meaning so given. It is proposed here that the (...)
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  • Harmonising Harmony.Luca Tranchini - 2015 - Review of Symbolic Logic 8 (3):411-423.
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  • On the Notion of Canonical Derivations From Open Assumptions and its Role in Proof-Theoretic Semantics.Nissim Francez - 2015 - Review of Symbolic Logic 8 (2):296-305.
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  • Bilateral Relevant Logic.Nissim Francez - 2014 - Review of Symbolic Logic 7 (2):250-272.
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  • On Flattening Elimination Rules.Grigory K. Olkhovikov & Peter Schroeder-Heister - 2014 - Review of Symbolic Logic 7 (1):60-72.
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  • Weak Disharmony: Some Lessons for Proof-Theoretic Semantics.Bogdan Dicher - 2016 - Review of Symbolic Logic (3):1-20.
    A logical constant is weakly disharmonious if its elimination rules are weaker than its introduction rules. Substructural weak disharmony is the weak disharmony generated by structural restrictions on the eliminations. I argue that substructural weak disharmony is not a defect of the constants which exhibit it. To the extent that it is problematic, it calls into question the structural properties of the derivability relation. This prompts us to rethink the issue of controlling the structural properties of a logic by means (...)
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  • Subatomic Natural Deduction for a Naturalistic First-Order Language with Non-Primitive Identity.Bartosz Więckowski - 2016 - Journal of Logic, Language and Information 25 (2):215-268.
    A first-order language with a defined identity predicate is proposed whose apparatus for atomic predication is sensitive to grammatical categories of natural language. Subatomic natural deduction systems are defined for this naturalistic first-order language. These systems contain subatomic systems which govern the inferential relations which obtain between naturalistic atomic sentences and between their possibly composite components. As a main result it is shown that normal derivations in the defined systems enjoy the subexpression property which subsumes the subformula property with respect (...)
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  • Are Uniqueness and Deducibility of Identicals the Same?Alberto Naibo & Mattia Petrolo - 2015 - Theoria 81 (2):143-181.
    A comparison is given between two conditions used to define logical constants: Belnap's uniqueness and Hacking's deducibility of identicals. It is shown that, in spite of some surface similarities, there is a deep difference between them. On the one hand, deducibility of identicals turns out to be a weaker and less demanding condition than uniqueness. On the other hand, deducibility of identicals is shown to be more faithful to the inferentialist perspective, permitting definition of genuinely proof-theoretical concepts. This kind of (...)
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  • On Harmony and Permuting Conversions.Nissim Francez - 2017 - Journal of Applied Logic 21:14-23.
    The paper exposes the relevance of permuting conversions (in natural-deduction systems) to the role of such systems in the theory of meaning known as proof-theoretic semantics, by relating permuting conversion to harmony, hitherto related to normalisation only. This is achieved by showing the connection of permuting conversion to the general notion of canonicity, once applied to arbitrary derivations from open assumption. In the course of exposing the relationship of permuting conversions to harmony, a general definition of the former is proposed, (...)
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  • On a Generality Condition in Proof‐Theoretic Semantics.Bogdan Dicher - 2017 - Theoria 83 (4):394-418.
    In the recent literature on proof-theoretic semantics, there is mention of a generality condition on defining rules. According to this condition, the schematic formulation of the defining rules must be maximally general, in the sense that no restrictions should be placed on the contexts of these rules. In particular, context variables must always be present in the schematic rules and they should range over arbitrary collections of formulae. I argue against imposing such a condition, by showing that it has undesirable (...)
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  • General-Elimination Stability.Bruno Miguel Jacinto & Stephen Louis Read - 2017 - Studia Logica 105 (2):361-405.
    General-elimination harmony articulates Gentzen’s idea that the elimination-rules are justified if they infer from an assertion no more than can already be inferred from the grounds for making it. Dummett described the rules as not only harmonious but stable if the E-rules allow one to infer no more and no less than the I-rules justify. Pfenning and Davies call the rules locally complete if the E-rules are strong enough to allow one to infer the original judgement. A method is given (...)
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  • Harmony in Multiple-Conclusion Natural-Deduction.Nissim Francez - 2014 - Logica Universalis 8 (2):215-259.
    The paper studies the extension of harmony and stability, major themes in proof-theoretic semantics, from single-conclusion natural-deduction systems to multiple -conclusions natural-deduction, independently of classical logic. An extension of the method of obtaining harmoniously-induced general elimination rules from given introduction rules is suggested, taking into account sub-structurality. Finally, the reductions and expansions of the multiple -conclusions natural-deduction representation of classical logic are formulated.
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