18 found
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  1.  25
    Modal Consequence Relations Extending $Mathbf{S4.3}$: An Application of Projective Unification.Wojciech Dzik & Piotr Wojtylak - 2016 - Notre Dame Journal of Formal Logic 57 (4):523-549.
    We characterize all finitary consequence relations over S4.3, both syntactically, by exhibiting so-called passive rules that extend the given logic, and semantically, by providing suitable strongly adequate classes of algebras. This is achieved by applying an earlier result stating that a modal logic L extending S4 has projective unification if and only if L contains S4.3. In particular, we show that these consequence relations enjoy the strong finite model property, and are finitely based. In this way, we extend the known (...)
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  2.  31
    Matrix Representations for Structural Strengthenings of a Propositional Logic.Piotr Wojtylak - 1979 - Studia Logica 38 (3):263 - 266.
    The aim of this paper is to show that the operations of forming direct products and submatrices suffice to construct exhaustive semantics for all structural strengthenings of the consequence determined by a given class of logical matrices.
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  3.  13
    Unification in Superintuitionistic Predicate Logics and its Applications.Wojciech Dzik & Piotr Wojtylak - 2019 - Review of Symbolic Logic 12 (1):37-61.
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  4.  61
    On Structural Completeness of Many-Valued Logics.Piotr Wojtylak - 1978 - Studia Logica 37 (2):139 - 147.
    In the paper some consequence operations generated by ukasiewicz's matrices are examined.
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  5.  24
    Strongly Finite Logics: Finite Axiomatizability and the Problem of Supremum.Piotr Wojtylak - 1979 - Bulletin of the Section of Logic 8 (2):99-111.
    This paper, which in its subject matter goes back to works on strongly nite logics , is concerned with the following problems: Let Cn1; Cn2 be two strongly nite logics over the same propositional language. Is the supremum of Cn1 and Cn2 also a strongly nite operation? Is any nite matrix axiomatizable by a nite set of standard rules? The rst question can be found in [9] . The second conjec- ture was formulated by Wolfgang Rautenberg, but investigations into this (...)
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  6.  7
    Almost Structurally Complete Infinitary Consequence Operations Extending S4.3.Wojciech Dzik & Piotr Wojtylak - 2015 - Logic Journal of the IGPL 23 (4):640-661.
  7.  4
    Finitary Unification in Locally Tabular Modal Logics Characterized.Wojciech Dzik, Sławomir Kost & Piotr Wojtylak - 2022 - Annals of Pure and Applied Logic 173 (4):103072.
  8.  19
    Independent Axiomatizability of Sets of Sentences.Piotr Wojtylak - 1989 - Annals of Pure and Applied Logic 44 (3):259-299.
    This is an expository paper on the problem of independent axiomatization of any set of sentences. This subject was investigated in 50's and 60's, and was abandoned later on, though not all fundamental questions were settled then. Besides, some papers written at that time are hardly available today and there are mistakes and misunderstandings there. We would like to get back to that unfinished business to clarify the subject matter, correct mistakes and answer questions left open by others. We shall (...)
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  9.  25
    On Structural Completeness of Implicational Logics.Piotr Wojtylak - 1991 - Studia Logica 50 (2):275 - 297.
    We consider the notion of structural completeness with respect to arbitrary (finitary and/or infinitary) inferential rules. Our main task is to characterize structurally complete intermediate logics. We prove that the structurally complete extension of any pure implicational in termediate logic C can be given as an extension of C with a certain family of schematically denned infinitary rules; the same rules are used for each C. The cardinality of the family is continuum and, in the case of (the pure implicational (...)
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  10.  12
    Entailment Relations and Matrices I.Piotr Wojtylak - 1979 - Bulletin of the Section of Logic 8 (2):112-115.
  11.  44
    A Proof System for Classical Logic.Witold A. Pogorzelski & Piotr Wojtylak - 2005 - Studia Logica 80 (1):95-104.
    An operation on inferential rules, called H-operation, is used to minimize the axiom basis for classical logic.
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  12.  22
    Generalizing Proofs in Monadic Languages.Matthias Baaz & Piotr Wojtylak - 2008 - Annals of Pure and Applied Logic 154 (2):71-138.
    This paper develops a proof theory for logical forms of proofs in the case of monadic languages. Among the consequences are different kinds of generalization of proofs in various schematic proof systems. The results use suitable relations between logical properties of partial proof data and algebraic properties of corresponding sets of linear diophantine equations.
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  13.  5
    Unification in First-Order Transitive Modal Logic.Wojciech Dzik & Piotr Wojtylak - forthcoming - Logic Journal of the IGPL.
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  14.  14
    A Syntactical Characterization of Structural Completeness for Implicational Logics.Piotr Wojtylak - 1990 - Bulletin of the Section of Logic 19 (1):2-8.
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  15.  55
    Cn-Definitions of Propositional Connectives.Witold A. Pogorzelski & Piotr Wojtylak - 2001 - Studia Logica 67 (1):1-26.
    We attempt to define the classical propositional logic by use of appropriate derivability conditions called Cn-definitions. The conditions characterize basic properties of propositional connectives.
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  16.  15
    A New Proof of Structural Completeness of Lukasiewicz's Logics.Piotr Wojtylak - 1976 - Bulletin of the Section of Logic 5 (4):145-150.
  17.  2
    Witold A. Pogorzelski.Piotr Wojtylak - 2005 - Studia Logica 80 (1):95-104.
    An operation on inferential rules, called H-operation, is used to minimize the axiom basis for classical logic.
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  18.  9
    On Structural Completeness of the Infinite-Valued Lukasiewicz's Propositional Calculus.Piotr Wojtylak - 1976 - Bulletin of the Section of Logic 5 (4):153-156.
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