Bulletin of the Section of Logic 55/3 (2026)

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  • A Note on the Number of Subnormal Modal Logics 

    Michalczenia, Patryk (Wydawnictwo Uniwersytetu Łódzkiego, 2026-09-08)
    In the article we discuss the notion of a subnormal modal logic and, in particular, the notion of an intermediate subnormal modal logic. The goal of the article is to determine the cardinality of the set of all intermediate ...

  • Valuation on L-Algebras 

    Borzooei, Rajab Ali; Aaly Kologani, Mona; Mohseni Takallo, Mohammad; Xin, Xiao Long (Wydawnictwo Uniwersytetu Łódzkiego, 2026-09-07)
    The purpose of this paper is to define the notion of valuation map on \(L\)-algebras and introduce its properties. For this, the concepts of  valuation and 1-valuation maps are introduced and some characterizations and ...

  • Perfect and Local Bounded Equality Algebras 

    Niazian, Sogol; Aaly Kologani, Mona; Jun, Young Bae; Borzooei, Rajab Ali (Wydawnictwo Uniwersytetu Łódzkiego, 2026-09-07)
    In this paper, by considering the notion of bounded equality algebra, we introduce the concepts of perfect, integral and local bounded equality algebras and we state and prove some related results. Specially, we define the ...

  • Pre-Hilbert Algebras with Condition (GE3) 

    Rezaei, Akbar; Borumand Saeid, Arsham (Wydawnictwo Uniwersytetu Łódzkiego, 2026-09-08)
    GE-algebras are introduced as a generalization of Hilbert algebras in 2020. In this paper, we show that a self distributive GE-algebra is equivalent to the pimpl-RML algebra, and a transitive GE algebra is equivalent to ...

  • Double Equivalential Algebras 

    Przybyło, Sławomir (Wydawnictwo Uniwersytetu Łódzkiego, 2026-09-04)
    In this paper, we introduce the notion of double equivalential algebras, defined as subreducts of double Heyting algebras with respect to the equivalence and dual equivalence operations. We establish the fundamental ...

  • On Certain Completeness Results for S4.2 Modal Logic and Its Applications in Modal Logics of Classes of Structures 

    Hałapacz, Maciej A. (Wydawnictwo Uniwersytetu Łódzkiego, 2026-09-07)
    In this paper, we obtain new classes of Kripke frames complete for the modal logic S4.2, through the means of the so-called control statements. We provide applications of the theorem in the field of modal logics of classes ...

  • Radical and Jacobson Radical in L-Algebras 

    Borzooei, Rajab Ali; Khajeh Nasir, Hamideh; Yavari, Mehdi (Wydawnictwo Uniwersytetu Łódzkiego, 2026-09-03)
    In this paper, inspired by the concepts of the radical of an ideal and the Jacobson radical in ring theory, we introduce these notions in the context of L-algebras. Our main goal is to explore the nature of the radical of ...

  • Applications of Commutators in Pseudo BL-Algebras 

    Najafi, Ardavan; Borumand Saeid, Arsham (Wydawnictwo Uniwersytetu Łódzkiego, 2026-08-27)
    In this paper, the concepts of commutativity relation, commutant of a subset, center and solvable pseudo BL-algebras are defined and their properties are investigated. The notion of n-Engel pseudo BL-algebras as a natural ...

  • Some New Kinds of BCK-Filters in Bounded BCK-Algebras 

    Khosravi Shoar, Sadegh; Borzooei, Rajab Ali (Wydawnictwo Uniwersytetu Łódzkiego, 2026-08-19)
    This paper investigates and characterizes some new types of BCK-filters in bounded BCK-algebras. We introduce the notions of EQI-filters, implicative BCK-filters, and commutative BCK-filters. We clarify the relationships ...