8 found
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  1.  43
    Dual Erotetic Calculi and the Minimal LFI.Szymon Chlebowski & Dorota Leszczyńska-Jasion - 2015 - Studia Logica 103 (6):1245-1278.
    An erotetic calculus for a given logic constitutes a sequent-style proof-theoretical formalization of the logic grounded in Inferential Erotetic Logic ). In this paper, a new erotetic calculus for Classical Propositional Logic ), dual with respect to the existing ones, is given. We modify the calculus to obtain complete proof systems for the propositional part of paraconsistent logic CLuN and its extensions CLuNs and mbC. The method is based on dual resolution. Moreover, the resolution rule is non-clausal. According to the (...)
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  2.  24
    Sequent Calculi for $${\mathsf {SCI}}$$ SCI.Szymon Chlebowski - 2018 - Studia Logica 106 (3):541-563.
    In this paper we are applying certain strategy described by Negri and Von Plato :418–435, 1998), allowing construction of sequent calculi for axiomatic theories, to Suszko’s Sentential calculus with identity. We describe two calculi obtained in this way, prove that the cut rule, as well as the other structural rules, are admissible in one of them, and we also present an example which suggests that the cut rule is not admissible in the other.
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  3.  28
    Sequent Calculi for SCI.Szymon Chlebowski - 2018 - Studia Logica 106 (3):541-563.
    In this paper we are applying certain strategy described by Negri and Von Plato :418–435, 1998), allowing construction of sequent calculi for axiomatic theories, to Suszko’s Sentential calculus with identity. We describe two calculi obtained in this way, prove that the cut rule, as well as the other structural rules, are admissible in one of them, and we also present an example which suggests that the cut rule is not admissible in the other.
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  4.  2
    An Investigation Into Intuitionistic Logic with Identity.Szymon Chlebowski & Dorota Leszczyńska-Jasion - 2019 - Bulletin of the Section of Logic 48 (4).
    We define Kripke semantics for propositional intuitionistic logic with Suszko’s identity. We propose sequent calculus for ISCI along with cut-elimination theorem. We sketch a constructive interpretation of Suszko’s propositional identity connective.
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  5.  3
    Natural Deduction Systems for Intuitionistic Logic with Identity.Szymon Chlebowski, Marta Gawek & Agata Tomczyk - forthcoming - Studia Logica:1-35.
    The aim of the paper is to present two natural deduction systems for Intuitionistic Sentential Calculus with Identity ; a syntactically motivated \ and a semantically motivated \. The formulation of \ is based on the axiomatic formulation of ISCI. Its rules cannot be straightforwardly classified as introduction or elimination rules; ISCI-specific rules are based on axioms characterizing the identity connective. The system does not enjoy the standard subformula property, but due to the normalization procedure non-subformulas can label only leaves (...)
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  6.  7
    An Abductive Question-Answer System for the Minimal Logic of Formal Inconsistency $$\mathsf {mbC}$$ mbC.Szymon Chlebowski, Andrzej Gajda & Mariusz Urbański - 2022 - Studia Logica 110 (2):479-509.
    The aim in this paper is to define an Abductive Question-Answer System for the minimal logic of formal inconsistency \. As a proof-theoretical basis we employ the Socratic proofs method. The system produces abductive hypotheses; these are answers to abductive questions concerning derivability of formulas from sets of formulas. We integrated the generation of and the evaluation of hypotheses via constraints of consistency and significance being imposed on the system rules.
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  7.  29
    Rasiowa–Sikorski Deduction Systems with the Rule of Cut: A Case Study.Dorota Leszczyńska-Jasion, Mateusz Ignaszak & Szymon Chlebowski - 2019 - Studia Logica 107 (2):313-349.
    This paper presents Rasiowa–Sikorski deduction systems for logics \, \, \ and \. For each of the logics two systems are developed: an R–S system that can be supplemented with admissible cut rule, and a \-version of R–S system in which the non-admissible rule of cut is the only branching rule. The systems are presented in a Smullyan-like uniform notation, extended and adjusted to the aims of this paper. Completeness is proved by the use of abstract refutability properties which are (...)
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  8. FREGE I ŁUKASIEWICZ O WARTOŚCIACH LOGICZNYCH.Hubert Jastrzębski & Szymon Chlebowski - 2014 - Hybris, Revista de Filosofí­A (27):121-135.
    FREGE AND ŁUKASIEWICZ ON LOGICAL VALUES Our article regards the connections between the views on semantics of Gottlob Frege and Jan Łukasiewicz. We are especially focused on the problem of logical values and their ontological interpetation. The paper is composed of three parts. In the first section we point out the general tendencies in the reception of Frege’s logical theory in the Lvov-Warsaw Philosophical School. The second section is dedicated to Frege’s semantics, especially his analysis of sense and meaning of (...)
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