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2017 | 46 | 1/2 |

Tytuł artykułu

Some Weak Variants of the Existence and Disjunction Properties in Intermediate Predicate Logics

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EN

Abstrakty

EN
We discuss relationships among the existence property, the disjunction property, and their weak variants in the setting of intermediate predicate logics. We deal with the weak and sentential existence properties, and the Z-normality, which is a weak variant of the disjunction property. These weak variants were presented in the author’s previous paper [16]. In the present paper, the Kripke sheaf semantics is used.

Rocznik

Tom

46

Numer

1/2

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Daty

wydano
2017-06-30

Twórcy

  • Shizuoka University, Department of Mathematics, Faculty of Science, Ohya 836, Suruga-Ku Shizuoka 422–8529, Japan

Bibliografia

  • [1] A. Church, Introduction toMathematical Logic I, Princeton University Press, Princeton (1956).
  • [2] L. M. Doorman, A note on the existence property for intuitionistic logic with function symbols, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 36 (1990), pp. 17–21.
  • [3] D. M. Gabbay, V. B. Shehtman and D. P. Skvortsov, Quantification in nonclassical logic. Vol. 1, Studies in Logic and the Foundations of Mathematics, 153. Elsevier, Amsterdam (2009).
  • [4] H. Ishihara and T. Nemoto, A note on the independence of premiss rule, Mathematical Logic Quarterly, to appear.
  • [5] S. C. Kleene, Introduction to metamathematics, D. Van Nostrand Co., Inc., New York 1952.
  • [6] S. C. Kleene, Disjunction and existence under implication in elementary intuitionistic formalisms, Journal of Symbolic Logic 27 (1962), pp. 11–18. (An addendum, the same journal 28 (1963), pp. 154–156.)
  • [7] Y. Komori, Some results on the super-intuitionistic predicate logics, Reports on Mathematical Logic 15 (1983), pp. 13–31.
  • [8] P. Minari, Disjunction and existence properties in intermediate predicate logics, Atti del Congresso Logica e Filosofia della Scienza, oggi. San Gimignano, 7–11 dicembre 1983. Vol. I – Logica. (1986), CLUEB, Bologna (Italy).
  • [9] T. Nakamura, Disjunction property for some intermediate predicate logics, Reports on Mathematical Logic 15 (1983), pp. 33–39.
  • [10] H. Ono, A study of intermediate predicate logics, Publications of the Research Institute for Mathematical Sciences 8 (1972/73), pp. 61–649.
  • [11] H. Ono, Some problems in intermediate predicate logics, Reports onMathematical Logic 21 (1987), pp. 55–67. (Supplement 22 (1988), pp. 117–118.)
  • [12] D. Prawitz, Natural deduction. A proof-theoretical study, Acta Universitatis Stockholmiensis. Stockholm Studies in Philosophy, No. 3 Almqvist & Wiksell, Stockholm 1965. (Reprint: Dover Publications, 2006)
  • [13] N.-Y. Suzuki, A remark on the delta operation and the Kripke sheaf semantics in super-intuitionistic predicate logics, Bulletin of the Section of Logic, University of Łódź, 25 (1996), pp. 21–28.
  • [14] N.-Y. Suzuki, Algebraic Kripke sheaf semantics for non-classical predicate logics Studia Logica 63 (1999), pp. 387–416.
  • [15] N.-Y. Suzuki, Halldén-completeness in super-intuitionistic predicate logics, Studia Logica 73 (2003), pp. 113–130
  • [16] N.-Y. Suzuki, A negative solution to Ono’s problem P52: Existence and disjunction properties in intermediate predicate Logics, to appear.
  • [17] A. S. Troelstra and D. van Dalen, Constructivism in mathematics, Vol. I. An introduction, Studies in Logic and the Foundations of Mathematics, 121. North-Holland, Amsterdam, 1988.
  • [18] T. Umezawa, “Chūkan jutsugo ronri” (Intermediate predicate logics) (in Japanese), Gekkan Masematikusu, Vol. 1, No. 2 (1980), pp. 162–168. Kaiyo Shuppan Co., Ltd.

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Bibliografia

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