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11.
Petr Hájek 《Studia Logica》2002,71(2):149-164
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The Hybrid Logic of Linear Set Spaces 总被引:1,自引:0,他引:1
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A finitary characterization for non-well-founded sets with finite transitive closure is established in terms of a greatest fixpoint formula of the modal -calculus. This generalizes the standard result in the literature where a finitary modal characterization is provided only for wellfounded sets with finite transitive closure. The proof relies on the concept of automaton, leading then to new interlinks between automata theory and non-well-founded sets. 相似文献
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This paper is the final part of the syntactic demonstration of the Arithmetical Completeness of the modal system G; in the
preceding parts [9] and [10] the tools for the proof were defined, in particular the notion of syntactic countermodel. Our
strategy is: PA-completeness of G as a search for interpretations which force the distance between G and a GL-LIN-theorem
to zero. If the GL-LIN-theorem S is not a G-theorem, we construct a formula H expressing the non G-provability of S, so that
⊢GL-LIN ∼ H and so that a canonical proof T of ∼ H in GL-LIN is a syntactic countermodel for S with respect to G, which has the height
θ(T) equal to the distance d(S, G) of S from G. Then we define the interpretation ξ of S which represents the proof-tree T
in PA. By induction on θ(T), we prove that ⊢PA Sξ and d(S, G) > 0 imply the inconsistency of PA.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Behthem's modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap's display logic by introduction rules for the existential and the universal quantifier. These rules for x and x are analogous to the display introduction rules for the modal operators and and do not themselves allow the Barcan formula or its converse to be derived. En route from the minimal modal predicate logic to full first-order logic, axiomatic extensions are captured by purely structural sequent rules. 相似文献
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Maciej Sendłak 《Metaphilosophy》2018,49(1-2):153-166
The distinction between quantitative and qualitative parsimony is supposed to allow David Lewis to dismiss one of the charges against his modal realism: that is, the charge of bloated ontology. The aim of this paper is to undermine Lewis's response to this objection. In order to do this, a distinction between multipliable and nonmultipliable objects is introduced. Based on this it is argued that the acceptance of Lewis's response requires one to believe in modal realism in the first place—that is, one has to believe in the view that the existence of nonactual spatiotemporal worlds does not affect the quality of the ontological commitment. Although the paper focuses on the problem of the metaphysics of possible worlds, this should be regarded merely as a case study. Accordingly, the results of this analysis should find applications in other metaphysical debates as well. 相似文献
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