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Refutation systems in modal logic

Studia Logica 53 (2):299 - 324 (1994)

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  1. Hybrid Deduction–Refutation Systems.Valentin Goranko - 2019 - Axioms 8 (4).
    Hybrid deduction–refutation systems are deductive systems intended to derive both valid and non-valid, i.e., semantically refutable, formulae of a given logical system, by employing together separate derivability operators for each of these and combining ‘hybrid derivation rules’ that involve both deduction and refutation. The goal of this paper is to develop a basic theory and ‘meta-proof’ theory of hybrid deduction–refutation systems. I then illustrate the concept on a hybrid derivation system of natural deduction for classical propositional logic, for which I (...)
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  • Rejection in Łukasiewicz's and Słupecki' Sense.Urszula Wybraniec-Skardowska - 2018 - Lvov-Warsaw School. Past and Present.
    The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz [20]. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions [22, 23]. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz (...)
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  • A Meta-Logic of Inference Rules: Syntax.Alex Citkin - 2015 - Logic and Logical Philosophy 24 (3).
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  • Rejection in Łukasiewicz's and Słupecki's Sense.Urszula Wybraniec-Skardowska - 2018 - In Urszula Wybraniec-Skardowska & Ángel Garrido (eds.), The Lvov-Warsaw School. Past and Present. Basel, Switzerland: pp. 575-597.
    The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz [20]. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions [22, 23]. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz (...)
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  • Proof and Truth. An Anti-Realist Perspective.Luca Tranchini - unknown
    In the first chapter, we discuss Dummett’s idea that the notion of truth arises from the one of the correctness of an assertion. We argue that, in a first-order language, the need of defining truth in terms of the notion of satisfaction, which is yielded by the presence of quantifiers, is structurally analogous to the need of a notion of truth as distinct from the one of correctness of an assertion. In the light of the analogy between predicates in Frege (...)
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  • A Generalisation of a Refutation-Related Method in Paraconsistent Logics.Adam Trybus - forthcoming - Logic and Logical Philosophy.
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  • Modal Hybrid Logic.Andrzej Indrzejczak - 2007 - Logic and Logical Philosophy 16 (2-3):147-257.
    This is an extended version of the lectures given during the 12-thConference on Applications of Logic in Philosophy and in the Foundationsof Mathematics in Szklarska Poręba. It contains a surveyof modal hybrid logic, one of the branches of contemporary modal logic. Inthe first part a variety of hybrid languages and logics is presented with adiscussion of expressivity matters. The second part is devoted to thoroughexposition of proof methods for hybrid logics. The main point is to showthat application of hybrid logics (...)
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  • Admissibility and Refutation: Some Characterisations of Intermediate Logics.Jeroen P. Goudsmit - 2014 - Archive for Mathematical Logic 53 (7-8):779-808.
    Refutation systems are formal systems for inferring the falsity of formulae. These systems can, in particular, be used to syntactically characterise logics. In this paper, we explore the close connection between refutation systems and admissible rules. We develop technical machinery to construct refutation systems, employing techniques from the study of admissible rules. Concretely, we provide a refutation system for the intermediate logics of bounded branching, known as the Gabbay–de Jongh logics. We show that this gives a characterisation of these logics (...)
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  • A Refutation Theory.Tomasz Skura - 2009 - Logica Universalis 3 (2):293-302.
    A general theory of refutation systems is given. Some applications (concerning maximality and minimality in lattices of logics) are also discussed.
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  • A Łukasiewicz-Style Refutation System for the Modal Logic S.Tomasz Skura - 1995 - Journal of Philosophical Logic 24 (6):573 - 582.
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  • Logics of Rejection: Two Systems of Natural Deduction.Allard Tamminga - 1994 - Logique Et Analyse 146:169-208.
    This paper presents two systems of natural deduction for the rejection of non-tautologies of classical propositional logic. The first system is sound and complete with respect to the body of all non-tautologies, the second system is sound and complete with respect to the body of all contradictions. The second system is a subsystem of the first. Starting with Jan Łukasiewicz's work, we describe the historical development of theories of rejection for classical propositional logic. Subsequently, we present the two systems of (...)
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  • Proofs and Countermodels in Non-Classical Logics.Sara Negri - 2014 - Logica Universalis 8 (1):25-60.
    Proofs and countermodels are the two sides of completeness proofs, but, in general, failure to find one does not automatically give the other. The limitation is encountered also for decidable non-classical logics in traditional completeness proofs based on Henkin’s method of maximal consistent sets of formulas. A method is presented that makes it possible to establish completeness in a direct way: For any given sequent either a proof in the given logical system or a countermodel in the corresponding frame class (...)
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