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22Arithmetic 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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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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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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31Deterministic Algorithms, Simple Languages And One‐to‐One Gentzen Type FormalizationsMathematical Logic Quarterly 32 (10-12): 181-188. 1986.
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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.
Areas of Specialization
Science, Logic, and Mathematics |
Areas of Interest
Science, Logic, and Mathematics |