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  1. Notions of Proof and Refutation in ‘Gentzensemantik’: Franz von Kutschera as an Early Proponent of (Bilateralist) Proof-Theoretic Semantics.Sara Ayhan - forthcoming - History and Philosophy of Logic:1-7.
    This is a comment on a translation of Franz von Kutschera's paper ‘Ein verallgemeinerter Widerlegungsbegriff für Gentzenkalküle’, which was published in German in 1969. The paper is an important predecessor of what is nowadays called ‘proof-theoretic semantics’, which describes the view that the meaning of logical connectives is determined by the rules governing their use in a proof system. Von Kutschera adopts this view in this paper, and more specifically, a bilateralist view on this subject in that his aim is (...)
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  • Intuitionistic logic versus paraconsistent logic. Categorical approach.Mariusz Kajetan Stopa - 2023 - Dissertation, Jagiellonian University
    The main research goal of the work is to study the notion of co-topos, its correctness, properties and relations with toposes. In particular, the dualization process proposed by proponents of co-toposes has been analyzed, which transforms certain Heyting algebras of toposes into co-Heyting ones, by which a kind of paraconsistent logic may appear in place of intuitionistic logic. It has been shown that if certain two definitions of topos are to be equivalent, then in one of them, in the context (...)
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  • Refutation-Aware Gentzen-Style Calculi for Propositional Until-Free Linear-Time Temporal Logic.Norihiro Kamide - 2023 - Studia Logica 111 (6):979-1014.
    This study introduces refutation-aware Gentzen-style sequent calculi and Kripke-style semantics for propositional until-free linear-time temporal logic. The sequent calculi and semantics are constructed on the basis of the refutation-aware setting for Nelson’s paraconsistent logic. The cut-elimination and completeness theorems for the proposed sequent calculi and semantics are proven.
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  • Rules of Explosion and Excluded Middle: Constructing a Unified Single-Succedent Gentzen-Style Framework for Classical, Paradefinite, Paraconsistent, and Paracomplete Logics.Norihiro Kamide - 2024 - Journal of Logic, Language and Information 33 (2):143-178.
    A unified and modular falsification-aware single-succedent Gentzen-style framework is introduced for classical, paradefinite, paraconsistent, and paracomplete logics. This framework is composed of two special inference rules, referred to as the rules of explosion and excluded middle, which correspond to the principle of explosion and the law of excluded middle, respectively. Similar to the cut rule in Gentzen’s LK for classical logic, these rules are admissible in cut-free LK. A falsification-aware single-succedent Gentzen-style sequent calculus fsCL for classical logic is formalized based (...)
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  • A modal translation for dual-intuitionistic logic.Yaroslav Shramko - 2016 - Review of Symbolic Logic 9 (2):251-265.
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  • A cut-free sequent calculus for bi-intuitionistic logic.Rajeev Gore - manuscript
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  • Dual Intuitionistic Logic and a Variety of Negations: The Logic of Scientific Research.Yaroslav Shramko - 2005 - Studia Logica 80 (2-3):347-367.
    We consider a logic which is semantically dual (in some precise sense of the term) to intuitionistic. This logic can be labeled as “falsification logic”: it embodies the Popperian methodology of scientific discovery. Whereas intuitionistic logic deals with constructive truth and non-constructive falsity, and Nelson's logic takes both truth and falsity as constructive notions, in the falsification logic truth is essentially non-constructive as opposed to falsity that is conceived constructively. We also briefly clarify the relationships of our falsification logic to (...)
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  • Falsification-Aware Semantics and Sequent Calculi for Classical Logic.Norihiro Kamide - 2021 - Journal of Philosophical Logic 51 (1):99-126.
    In this study, falsification-aware semantics and sequent calculi for first-order classical logic are introduced and investigated. These semantics and sequent calculi are constructed based on a falsification-aware setting for first-order Nelson constructive three-valued logic. In fact, these semantics and sequent calculi are regarded as those for a classical variant of N3. The completeness and cut-elimination theorems for the proposed semantics and sequent calculi are proved using Schütte’s method. Similar results for the propositional case are also obtained.
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  • On the validity of the definition of a complement-classifier.Mariusz Stopa - 2020 - Philosophical Problems in Science 69:111-128.
    It is well-established that topos theory is inherently connected with intuitionistic logic. In recent times several works appeared concerning so-called complement-toposes, which are allegedly connected to the dual to intuitionistic logic. In this paper I present this new notion, some of the motivations for it, and some of its consequences. Then, I argue that, assuming equivalence of certain two definitions of a topos, the concept of a complement-classifier is, at least in general and within the conceptual framework of category theory, (...)
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  • On the unity of duality.Noam Zeilberger - 2008 - Annals of Pure and Applied Logic 153 (1-3):66-96.
    Most type systems are agnostic regarding the evaluation strategy for the underlying languages, with the value restriction for ML which is absent in Haskell as a notable exception. As type systems become more precise, however, detailed properties of the operational semantics may become visible because properties captured by the types may be sound under one strategy but not the other. For example, intersection types distinguish between call-by-name and call-by-value functions, because the subtyping law ∩≤A→ is unsound for the latter in (...)
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  • (1 other version)Natural Deduction for Dual-intuitionistic Logic.Luca Tranchini - 2012 - Studia Logica 100 (3):631-648.
    We present a natural deduction system for dual-intuitionistic logic. Its distinctive feature is that it is a single-premise multiple-conclusions system. Its relationships with the natural deduction systems for intuitionistic and classical logic are discussed.
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  • Complement-Topoi and Dual Intuitionistic Logic.Luis Estrada-González - 2010 - Australasian Journal of Logic 9:26-44.
    Mortensen studies dual intuitionistic logic by dualizing topos internal logic, but he did not study a sequent calculus. In this paper I present a sequent calculus for complement-topos logic, which throws some light on the problem of giving a dualization for LJ.
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  • LK, LJ, Dual Intuitionistic Logic, and Quantum Logic.Hiroshi Aoyama - 2004 - Notre Dame Journal of Formal Logic 45 (4):193-213.
    In this paper, we study the relationship among classical logic, intuitionistic logic, and quantum logic . These logics are related in an interesting way and are not far apart from each other, as is widely believed. The results in this paper show how they are related with each other through a dual intuitionistic logic . Our study is completely syntactical.
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  • Symmetric and conflated intuitionistic logics.Norihiro Kamide - forthcoming - Logic Journal of the IGPL.
    Two new propositional non-classical logics, referred to as symmetric intuitionistic logic (SIL) and conflated intuitionistic logic (CIL), are introduced as indexed and non-indexed Gentzen-style sequent calculi. SIL is regarded as a natural hybrid logic combining intuitionistic and dual-intuitionistic logics, whereas CIL is regarded as a variant of intuitionistic paraconsistent logic with conflation and without paraconsistent negation. The cut-elimination theorems for SIL and CIL are proved. CIL is shown to be conservative over SIL.
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  • The Semi Heyting–Brouwer Logic.Juan Manuel Cornejo - 2015 - Studia Logica 103 (4):853-875.
    In this paper we introduce a logic that we name semi Heyting–Brouwer logic, \, in such a way that the variety of double semi-Heyting algebras is its algebraic counterpart. We prove that, up to equivalences by translations, the Heyting–Brouwer logic \ is an axiomatic extension of \ and that the propositional calculi of intuitionistic logic \ and semi-intuitionistic logic \ turn out to be fragments of \.
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  • Dual-Intuitionistic Logic.Igor Urbas - 1996 - Notre Dame Journal of Formal Logic 37 (3):440-451.
    The sequent system LDJ is formulated using the same connectives as Gentzen's intuitionistic sequent system LJ, but is dual in the following sense: (i) whereas LJ is singular in the consequent, LDJ is singular in the antecedent; (ii) whereas LJ has the same sentential counter-theorems as classical LK but not the same theorems, LDJ has the same sentential theorems as LK but not the same counter-theorems. In particular, LDJ does not reject all contradictions and is accordingly paraconsistent. To obtain a (...)
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  • Falsification-Aware Calculi and Semantics for Normal Modal Logics Including S4 and S5.Norihiro Kamide - 2023 - Journal of Logic, Language and Information 32 (3):395-440.
    Falsification-aware (hyper)sequent calculi and Kripke semantics for normal modal logics including S4 and S5 are introduced and investigated in this study. These calculi and semantics are constructed based on the idea of a falsification-aware framework for Nelson’s constructive three-valued logic. The cut-elimination and completeness theorems for the proposed calculi and semantics are proved.
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  • A relationship between Rauszer's HB logic and Nelson's logic'.Norihiro Kamide - 2004 - Bulletin of the Section of Logic 33 (4):237-249.
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  • A note on dual-intuitionistic logic.Norihiro Kamide - 2003 - Mathematical Logic Quarterly 49 (5):519.
    Dual-intuitionistic logics are logics proposed by Czermak , Goodman and Urbas . It is shown in this paper that there is a correspondence between Goodman's dual-intuitionistic logic and Nelson's constructive logic N−.
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