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  1.  29
    On the Degree of Complexity of Sentential Logics. A Couple of Examples.Jacek Hawranek & Jan Zygmunt - 1981 - Studia Logica 40 (2):141 - 153.
    The first part of the paper is a reminder of fundamental results connected with the adequacy problem for sentential logics with respect to matrix semantics. One of the main notions associated with the problem, namely that of the degree of complexity of a sentential logic, is elucidated by a couple of examples in the second part of the paper. E.g., it is shown that the minimal logic of Johansson and some of its extensions have degree of complexity 2. This is (...)
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  2.  21
    A Matrix Adequate for S5 with Mp and Rn.Jacek Hawranek - 1980 - Bulletin of the Section of Logic 9 (3):122-123.
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  3.  36
    A Theorem of the Degree of Complexity of Some Sentential Logics.Jacek Hawranek & Jan Zygmunt - 1980 - Bulletin of the Section of Logic 9 (2):67-69.
    x1. This paper is a contribution to matrix semantics for sentential logics as presented in Los and Suszko [1] and Wojcicki [3], [4]. A generalization of Lindenbaum completeness lemma says that for each sentential logic there is a class K of matrices of the form such that the class is adequate for the logic, i.e., C = CnK.
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  4.  27
    Some Elementary Properties of Conditionally Distributive Lattices.Jacek Hawranek & Jan Zygmunt - 1983 - Bulletin of the Section of Logic 12 (3):117-120.
    The notion of a conditionally distributive lattice was introduced by B. Wolniewicz while formally investigating the ontology of situations . In several of this lectures he has appealed for a study of that class of lattices. The present abstract is a response to that request.
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  5.  26
    On the Degree of Complexity of Sentential Logics.II. An Example of the Logic with Semi-Negation.Jacek Hawranek & Jan Zygmunt - 1984 - Studia Logica 43 (4):405 - 413.
    In this paper being a sequel to our [1] the logic with semi-negation is chosen as an example to elucidate some basic notions of the semantics for sentential calculi. E.g., there are shown some links between the Post number and the degree of complexity of a sentential logic, and it is proved that the degree of complexity of the sentential logic with semi-negation is 20. This is the first known example of a logic with such a degree of complexity. The (...)
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  6.  15
    Some Examples Concerning Uniformity and Complexity of Sentential Logics.Jacek Hawranek - 1980 - Bulletin of the Section of Logic 9 (2):71-72.
    This abstract is a contribution to the paper by R. Wojcicki [2]. We use the terminology introduced there, . In this note we show that 1 0 For each n 2 there exists a logic whose degree of uniformity and degree of complexity are both equal to n. 2 0 There is a logic with the degree of uniformity equal to 2 @0 but with the degree of complexity equal to @0.
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  7.  27
    Another Proof of Wojtylak's Theorem.Jacek Hawranek & Jan Zygmunt - 1981 - Bulletin of the Section of Logic 10 (2):80-81.
    The aim of this note is to give an example of application of model theory to the theory of logical matrices. . More precisely, we show that Wojtylak's representation theorem is an immediate consequence of a result due to Mal'cev . Throughout the present note we assume that matrices, and classes of matrices under consideration are of the same xed similarity type. Suppose that K is an arbitrary class of matrices, and M is a matrix . We say that M1 (...)
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  8.  33
    A Representation Theorem for Co-Diagonalizable Algebras.Jacek Hawranek - 1985 - Bulletin of the Section of Logic 14 (3):124-125.
    The present work refers directly to the investigations of Buszkowski and Prucnal [1] and that of Esakia [2], generalizing their results. Our main representation theorem for co-diagonalizable algebras is obtained by application of certain methods taken from J´onsson-Tarski [3].
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  9.  20
    A Topological Interpretation of Diagonalizable Algebras.Jacek Hawranek - 1990 - Bulletin of the Section of Logic 19 (4):117-121.
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  10.  30
    Comments on a Question of Wolniewicz.Jacek Hawranek & Jan Zygmunt - 1990 - Bulletin of the Section of Logic 19 (4):128-132.
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  11.  15
    Notes on the Semantics for the Logic with Semi-Negation.Jacek Hawranek & Jan Zygmunt - 1983 - Bulletin of the Section of Logic 12 (4):152-155.
    . In our paper, presented here in abstract form, we consider the sentential logic with semi-negation. It should be stressed, however, that our main interest is not that logic itself but rather more general matters concerning the theory of matrix semantics for sentential logics. The logic with semi-negation provides a relevant example for elucidating such basic notions of matrix semantics as degree of complexity, degree of uniformity, and self-referentiality. Thus our paper being a contribution to the theory of matrix semantics (...)
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  12.  24
    On the Degree of Complexity of Sentential Logics, III. An Example of Johansson's Minimal Logic.Jacek Hawranek - 1987 - Studia Logica 46 (4):283 - 289.
    The present paper is to be considered as a sequel to [1], [2]. It is known that Johansson's minimal logic is not uniform, i.e. there is no single matrix which determines this logic. Moreover, the logic C J is 2-uniform. It means that there are two uniform logics C 1, C 2 (each of them is determined by a single matrix) such that the infimum of C 1 and C 2 is C J. The aim of this paper is to (...)
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  13.  16
    On the Degree of Matrix Complexity of Johansson's Minimal Logic.Jacek Hawranek - 1984 - Bulletin of the Section of Logic 13 (1):50-52.
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