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Wieslaw Dziobiak [25]W. Dziobiak [11]Wiesław Dziobiak [7]Wies?aw Dziobiak [6]
Wles?aw Dziobiak [1]
  1.  35
    Open Questions Related to the Problem of Birkhoff and Maltsev.M. E. Adams, K. V. Adaricheva, W. Dziobiak & A. V. Kravchenko - 2004 - Studia Logica 78 (1-2):357-378.
    The Birkhoff-Maltsev problem asks for a characterization of those lattices each of which is isomorphic to the lattice L(K) of all subquasivarieties for some quasivariety K of algebraic systems. The current status of this problem, which is still open, is discussed. Various unsolved questions that are related to the Birkhoff-Maltsev problem are also considered, including ones that stem from the theory of propositional logics.
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  2.  39
    A Deduction Theorem Schema for Deductive Systems of Propositional Logics.Janusz Czelakowski & Wies?aw Dziobiak - 1991 - Studia Logica 50 (3-4):385 - 390.
    We propose a new schema for the deduction theorem and prove that the deductive system S of a prepositional logic L fulfills the proposed schema if and only if there exists a finite set A(p, q) of propositional formulae involving only prepositional letters p and q such that A(p, p) L and p, A(p, q) s q.
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  3.  24
    On the Lattice of Quasivarieties of Sugihara Algebras.W. J. Blok & W. Dziobiak - 1986 - Studia Logica 45 (3):275 - 280.
    Let S denote the variety of Sugihara algebras. We prove that the lattice (K) of subquasivarieties of a given quasivariety K S is finite if and only if K is generated by a finite set of finite algebras. This settles a conjecture by Tokarz [6]. We also show that the lattice (S) is not modular.
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  4.  27
    The Lattice of Strengthenings of a Strongly Finite Consequence Operation.Wiesław Dziobiak - 1981 - Studia Logica 40 (2):177 - 193.
    First, we prove that the lattice of all structural strengthenings of a given strongly finite consequence operation is both atomic and coatomic, it has finitely many atoms and coatoms, each coatom is strongly finite but atoms are not of this kind — we settle this by constructing a suitable counterexample. Second, we deal with the notions of hereditary: algebraicness, strong finitisticity and finite approximability of a strongly finite consequence operation. Third, we formulate some conditions which tell us when the lattice (...)
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  5.  43
    Equivalents for a Quasivariety to Be Generated by a Single Structure.Wieslaw Dziobiak, A. V. Kravchenko & Piotr J. Wojciechowski - 2009 - Studia Logica 91 (1):113-123.
    We present some equivalent conditions for a quasivariety K of structures to be generated by a single structure. The first such condition, called the embedding property was found by A. I. Mal'tsev in [6]. It says that if A, B Є K are nontrivial, then there exists C Є X such that A and B are embeddable into C. One of our equivalent conditions states that the set of quasi-identities valid in X is closed under a certain Gentzen type rule (...)
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  6.  17
    Modal Logics Connected with Systems S4n of Sobociński.Jerzy J. Blaszczuk & Wieslaw Dziobiak - 1977 - Studia Logica 36 (3):151-164.
  7.  20
    There Are 2à0 Logics with the Relevance Principle Betweenr andRM.Wies?aw Dziobiak - 1983 - Studia Logica 42 (1):49-61.
    The aim of the paper is to prove the result announced by the title.
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  8.  28
    Joins of Minimal Quasivarieties.M. E. Adams & W. Dziobiak - 1995 - Studia Logica 54 (3):371 - 389.
    LetL(K) denote the lattice (ordered by inclusion) of quasivarieties contained in a quasivarietyK and letD 2 denote the variety of distributive (0, 1)-lattices with 2 additional nullary operations. In the present paperL(D 2) is described. As a consequence, ifM+N stands for the lattice join of the quasivarietiesM andN, then minimal quasivarietiesV 0,V 1, andV 2 are given each of which is generated by a 2-element algebra and such that the latticeL(V 0+V1), though infinite, still admits an easy and nice description (...)
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  9.  37
    In Memory of Willem Johannes Blok 1947-2003.Joel Berman, Wieslaw Dziobiak, Don Pigozzi & James Raftery - 2006 - Studia Logica 83 (1-3):5-14.
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  10.  29
    Strong Completeness with Respect to Finite Kripke Models.Wiesław Dziobiak - 1981 - Studia Logica 40 (3):249-252.
    We prove that each intermediate or normal modal logic is strongly complete with respect to a class of finite Kripke frames iff it is tabular, i.e. the respective variety of pseudo-Boolean or modal algebras, corresponding to it, is generated by a finite algebra.
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  11.  35
    From the Editors.M. E. Adams, K. V. Adaricheva, W. Dziobiak & A. V. Kravchenko - 2004 - Studia Logica 78 (1-2):3-5.
  12.  34
    The Degrees of Maximality of the Intuitionistic Propositional Logic and of Some of its Fragments.Wiesław Dziobiak - 1981 - Studia Logica 40 (2):195 - 198.
    Professor Ryszard Wójcicki once asked whether the degree of maximality of the consequence operationC determined by the theorems of the intuitionistic propositional logic and the detachment rule for the implication connective is equal to ? The aim of the present paper is to give the affirmative answer to the question. More exactly, it is proved here that the degree of maximality ofC — the — fragment ofC, is equal to , for every such that.
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  13.  25
    Cardinalities of Proper Ideals in Some Lattices of Strengthenings of the Intuitionistic Propositional Logic.Wies?aw Dziobiak - 1983 - Studia Logica 42 (2-3):173 - 177.
    We prove that each proper ideal in the lattice of axiomatic, resp. standard strengthenings of the intuitionistic propositional logic is of cardinality 20. But, each proper ideal in the lattice of structural strengthenings of the intuitionistic propositional logic is of cardinality 220. As a corollary we have that each of these three lattices has no atoms.
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  14.  43
    From the Editors.M. E. Adams & W. Dziobiak - 1996 - Studia Logica 56 (1-2):3-5.
  15.  46
    Concerning Axiomatizability of the Quasivariety Generated by a Finite Heyting or Topological Boolean Algebra.Wles?aw Dziobiak - 1982 - Studia Logica 41 (4):415 - 428.
    In classes of algebras such as lattices, groups, and rings, there are finite algebras which individually generate quasivarieties which are not finitely axiomatizable (see [2], [3], [8]). We show here that this kind of algebras also exist in Heyting algebras as well as in topological Boolean algebras. Moreover, we show that the lattice join of two finitely axiomatizable quasivarieties, each generated by a finite Heyting or topological Boolean algebra, respectively, need not be finitely axiomatizable. Finally, we solve problem 4 asked (...)
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  16.  24
    An Example of Strongly Finite Consequence Operation with 2ℵ0 Standard Strengthenings.Wies?aw Dziobiak - 1980 - Studia Logica 39 (4):375 - 379.
    Using ideas from Murskii [3], Tokarz [4] and Wroski [7] we construct some strongly finite consequence operation having 2%0 standard strengthenings. In this way we give the affirmative answer to the following question, stated in Tokarz [4]: are there strongly finite logics with the degree of maximality greater than 0?
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  17.  29
    Another Proof That ISP R is the Least Quasivariety Containing K.Janusz Czelakowski & Wies?aw Dziobiak - 1982 - Studia Logica 41 (4):343 - 345.
    Let q(K) denote the least quasivariety containing a given class K of algebraic structures. Mal'cev [3] has proved that q(K) = ISP r(K)(1). Another description of q(K) is given in Grätzer and Lakser [2], that is, q(K) = ISPP u(K)2. We give here other proofs of these results. The method which enables us to do that is borrowed from prepositional logics (cf. [1]).
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  18.  26
    On Detachment-Substitutional Formalization in Normal Modal Logics.Wieslaw Dziobiak - 1977 - Studia Logica 36 (3):165 - 171.
    The aim of this paper is to propose a criterion of finite detachment-substitutional formalization for normal modal systems. The criterion will comprise only those normal modal systems which are finitely axiomatizable by means of the substitution, detachment for material implication and Gödel rules.
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  19.  22
    Books Received. [REVIEW]Wiesław Dziobiak, Andrzej Wroński, Wojciech Suchoń, Jan Zygmunt & Ryszard Wójcicki - 1981 - Studia Logica 40 (4):415-421.
  20. Remarks on Perzanowski's Modal System'.J. J. Blaszczuk & W. Dziobiak - 1975 - Bulletin of the Section of Logic 4 (2):57-64.
    This paper was presented at the Seminar of the Section of Logic, In- stitute of Mathematics Nicholas Copernicus University, held by Professor Jerzy Kotas, Torun, March 1975. An altered version of the paper will be published in Studia Logica.
     
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  21.  13
    Foreword.Janusz Czelakowski, Wiesław Dziobiak & Jacek Malinowski - 2011 - Studia Logica 99 (1-3):1-6.
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  22. List of Published Papers Studia Logica 56 (1996), 277-290 Special Issue: Priestley Duality.M. E. Adams & W. Dziobiak - 1996 - Studia Logica 56:277-290.
     
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  23. Special Issue on Priestley Duality.M. Adams & W. Dziobiak - 1996 - Studia Logica 56:1-2.
  24. Modal Systems “Placed” in the Triangle S4− T 1*− T.J. J. Blaszczuk & W. Dziobiak - 1975 - Bulletin of the Section of Logic 4 (4):138-142.
     
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  25. On Truth-Schemes for Intensional Logics.Janusz Czelakowski & Wieslaw Dziobiak - 2006 - Reports on Mathematical Logic.
     
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  26.  31
    Deduction Theorems Within RM and Its Extensions.J. Czelakowski & W. Dziobiak - 1999 - Journal of Symbolic Logic 64 (1):279-290.
    In [13], M. Tokarz specified some infinite family of consequence operations among all ones associated with the relevant logic RM or with the extensions of RM and proved that each of them admits a deduction theorem scheme. In this paper, we show that the family is complete in a sense that if C is a consequence operation with $C_{RM} \leq C$ and C admits a deduction theorem scheme, then C is equal to a consequence operation specified in [13]. In algebraic (...)
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  27.  19
    There Are $2^{\Scr{N}_{0}}$ Logics with the Relevance Principle Between R and RM.Wiesław Dziobiak - 1983 - Studia Logica 42 (1):49-61.
    The aim of the paper is to prove the result announced by the title.
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  28.  33
    On finite approximability of psi-intermediate logics.Wies?aw Dziobiak - 1982 - Studia Logica 41:67.
    The aim of this note is to show (Theorem 1.6) that in each of the cases: = {, }, or {, , }, or {, , } there are uncountably many -intermediate logics which are not finitely approximable. This result together with the results known in literature allow us to conclude (Theorem 2.2) that for each : either all -intermediate logics are finitely approximate or there are uncountably many of them which lack the property.
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  29. Non-Existence of a Countable Strongly Adequate Matrix Semantics for Neighbours of E.Wieslaw Dziobiak - 1981 - Bulletin of the Section of Logic 10 (4):170-174.
    Very often logics are dened by means of the axiomatic method which depends, roughly speaking, on selecting some set of axiom schemas together with certain rules of inferences; here we consider only log- ics that are dened in this way. The representative examples are: E, R and INT. In the case of E and R the modus ponens rule and the rule of adjunction are used, while for INT the modus ponens only; all of them, of course, together with some (...)
     
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