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  1. Natural deduction for intuitionistic linear logic.A. S. Troelstra - 1995 - Annals of Pure and Applied Logic 73 (1):79-108.
    The paper deals with two versions of the fragment with unit, tensor, linear implication and storage operator of intuitionistic linear logic. The first version, ILL, appears in a paper by Benton, Bierman, Hyland and de Paiva; the second one, ILL+, is described in this paper. ILL has a contraction rule and an introduction rule !I for the exponential; in ILL+, instead of a contraction rule, multiple occurrences of labels for assumptions are permitted under certain conditions; moreover, there is a different (...)
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  • Relevance Logic.Michael Dunn & Greg Restall - 1983 - In Dov M. Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic. Dordrecht, Netherland: Kluwer Academic Publishers.
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  • (1 other version)The runabout inference ticket.Arthur Prior - 1967 - In Peter Frederick Strawson (ed.), Philosophical logic. London,: Oxford University Press. pp. 38-9.
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  • (1 other version)On an Intuitionistic Modal Logic.G. M. Bierman & V. C. V. De Paiva - 2000 - Studia Logica 65 (3):383 - 416.
    In this paper we consider an intuitionistic variant of the modal logic S4 (which we call IS4). The novelty of this paper is that we place particular importance on the natural deduction formulation of IS4 -- our formulation has several important metatheoretic properties. In addition, we study models of IS4 -- not in the framework of Kripke semantics, but in the more general framework of category theory. This allows not only a more abstract definition of a whole class of models (...)
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  • (2 other versions)Truth and Other Enigmas.Michael Dummett - 1978 - British Journal for the Philosophy of Science 32 (4):419-425.
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  • Logical constants as punctuation marks.Kosta Došen - 1989 - Notre Dame Journal of Formal Logic 30 (3):362-381.
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  • Basic logic: Reflection, symmetry, visibility.Giovanni Sambin, Giulia Battilotti & Claudia Faggian - 2000 - Journal of Symbolic Logic 65 (3):979-1013.
    We introduce a sequent calculus B for a new logic, named basic logic. The aim of basic logic is to find a structure in the space of logics. Classical, intuitionistic, quantum and non-modal linear logics, are all obtained as extensions in a uniform way and in a single framework. We isolate three properties, which characterize B positively: reflection, symmetry and visibility. A logical constant obeys to the principle of reflection if it is characterized semantically by an equation binding it with (...)
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  • Advances in Proof-Theoretic Semantics.Peter Schroeder-Heister & Thomas Piecha (eds.) - 2015 - Cham, Switzerland: Springer Verlag.
    This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory. The field of proof-theoretic semantics has existed for almost 50 years, but the term (...)
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  • (1 other version)The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38-39.
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  • (2 other versions)Truth and Other Enigmas.Michael Dummett - 1978 - Philosophical Quarterly 31 (122):47-67.
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  • Some Remarks on Proof-Theoretic Semantics.Roy Dyckhoff - 2015 - In Peter Schroeder-Heister & Thomas Piecha (eds.), Advances in Proof-Theoretic Semantics. Cham, Switzerland: Springer Verlag.
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  • A normalizing system of natural deduction for intuitionistic linear logic.Sara Negri - 2002 - Archive for Mathematical Logic 41 (8):789-810.
    The main result of this paper is a normalizing system of natural deduction for the full language of intuitionistic linear logic. No explicit weakening or contraction rules for -formulas are needed. By the systematic use of general elimination rules a correspondence between normal derivations and cut-free derivations in sequent calculus is obtained. Normalization and the subformula property for normal derivations follow through translation to sequent calculus and cut-elimination.
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  • A natural extension of natural deduction.Peter Schroeder-Heister - 1984 - Journal of Symbolic Logic 49 (4):1284-1300.
    The framework of natural deduction is extended by permitting rules as assumptions which may be discharged in the course of a derivation. this leads to the concept of rules of higher levels and to a general schema for introduction and elimination rules for arbitrary n-ary sentential operators. with respect to this schema, (functional) completeness "or", "if..then" and absurdity is proved.
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  • (1 other version)On an intuitionistic modal logic.G. M. Bierman & V. C. V. de Paiva - 2000 - Studia Logica 65 (3):383-416.
    In this paper we consider an intuitionistic variant of the modal logic S4 (which we call IS4). The novelty of this paper is that we place particular importance on the natural deduction formulation of IS4— our formulation has several important metatheoretic properties. In addition, we study models of IS4— not in the framework of Kirpke semantics, but in the more general framework of category theory. This allows not only a more abstract definition of a whole class of models but also (...)
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  • The Semantics and Proof Theory of Linear Logic.Arnon Avron - 1988 - Theoretical Computer Science 57 (2):161-184.
    Linear logic is a new logic which was recently developed by Girard in order to provide a logical basis for the study of parallelism. It is described and investigated in Gi]. Girard's presentation of his logic is not so standard. In this paper we shall provide more standard proof systems and semantics. We shall also extend part of Girard's results by investigating the consequence relations associated with Linear Logic and by proving corresponding str ong completeness theorems. Finally, we shall investigate (...)
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  • Natural Deduction Bottom Up.Ernst Zimmermann - 2021 - Journal of Logic, Language and Information 30 (3):601-631.
    The paper introduces a new type of rules into Natural Deduction, elimination rules by composition. Elimination rules by composition replace usual elimination rules in the style of disjunction elimination and give a more direct treatment of additive disjunction, multiplicative conjunction, existence quantifier and possibility modality. Elimination rules by composition have an enormous impact on proof-structures of deductions: they do not produce segments, deduction trees remain binary branching, there is no vacuous discharge, there is only few need of permutations. This new (...)
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  • Substructural Logics in Natural Deduction.Ernst Zimmermann - 2007 - Logic Journal of the IGPL 15 (3):211-232.
    Extensions of Natural Deduction to Substructural Logics of Intuitionistic Logic are shown: Fragments of Intuitionistic Linear, Relevant and BCK Logic. Rules for implication, conjunction, disjunction and falsum are defined, where conjunction and disjunction respect contexts of assumptions. So, conjunction and disjunction are additive in the terminology of linear logic. Explicit contraction and weakening rules are given. It is shown that conversions and permutations can be adapted to all these rules, and that weak normalisation and subformula property holds. The results generalise (...)
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