Now showing items 1-20 of 76

    • Erratum to: Congruences and Ideals in a Distributive Lattice with Respect to a Derivation 

      Barzegar, Hasan (Wydawnictwo Uniwersytetu Łódzkiego, 2019)
      The present note is an Erratum for the two theorems of the paper "Congruences and ideals in a distributive lattice with respect to a derivation" by M. Sambasiva Rao.
    • Functional Completeness in CPL via Correspondence Analysis 

      Leszczyńska-Jasion, Dorota; Petrukhin, Yaroslav; Shangin, Vasilyi; Jukiewicz, Marcin (Wydawnictwo Uniwersytetu Łódzkiego, 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 ...
    • Two Infinite Sequences of Pre-Maximal Extensions of the Relevant Logic E 

      Typańska-Czajka, Lidia (Wydawnictwo Uniwersytetu Łódzkiego, 2019)
      The only maximal extension of the logic of relevant entailment E is the classical logic CL. A logic L ⊆ [E,CL] called pre-maximal if and only if L is a coatom in the interval [E,CL]. We present two denumerable infinite ...
    • A Modified Subformula Property for the Modal Logic S4.2 

      Takano, Mitio (Wydawnictwo Uniwersytetu Łódzkiego, 2019)
      The modal logic S4.2 is S4 with the additional axiom ◊□A ⊃ □◊A. In this article, the sequent calculus GS4.2 for this logic is presented, and by imposing an appropriate restriction on the application of the cut-rule, it is ...
    • Positive Implicative Soju Ideals in BCK-Algebras 

      Xin, Xiao Long; Borzooei, Rajab Ali; Jun, Young Bae (Wydawnictwo Uniwersytetu Łódzkiego, 2019)
      The notion of positive implicative soju ideal in BCK-algebra is introduced, and several properties are investigated. Relations between soju ideal and positive implicative soju ideal are considered, and characterizations ...
    • Full Cut Elimination and Interpolation for Intuitionistic Logic with Existence Predicate 

      Maffezioli, Paolo; Orlandelli, Eugenio (Wydawnictwo Uniwersytetu Łódzkiego, 2019)
      In previous work by Baaz and Iemhoff, a Gentzen calculus for intuitionistic logic with existence predicate is presented that satisfies partial cut elimination and Craig's interpolation property; it is also conjectured that ...
    • Semi-Heyting Algebras and Identities of Associative Type 

      Cornejo, Juan M.; Sankappanavar, Hanamantagouda P. (Wydawnictwo Uniwersytetu Łódzkiego, 2019)
      An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ (x → y) ≈ x ∧ y, x ∧ (y → z) ≈ x ∧ [(x ∧ y) → (x ∧ z)], and x → x ≈ 1. SH denotes ...
    • A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation 

      Kürbis, Nils (Wydawnictwo Uniwersytetu Łódzkiego, 2019)
      This paper presents a way of formalising definite descriptions with a binary quantifier ℩, where ℩x[F, G] is read as `The F is G'. Introduction and elimination rules for ℩ in a system of intuitionist negative free logic ...
    • The Method of Socratic Proofs Meets Correspondence Analysis 

      Leszczyńska-Jasion, Dorota; Petrukhin, Yaroslav; Shangin, Vasilyi (Wydawnictwo Uniwersytetu Łódzkiego, 2019)
      The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic (i.e. pertaining to the logic of questions) calculi which constitute the method of Socratic proofs by Andrzej ...
    • On Injective MV-Modules 

      Borzooei, Rajabali A.; Goraghani, S. Saidi (Wydawnictwo Uniwersytetu Łódzkiego, 2018)
      In this paper, by considering the notion of MV-module, which is the structure that naturally correspond to lu-modules over lu-rings, we study injective MV-modules and we investigate some conditions for constructing injective ...
    • Rule-Generation Theorem and its Applications 

      Indrzejczak, Andrzej (Wydawnictwo Uniwersytetu Łódzkiego, 2018)
      In several applications of sequent calculi going beyond pure logic, an introduction of suitably defined rules seems to be more profitable than addition of extra axiomatic sequents. A program of formalization of mathematical ...
    • On the Definability of Leśniewski’s Copula ‘is’ in Some Ontology-Like Theories 

      Łyczak, Marcin; Pietruszczak, Andrzej (Wydawnictwo Uniwersytetu Łódzkiego, 2018)
      We formulate a certain subtheory of Ishimoto’s [1] quantifier-free fragment of Leśniewski’s ontology, and show that Ishimoto’s theory can be reconstructed in it. Using an epimorphism theorem we prove that our theory is ...
    • Labeled Sequent Calculus for Orthologic 

      Kawano, Tomoaki (Wydawnictwo Uniwersytetu Łódzkiego, 2018)
      Orthologic (OL) is non-classical logic and has been studied as a part of quantumlogic. OL is based on an ortholattice and is also called minimal quantum logic.Sequent calculus is used as a tool for proof in logic and has ...
    • A post-style proof of completeness theorem for symmetric relatedness Logic S 

      Klonowski, Mateusz (Wydawnictwo Uniwersytetu Łódzkiego, 2018)
      One of the logic defined by Richard Epstein in a context of an analysis of subject matter relationship is Symmetric Relatedness Logic S. In the monograph [2] we can find some open problems concerning relatedness logic, a ...
    • A comparison of two systems of point-free topology 

      Gruszczyński, Rafał; Pietruszczak, Andrzej (Wydawnictwo Uniwersytetu Łódzkiego, 2018)
      This is a spin-off paper to [3, 4] in which we carried out an extensive analysis of Andrzej Grzegorczyk’s point-free topology from [5]. In [1] Loredana Biacino and Giangiacomo Gerla presented an axiomatization which was ...
    • B-almost distributive fuzzy lattice 

      Assaye, Berhanu; Alemneh, Mihret; Tefera, Gerima (Wydawnictwo Uniwersytetu Łódzkiego, 2018)
      The paper introduces the concept of B-Almost distributive fuzzy lattice (BADFL) in terms of its principal ideal fuzzy lattice. Necessary and sufficient conditions for an ADFL to become a B-ADFL are investigated. We also ...
    • On interpolation in next (kb.alt(2)) 

      Kostrzycka, Zofia (Wydawnictwo Uniwersytetu Łódzkiego, 2018)
      We prove that there is infinitely many tabular modal logics extending KB.Alt(2) which have interpolation.
    • Identity, equality, nameability and completeness. Part II 

      Manzano, María; Moreno, Manuel Crescencio (Wydawnictwo Uniwersytetu Łódzkiego, 2018)
      This article is a continuation of our promenade along the winding roads of identity, equality, nameability and completeness. We continue looking for a place where all these concepts converge. We assume that identity is a ...
    • Grzegorczyk Algebras Revisited 

      Stronkowski, Michał M. (Wydawnictwo Uniwersytetu Łódzkiego, 2018)
      We provide simple algebraic proofs of two important facts, due to Zakharyaschev and Esakia, about Grzegorczyk algebras.
    • Pseudo-BCH Semilattices 

      Walendziak, Andrzej (Wydawnictwo Uniwersytetu Łódzkiego, 2018)
      In this paper we study pseudo-BCH algebras which are semilattices or lattices with respect to the natural relations ≤; we call them pseudo-BCH join-semilattices, pseudo-BCH meet-semilattices and pseudo-BCH lattices, ...