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On Some Kripke Complete and Kripke Incomplete Intermediate Predicate Logics

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Abstract

The Kripke-completeness and incompleteness of some intermediate predicate logics is established. In particular, we obtain a Kripke-incomplete logic (H* +A+D+K) where H* is the intuitionistic predicate calculus, A is a disjunction-free propositional formula, D = ∀x(P(x) V Q) ⊃ ∀xP(x) V Q, K = ¬¬∀x(P(x) V ¬P(x)) (the negative answer to a question of T. Shimura).

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References

  1. Corsi, G., S. Ghilardi, 1989, ‘Directed frames’, Archive for Math. Logic 29, 53–67.

    Google Scholar 

  2. Gerchiu, V., A. Kuznetsov, 1970, ‘On finitely axiomatizable superintuitionistic logics’, Doklady Akademii Nauk SSSR (Soviet Mathematics, Doklady) 195, 1263–1266.

    Google Scholar 

  3. Ghilardi, S., 1989, ‘Presheaf semantics and independence results for some non-classical first-order logics’, Archive for Math. Logic 29, 125–136.

    Google Scholar 

  4. Ghilardi, S., 1991, ‘Incompleteness results in Kripke semantics’, Journal of Symbolic Logic 56, 517–538.

    Google Scholar 

  5. Shehtman, V., D. Skvortsov, 1990, ‘Semantics of non-classical first order predicate logics’, in Mathematical Logic, P. Petkov (ed.), Plenum Press, N. Y., 1990 (Proc. of Summer school and conference in math. logic Heyting'88), 105–116.

    Google Scholar 

  6. Shimura, T., 1993, ‘Kripke completeness of some intermediate predicate logics with the axiom of constant domain and a variant of canonical formulas’, Studia Logica 52, 23–40.

    Google Scholar 

  7. Skvortsov, D., 1996, ‘On finite intersections of intermediate predicate logics’, in Logic and Algebra, A. Ursini and P. Agliano (eds.), Marcel Decker, N. Y., (Proc. of Intern. Conf. on Logic and Algebra in memory of R. Magari, Siena, 1994), 667–688.

    Google Scholar 

  8. Skvortsov, D., ‘Some incompleteness result for predicate versions of propositional logics’ (in preparation).

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  1. All-Russian Institute of Scientific and Technical Information (VINITI), Usievicha 20A, 125219, Moscow, Russia

    Dmitrij Skvortsov

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  1. Dmitrij Skvortsov
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Skvortsov, D. On Some Kripke Complete and Kripke Incomplete Intermediate Predicate Logics. Studia Logica 61, 281–292 (1998). https://doi.org/10.1023/A:1005029515564

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