
15Natural Deduction for Fitting’s FourValued Generalizations of Kleene’s LogicsLogica Universalis 11 (4): 525532. 2017.In this paper, we present sound and complete natural deduction systems for Fitting’s fourvalued generalizations of Kleene’s threevalued regular logics.

12Functional Completeness in CPL via Correspondence AnalysisBulletin 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 twoargument Boolean function to the negation fragment of classical propositional logic. The propert…Read more

12Simplified KripkeStyle Semantics for Some Normal Modal LogicsStudia Logica 126. 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

10Natural Deduction for Post’s Logics and their DualsLogica Universalis 12 (12): 83100. 2018.In this paper, we introduce the notion of dual Post’s negation and an infinite class of Dual Post’s finitelyvalued 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 kvalued ) logics as well as for all Dual Post’s kvalued logics.

9Generalized Correspondence Analysis for ThreeValued LogicsLogica Universalis 12 (34): 423460. 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 manyvalued 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 threevalued connectives of LP language) by the addition of unary and binary…Read more

7Two proofs of the algebraic completeness theorem for multilattice logicJournal of Applied NonClassical Logics 29 (4): 358381. 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...

7The Method of Socratic Proofs Meets Correspondence AnalysisBulletin of the Section of Logic 48 (2): 99116. 2019.The goal of this paper is to propose correspondence analysis as a technique for generating the socalled 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 sequentcalculusstyle 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

5Natural Deduction for FourValued both Regular and Monotonic LogicsLogic and Logical Philosophy 27 (1): 5366. 2018.The development of recursion theory motivated Kleene to create regular threevalued logics. Remove it taking his inspiration from the computer science, Fitting later continued to investigate regular threevalued logics and defined them as monotonic ones. Afterwards, Komendantskaya proved that there are four regular threevalued logics and in the threevalued case the set of regular logics coincides with the set of monotonic logics. Next, Tomova showed that in the fourvalued case regularity and …Read more

5On a multilattice analogue of a hypersequent S5 calculusLogic and Logical Philosophy 1. forthcoming.

5Automated Proofsearching for Strong Kleene Logic and its Binary Extensions via Correspondence AnalysisLogic and Logical Philosophy 1. forthcoming.

Axiomatization of nonassociative generalisations of Hájek's BL and psBLJournal of Applied NonClassical Logics 30 (1): 115. 2019.ABSTRACTIn this paper, we consider nonassociative 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 tnorms and their residua. Botur introduced logic naBL which is the logic of nonassociative continuous tnorms and their residua. Thus, naBL can be viewed as a nonassociative generalisation of BL. However, Botur has not presented axiomatization of naBL. We fill this gap by constructing an adequate Hilbert…Read more