Studia Logica

, Volume 39, Issue 4, pp 335–345 | Cite as

Set theory as modal logic

  • Herman Dishkant
Article
  • 53 Downloads

Abstract

A logical systemBM+ is proposed, which, is a prepositional calculus enlarged with prepositional quantifiers and with two modal signs, □ and Δ These modalities are submitted to a finite number of axioms. □ is the usual sign of necessity, Δ corresponds to transmutation of a property (to be white) into the abstract property (to be the whiteness). An imbeddingσ of the usual theory of classesM intoBM+ is constructed, such that a formulaA is provable inM if and only ifσ(A) is provable inBM+. There is also an inverse imbeddingπ with an analogous property.

Keywords

Finite Number Mathematical Logic Modal Logic Modal Sign Computational Linguistic 

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References

  1. [1]
    A. Tarski,Logic, Semantics, Metamathematics, Oxford, 1956.Google Scholar
  2. [2]
    K. Fine,Propositional quantifiers in modal logic,Theoria 36 (1970), pp. 336–346.Google Scholar
  3. [3]
    A. Morse,A theory of sets, Academic Press, N.-Y., 1965.Google Scholar
  4. [4]
    A. Mostowski,Constructible sets with applications, Amsterdam, 1969.Google Scholar

Copyright information

© Polish Academy of Sciences 1980

Authors and Affiliations

  • Herman Dishkant
    • 1
  1. 1.University of KalininUSSR

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