14 found
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  1.  12
    Functional Completeness in CPL Via Correspondence Analysis.Dorota Leszczyńska-Jasion, Yaroslav Petrukhin, Vasilyi Shangin & Marcin Jukiewicz - 2019 - Bulletin of the Section of Logic 48 (1).
    Kooi and Tamminga's correspondence analysis is a technique for designing proof systems, mostly, natural deduction and sequent systems. In this paper it is used to generate sequent calculi with invertible rules, whose only branching rule is the rule of cut. The calculi pertain to classical propositional logic and any of its fragments that may be obtained from adding a set of rules characterizing a two-argument Boolean function to the negation fragment of classical propositional logic. The properties of soundness and completeness (...)
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  2.  39
    Socratic Trees.Dorota Leszczyńska-Jasion, Mariusz Urbański & Andrzej Wiśniewski - 2013 - Studia Logica 101 (5):959-986.
    The method of Socratic proofs (SP-method) simulates the solving of logical problem by pure questioning. An outcome of an application of the SP-method is a sequence of questions, called a Socratic transformation. Our aim is to give a method of translation of Socratic transformations into trees. We address this issue both conceptually and by providing certain algorithms. We show that the trees which correspond to successful Socratic transformations—that is, to Socratic proofs—may be regarded, after a slight modification, as Gentzen-style proofs. (...)
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  3.  18
    Erotetic Search Scenarios and Three-Valued Logic.Dorota Leszczyńska-Jasion & Paweł Łupkowski - 2016 - Journal of Logic, Language and Information 25 (1):51-76.
    Our aim is to model the behaviour of a cognitive agent trying to solve a complex problem by dividing it into sub-problems, but failing to solve some of these sub-problems. We use the powerful framework of erotetic search scenarios combined with Kleene’s strong three-valued logic. ESS, defined on the grounds of Inferential Erotetic Logic, has appeared to be a useful logical tool for modelling cognitive goal-directed processes. Using the logical tools of ESS and the three-valued logic, we will show how (...)
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  4.  35
    Inferential Erotetic Logic Meets Inquisitive Semantics.Andrzej Wiśniewski & Dorota Leszczyńska-Jasion - 2015 - Synthese 192 (6):1585-1608.
    Inferential erotetic logic and inquisitive semantics give accounts of questions and model various aspects of questioning. In this paper we concentrate upon connections between inquisitiveness, being the core concept of INQ, and question raising, characterized in IEL by means of the concepts of question evocation and erotetic implication. We consider the basic system InqB of INQ, remain at the propositional level and show, inter alia, that: a disjunction of all the direct answers to an evoked question is always inquisitive; a (...)
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  5.  31
    The Method of Socratic Proofs for Modal Propositional Logics: K5, S4.2, S4.3, S4F, S4R, S4M and G.Dorota Leszczyńska-Jasion - 2008 - Studia Logica 89 (3):365-399.
    The aim of this paper is to present the method of Socratic proofs for seven modal propositional logics: K5, S4.2, S4.3, S4M, S4F, S4R and G. This work is an extension of [10] where the method was presented for the most common modal propositional logics: K, D, T, KB, K4, S4 and S5.
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  6.  22
    Automatic Proof Generation in an Axiomatic System for $\Mathsf{CPL}$ by Means of the Method of Socratic Proofs.Aleksandra Grzelak & Dorota Leszczyńska-Jasion - 2018 - Logic Journal of the IGPL 26 (1):109-148.
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  7.  16
    Dual Erotetic Calculi and the Minimal $${\Mathsf{LFI}}$$ LFI.Dorota Leszczyńska-Jasion & Szymon Chlebowski - 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 $${\mathsf{CLuN}}$$ CLuN and its extensions $${\mathsf{CLuNs}}$$ CLuNs and $${\mathsf{mbC}}$$ mbC. The method is based on dual resolution. Moreover, the resolution rule is non-clausal. According to (...)
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  8.  18
    Dual Erotetic Calculi and the Minimal {Mathsf{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 \ and its extensions \ and \. The method is based on dual resolution. Moreover, the resolution rule is non-clausal. According to the (...)
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  9.  23
    Generating Cooperative Question-Responses by Means of Erotetic Search Senarios.Paweł Łupkowskim & Dorota Leszczyńska-Jasion - 2014 - Logic and Logical Philosophy 24 (1):61-78.
    The concept of cooperative question-responses as an extension of cooperative behaviours used by interfaces for databases and information systems is proposed. A procedure to generate question-responses based on question dependency and erotetic search scenarios is presented. The procedure is implemented in Prolog.
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  10. The Method of Socratic Proofs for Normal Modal Propositional Logics.Dorota Leszczynska-Jasion - 2007 - Wydawn. Naukowe Uniwersytetu Im. Adama Mickiewicza.
     
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  11.  7
    The Method of Socratic Proofs Meets Correspondence Analysis.Dorota Leszczyńska-Jasion, Yaroslav Petrukhin & Vasilyi Shangin - 2019 - Bulletin of the Section of Logic 48 (2):99-116.
    The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic calculi which constitute the method of Socratic proofs by Andrzej Wiśniewski. As we explain in the paper, in order to successfully design an erotetic calculus one needs invertible sequent-calculus-style rules. For this reason, the proposed correspondence analysis resulting in invertible rules can constitute a new foundation for the method of Socratic proofs. Correspondence analysis is Kooi and Tamminga's technique for designing proof systems. (...)
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  12.  48
    A Loop-Free Decision Procedure for Modal Propositional Logics K4, S4 and S.Dorota Leszczyńska-Jasion - 2009 - Journal of Philosophical Logic 38 (2):151 - 177.
    The aim of this paper is to present a loop-free decision procedure for modal propositional logics K4, S4 and S5. We prove that the procedure terminates and that it is sound and complete. The procedure is based on the method of Socratic proofs for modal logics, which is grounded in the logic of questions IEL.
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  13.  21
    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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  14.  5
    A Loop-Free Decision Procedure for Modal Propositional Logics K4, S4 and S5.Dorota Leszczyńska-Jasion - 2009 - Journal of Philosophical Logic 38 (2):151-177.
    The aim of this paper is to present a loop-free decision procedure for modal propositional logics K4, S4 and S5. We prove that the procedure terminates and that it is sound and complete. The procedure is based on the method of Socratic proofs for modal logics, which is grounded in the logic of questions IEL.
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