Now showing items 1-20 of 67

    • Tense Polyadic N × M-Valued Łukasiewicz–Moisil Algebras 

      Figallo, Aldo V.; Pelaitay, Gustavo (Wydawnictwo Uniwersytetu Łódzkiego, 2015)
      In 2015, A.V. Figallo and G. Pelaitay introduced tense n×m-valued Łukasiewicz–Moisil algebras, as a common generalization of tense Boolean algebras and tense n-valued Łukasiewicz–Moisil algebras. Here we initiate an ...
    • On Some Applied First-Order Theories which Can Be Represented by Definitions 

      Shalack, Vladimir (Wydawnictwo Uniwersytetu Łódzkiego, 2015)
      In the paper we formulate a sufficient criterion in order for the first order theory with finite set of axioms to be represented by definitions in predicate calculus. We prove the corresponding theorem. According to this ...
    • Closure Operators on Complete Almost Distributive Lattices-III 

      Rao, Calyampudi Radhakrishna; Undurthi, Venugopalam (Wydawnictwo Uniwersytetu Łódzkiego, 2015)
      In this paper, we prove that the lattice of all closure operators of a complete Almost Distributive Lattice L with fixed maximal element m is dual atomistic. We define the concept of a completely meet-irreducible element ...
    • Non-Fregean Logics of Analytic Equivalence (II) 

      Biłat, Andrzej (Wydawnictwo Uniwersytetu Łódzkiego, 2015)
      This paper presents the main assumptions of Andrzej Grzegorczyk’s last research project concerning the logic of synonymity. It shows that the basis of logic of analytic equivalence, presented in the first part of the work, ...
    • On Halldén Completeness of Modal Logics Determined by Homogeneous Kripke Frames 

      Kostrzycka, Zofia (Wydawnictwo Uniwersytetu Łódzkiego, 2015)
      Halldén complete modal logics are defined semantically. They have a nice characterization as they are determined by homogeneous Kripke frames.
    • A Short and Readable Proof of Cut Elimination for Two First-Order Modal Logics 

      Gao, Feng; Tourlakis, George (Wydawnictwo Uniwersytetu Łódzkiego, 2015)
      A well established technique toward developing the proof theory of a Hilbert-style modal logic is to introduce a Gentzen-style equivalent (a Gentzenisation), then develop the proof theory of the latter, and finally transfer ...
    • A Note on some Characterization of Distributive Lattices of Finite Length 

      Łazarz, Marcin; Siemieńczuk, Krzysztof (Wydawnictwo Uniwersytetu Łódzkiego, 2015)
      Using known facts we give a simple characterization of the distributivity of lattices of finite length.
    • Minimal Sequent Calculi for Łukasiewicz’s Finitely-Valued Logics 

      Pynko, Alexej P. (Wydawnictwo Uniwersytetu Łódzkiego, 2015)
      The primary objective of this paper, which is an addendum to the author’s [8], is to apply the general study of the latter to Łukasiewicz’s n-valued logics [4]. The paper provides an analytical expression of a 2(n−1)-place ...
    • Categorical Abstract Algebraic Logic: Referential π-Institutions 

      Voutsadakis, George (Wydawnictwo Uniwersytetu Łódzkiego, 2015)
      Wójcicki introduced in the late 1970s the concept of a referential semantics for propositional logics. Referential semantics incorporate features of the Kripke possible world semantics for modal logics into the realm of ...
    • Non-Fregean Logics of Analytic Equivalence (I) 

      Biłat, Andrzej (Wydawnictwo Uniwersytetu Łódzkiego, 2015)
      The identity connective is usually interpreted in non-Fregean logic as an operator representing the identity of situations. This interpretation is related to the modal criterion of the identity of sentence correlates, ...
    • An Observation Concerning Porte’s Rule in Modal Logic 

      French, Rohan; Humberstone, Lloyd (Wydawnictwo Uniwersytetu Łódzkiego, 2015)
      It is well known that no consistent normal modal logic contains (as theorems) both ◊A and ◊¬A (for any formula A). Here we observe that this claim can be strengthened to the following: for any formula A, either no consistent ...
    • Unifiability and Structural Completeness in Relation Algebras and in Products of Modal Logic S5 

      Dzik, Wojciech; Wróbel, Beniamin (Wydawnictwo Uniwersytetu Łódzkiego, 2015)
      Unifiability of terms (and formulas) and structural completeness in the variety of relation algebras RA and in the products of modal logic S5 is investigated. Nonunifiable terms (formulas) which are satisfiable in varieties ...
    • Simple Logics for Basic Algebras 

      Cı̅rulis, Ja̅nis (Wydawnictwo Uniwersytetu Łódzkiego, 2015)
      An MV-algebra is an algebra (A, ⊕, ¬, 0), where (A, ⊕, 0) is a commutative monoid and ¬ is an idempotent operation on A satisfying also some additional axioms. Basic algebras are similar algebras that can roughly be ...
    • An Elementary Proof of Strong Normalization for Atomic F 

      Ferreira, Fernando; Ferreira, Gilda (Uniwersytet Łódzki. Katedra Logiki i Metodologii Nauk, 2016)
      We give an elementary proof (in the sense that it is formalizable in Peano arithmetic) of the strong normalization of the atomic polymorphic calculus F_{at} (a predicative restriction of Girard’s system F).
    • Irredundant Decomposition of Algebras into One-Dimensional Factors 

      Staruch, Bogdan (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      We introduce a notion of dimension of an algebraic lattice and, treating such a lattice as the congruence lattice of an algebra, we introduce the dimension of an algebra, too. We define a star-product as a special kind of ...
    • Preserving Filtering Unification by Adding Compatible Operations to Some Heyting Algebras 

      Dzik, Wojciech; Radeleczki, Sándor (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      We show that adding compatible operations to Heyting algebras and to commutative residuated lattices, both satisfying the Stone law ¬x ⋁ ¬¬x = 1, preserves filtering (or directed) unification, that is, the property that ...
    • Interpolation in Normal Extensions of the Brouwer Logic 

      Kostrzycka, Zofia (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      The Craig interpolation property and interpolation property for deducibility are considered for special kind of normal extensions of the Brouwer logic.
    • On Direct Limit Closed Classes of Algebras 

      Halušková, Emília (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      Axiomatic classes of algebras of a given type which are closed with respect to direct limits are studied in this paper.
    • Decomposition of Congruence Modular Algebras into Atomic, Atomless Locally Uniform and Anti-Uniform Parts 

      Staruch, Bogdan; Staruch, Bożena (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      We describe here a special subdirect decomposition of algebras with modular congruence lattice. Such a decomposition (called a star-decomposition) is based on the properties of the congruence lattices of algebras. We ...
    • Characterization of Birkhoff’s Conditions by Means of Cover-Preserving and Partially Cover-Preserving Sublattices 

      Łazarz, Marcin (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      In the paper we investigate Birkhoff’s conditions (Bi) and (Bi*). We prove that a discrete lattice L satisfies the condition (Bi) (the condition (Bi*)) if and only if L is a 4-cell lattice not containing a cover-preserving ...