Now showing items 1-20 of 76

    • 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 ...
    • 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 ...
    • An Alternative Natural Deduction for the Intuitionistic Propositional Logic 

      Ilić, Mirjana (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      A natural deduction system NI, for the full propositional intuitionistic logic, is proposed. The operational rules of NI are obtained by the translation from Gentzen’s calculus LJ and the normalization is proved, via ...
    • Commutative Energetic Subsets of BCK-Algebras 

      Jun, Young Bae; Roh, Eun Hwan; Song, Seok Zun (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      The notions of a C-energetic subset and (anti) permeable C-value in BCK-algebras are introduced, and related properties are investigated. Conditions for an element t in [0, 1] to be an (anti) permeable C-value are provided. ...
    • Elementary Proof of Strong Normalization for Atomic F 

      Ferreira, Fernando; Ferreira, Gilda (Wydawnictwo Uniwersytetu Łódzkiego, 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 Fₐₜ (a predicative restriction of Girard’s system F).
    • Some Algebraic and Algorithmic Problems in Acoustocerebrography 

      Kolany, Adam; Wrobel, Miroslaw (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      Progress in the medical diagnostic is relentlessly pushing the measurement technology as well with its intertwined mathematical models and solutions. Mathematics has applications to many problems that are vital to human ...
    • Simple Decision Procedure for S5 in Standard Cut-Free Sequent Calculus 

      Indrzejczak, Andrzej (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      In the paper a decision procedure for S5 is presented which uses a cut-free sequent calculus with additional rules allowing a reduction to normal modal forms. It utilizes the fact that in S5 every formula is equivalent to ...
    • A 2-set-up Routley-Meyer Semantics for the 4-valued Relevant Logic E4 

      Robles, Gemma; López, Sandra M.; Blanco, José M.; Recio, Marcos M.; Paradela, Jesús R. (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      The logic BN4 can be considered as the 4-valued logic of the relevant conditional and the logic E4, as the 4-valued logic of (relevant) entailment. The aim of this paper is to endow E4 with a 2-set-up Routley-Meyer semantics. ...
    • Categorical Abstract Logic: Hidden Multi-Sorted Logics as Multi-Term Institutions 

      Voutsadakis, George (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      Babenyshev and Martins proved that two hidden multi-sorted deductive systems are deductively equivalent if and only if there exists an isomorphism between their corresponding lattices of theories that commutes with ...