8 found
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  1.  20
    On Interpretability in the Theory of Concatenation.Vítězslav Švejdar - 2009 - Notre Dame Journal of Formal Logic 50 (1):87-95.
    We prove that a variant of Robinson arithmetic $\mathsf{Q}$ with nontotal operations is interpretable in the theory of concatenation $\mathsf{TC}$ introduced by A. Grzegorczyk. Since $\mathsf{Q}$ is known to be interpretable in that nontotal variant, our result gives a positive answer to the problem whether $\mathsf{Q}$ is interpretable in $\mathsf{TC}$. An immediate consequence is essential undecidability of $\mathsf{TC}$.
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  2.  44
    The Decision Problem of Provability Logic with Only One Atom.Vítězslav Švejdar - 2003 - Archive for Mathematical Logic 42 (8):763-768.
    The decision problem for provability logic remains PSPACE-complete even if the number of propositional atoms is restricted to one.
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  3.  17
    Modal Analysis of Generalized Rosser Sentences.Vítězslav Švejdar - 1983 - Journal of Symbolic Logic 48 (4):986-999.
    A modal theory Z using the Guaspari witness comparison signs $\leq, is developed. The theory Z is similar to, but weaker than, the theory R of Guaspari and Solovay. Nevertheless, Z proves the independence of the Rosser fixed-point. A Kripke semantics for Z is presented and some arithmetical interpretations of Z are investigated. Then Z is enriched to ZI by adding a new modality sign for interpretability and by axioms expressing some facts about interpretability of theories. Two arithmetical interpretations of (...)
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  4.  79
    On the Polynomial-Space Completeness of Intuitionistic Propositional Logic.Vítězslav Švejdar - 2003 - Archive for Mathematical Logic 42 (7):711-716.
    We present an alternative, purely semantical and relatively simple, proof of the Statman's result that both intuitionistic propositional logic and its implicational fragment are PSPACE-complete.
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  5.  32
    Some Independence Results in Interpretability Logic.Vítězslav Švejdar - 1991 - Studia Logica 50 (1):29 - 38.
    A Kripke-style semantics developed by de Jongh and Veltman is used to investigate relations between several extensions of interpretability logic, IL.
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  6.  37
    On Interplay of Quantifiers in Gödel-Dummett Fuzzy Logics.Blanka Kozlíková & Vítězslav Švejdar - 2006 - Archive for Mathematical Logic 45 (5):569-580.
    Axiomatization of Gödel-Dummett predicate logics S2G, S3G, and PG, where PG is the weakest logic in which all prenex operations are sound, and the relationships of these logics to logics known from the literature are discussed. Examples of non-prenexable formulas are given for those logics where some prenex operation is not available. Inter-expressibility of quantifiers is explored for each of the considered logics.
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  7.  18
    On Provability Logic.Vıtezslav Švejdar - 1999 - Nordic Journal of Philosophical Logic 4 (2):95-116.
  8.  24
    A Note on the Normal Form of Closed Formulas of Interpretability Logic.Petr Hájek & Vítězslav Švejdar - 1991 - Studia Logica 50 (1):25 - 28.
    Each closed (i.e. variable free) formula of interpretability logic is equivalent in ILF to a closed formula of the provability logic G, thus to a Boolean combination of formulas of the form n.
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