•  15
    In this paper, we present sound and complete natural deduction systems for Fitting’s four-valued generalizations of Kleene’s three-valued regular logics.
  •  12
    Functional Completeness in CPL via Correspondence Analysis
    with Dorota Leszczyńska-Jasion, Vasilyi Shangin, and Marcin Jukiewicz
    Bulletin of the Section of Logic 48 (1). 2019.
    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 propert…Read more
  •  12
    Simplified Kripke-Style Semantics for Some Normal Modal Logics
    with Andrzej Pietruszczak and Mateusz Klonowski
    Studia Logica 1-26. forthcoming.
    Pietruszczak :163–171, 2009. https://doi.org/10.12775/LLP.2009.013) proved that the normal logics \, \ ), \ are determined by suitable classes of simplified Kripke frames of the form \, where \. In this paper, we extend this result. Firstly, we show that a modal logic is determined by a class composed of simplified frames if and only if it is a normal extension of \. Furthermore, a modal logic is a normal extension of \ ; \; \) if and only if it is determined by a set consisting of finite simpli…Read more
  •  10
    Natural Deduction for Post’s Logics and their Duals
    Logica Universalis 12 (1-2): 83-100. 2018.
    In this paper, we introduce the notion of dual Post’s negation and an infinite class of Dual Post’s finitely-valued logics which differ from Post’s ones with respect to the definitions of negation and the sets of designated truth values. We present adequate natural deduction systems for all Post’s k-valued ) logics as well as for all Dual Post’s k-valued logics.
  •  9
    Generalized Correspondence Analysis for Three-Valued Logics
    Logica Universalis 12 (3-4): 423-460. 2018.
    Correspondence analysis is Kooi and Tamminga’s universal approach which generates in one go sound and complete natural deduction systems with independent inference rules for tabular extensions of many-valued functionally incomplete logics. Originally, this method was applied to Asenjo–Priest’s paraconsistent logic of paradox LP. As a result, one has natural deduction systems for all the logics obtainable from the basic three-valued connectives of LP -language) by the addition of unary and binary…Read more
  •  7
    Two proofs of the algebraic completeness theorem for multilattice logic
    with Oleg Grigoriev
    Journal of Applied Non-Classical Logics 29 (4): 358-381. 2019.
    Shramko [. Truth, falsehood, information and beyond: The American plan generalized. In K. Bimbo, J. Michael Dunn on information based logics, outstanding contributions to logic...
  •  7
    The Method of Socratic Proofs Meets Correspondence Analysis
    with Dorota Leszczyńska-Jasion and Vasilyi Shangin
    Bulletin of the Section of Logic 48 (2): 99-116. 2019.
    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 i…Read more
  •  5
    Natural Deduction for Four-Valued both Regular and Monotonic Logics
    Logic and Logical Philosophy 27 (1): 53-66. 2018.
    The development of recursion theory motivated Kleene to create regular three-valued logics. Remove it taking his inspiration from the computer science, Fitting later continued to investigate regular three-valued logics and defined them as monotonic ones. Afterwards, Komendantskaya proved that there are four regular three-valued logics and in the three-valued case the set of regular logics coincides with the set of monotonic logics. Next, Tomova showed that in the four-valued case regularity and …Read more
  •  5
    On a multilattice analogue of a hypersequent S5 calculus
    with Oleg Grigoriev
    Logic and Logical Philosophy 1. forthcoming.
  • Axiomatization of non-associative generalisations of Hájek's BL and psBL
    Journal of Applied Non-Classical Logics 30 (1): 1-15. 2019.
    ABSTRACTIn this paper, we consider non-associative generalisations of Hájek's logics BL and psBL. As it was shown by Cignoli, Esteva, Godo, and Torrens, the former is the logic of continuous t-norms and their residua. Botur introduced logic naBL which is the logic of non-associative continuous t-norms and their residua. Thus, naBL can be viewed as a non-associative generalisation of BL. However, Botur has not presented axiomatization of naBL. We fill this gap by constructing an adequate Hilbert-…Read more