Bulletin of the Section of Logic: Recent submissions

Now showing items 181-200 of 214

    • Three Doctrines of the Nature of Mathematics (Some Comments of a Knowledge Theorist) 

      Wójcicki, Ryszard (Wydawnictwo Uniwersytetu Łódzkiego, 2017)
      In this note I am reflecting on interrelations between three concepts of truth: (1) that employed by Hilbert arguing his formalist view on the nature of mathematics, (2) Freges idea of truth supported by mathematical ...

    • Cut Elimination Theorem for Non-Commutative Hypersequent Calculus 

      Indrzejczak, Andrzej (Wydawnictwo Uniwersytetu Łódzkiego, 2017)
      Hypersequent calculi (HC) can formalize various non-classical logics. In [9] we presented a non-commutative variant of HC for the weakest temporal logic of linear frames Kt4.3 and some its extensions for dense and serial ...

    • Professor Grzegorz Malinowski in Honorem 

      Indrzejczak, Andrzej; Ciuciura, Janusz (Wydawnictwo Uniwersytetu Łódzkiego, 2017)

    • 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 ...

    • 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 ...

    • 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 ...

    • 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 ...

    • 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.

    • Monadic Fragments of Intuitionistic Control Logic 

      Glenszczyk, Anna (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      We investigate monadic fragments of Intuitionistic Control Logic (ICL), which is obtained from Intuitionistic Propositional Logic (IPL) by extending language of IPL by a constant distinct from intuitionistic constants. In ...

    • 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. ...

    • 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 ...

    • A New Arithmetically Incomplete First- Order Extension of Gl All Theorems of Which Have Cut Free Proofs 

      Tourlakis, George (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      Reference [12] introduced a novel formula to formula translation tool (“formulators”) that enables syntactic metatheoretical investigations of first-order modal logics, bypassing a need to convert them first into Gentzen ...

    • 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).

    • 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 ...

    • 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 ...

    • 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. ...

    • Axiomatization of a Basic Logic of Logical Bilattices 

      Takano, Mitio (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      A sequential axiomatization is given for the 16-valued logic that has been proposed by Shramko-Wansing (J Philos Logic 34:121–153, 2005) as a candidate for the basic logic of logical bilattices.

    • Quasiorders, Tolerance Relations and Corresponding “Partitions” 

      Nowak, Marek (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      The paper deals with a generalization of the notion of partition for wider classes of binary relations than equivalences: for quasiorders and tolerance relations. The counterpart of partition for the quasiorders is based ...