IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4613-0609-2_19.html

Normal Modal Logics in Which the Heyting Propositional Calculus can be Embedded

In: Mathematical Logic

Author

Listed:
  • Kosta Došen

    (Matematički Institut)

Abstract

Let t(A) be the result of prefixing the necessity operator ❑ to every proper subformula, save conjunctions and disjunctions, of the formula A of the language of the Heyting propositional calculus H. It is well-known that H can be embedded by t in S4, i.e. A is provable in H iff t(A) is provable in S4. Esakia (1979), and also Blok (1976), have shown that S4Grz (defined below) is the maximal normal extension of S4 in which H can be embedded by t (as a matter of fact, we find in Esakia (1979) not t, but the translation which prefixes ❑ to every subformula; this translation is equivalent to t as far as S4 and its normal extensions are concerned).

Suggested Citation

  • Kosta Došen, 1990. "Normal Modal Logics in Which the Heyting Propositional Calculus can be Embedded," Springer Books, in: Petio Petrov Petkov (ed.), Mathematical Logic, pages 281-291, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0609-2_19
    DOI: 10.1007/978-1-4613-0609-2_19
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-1-4613-0609-2_19. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.