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25Arithmetic of divisibility in finite modelsMathematical Logic Quarterly 50 (2): 169. 2004.We prove that the finite-model version of arithmetic with the divisibility relation is undecidable . Additionally we prove FM-representability theorem for this class of finite models. This means that a relation R on natural numbers can be described correctly on each input on almost all finite divisibility models if and only if R is of degree ≤0′. We obtain these results by interpreting addition and multiplication on initial segments of finite models with divisibility only
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22The Diagrams of Formulas of the Modal Propositional $\text{S}4^{\ast}$ CalculusStudia Logica 30 (1): 69-78. 1972.
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28The diagrams of formulas of the intuitionistic propositional calculusStudia Logica 32 (1). 1973.
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30The diagrams of formulas of the modal propositional S4* calculusStudia Logica 30 (1): 69-76. 1972.
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30Trees and diagrams of decompositionStudia Logica 44 (2). 1985.We introduce here and investigate the notion of an alternative tree of decomposition. We show (Theorem 5) a general method of finding out all non-alternative trees of the alternative tree determined by a diagram of decomposition.
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27Some Remarks on Theorem Proving Systems and Mazurkiewicz Algorithms Associated with themZeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (19-20): 289-294. 1985.
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23A sequence formalization for SCIStudia Logica 35 (3). 1976.This paper can be treated as a simplification of the Gentzen formalization of SCI-tautologies presented by A. Michaels in [1].
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16Some Remarks on Theorem Proving Systems and Mazurkiewicz Algorithms Associated with themMathematical Logic Quarterly 31 (19‐20): 289-294. 1985.
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15Deterministic Algorithms, Simple Languages And One‐to‐One Gentzen Type FormalizationsMathematical Logic Quarterly 32 (10‐12): 181-188. 1986.
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35DFC-algorithms for Suszko logic and one-to-one Gentzen type formalizationsStudia Logica 43 (4). 1984.We use here the notions and results from algebraic theory of programs in order to give a new proof of the decidability theorem for Suszko logic SCI (Theorem 3).We generalize the method used in the proof of that theorem in order to prove a more general fact that any prepositional logic which admits a cut-free Gentzen type formalization is decidable (Theorem 6).
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30Programs and logicsStudia Logica 44 (2). 1985.We use the algebraic theory of programs as in Blikle [2], Mazurkiewicz [5] in order to show that the difference between programs with and without recursion is of the same kind as that between cut free Gentzen type formalizations of predicate and prepositional logics.
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31Deterministic Algorithms, Simple Languages And One‐to‐One Gentzen Type FormalizationsMathematical Logic Quarterly 32 (10-12): 181-188. 1986.
Areas of Specialization
Science, Logic, and Mathematics |
Areas of Interest
Science, Logic, and Mathematics |