The Modal Logic of Gödel Sentences

Journal of Philosophical Logic 39 (5):577 - 590 (2010)
Abstract
The modal logic of Gödel sentences, termed as GS, is introduced to analyze the logical properties of 'true but unprovable' sentences in formal arithmetic. The logic GS is, in a sense, dual to Grzegorczyk's Logic, where modality can be interpreted as 'true and provable'. As we show, GS and Grzegorczyk's Logic are, in fact, mutually embeddable. We prove Kripke completeness and arithmetical completeness for GS. GS is also an extended system of the logic of 'Essence and Accident' proposed by Marcos (Bull Sect Log 34(1):43-56, 2005). We also clarify the relationships between GS and the provability logic GL and between GS and Intuitionistic Propositional Logic
Keywords Modal logic  Gödel incompleteness theorems
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,360
External links
  • Through your library Configure
    References found in this work BETA
    Joao Marcos (2005). Logics of Essence and Accident. Bulletin of the Section of Logic 34 (1):43-56.

    View all 6 references

    Citations of this work BETA

    No citations found.

    Similar books and articles
    Analytics

    Monthly downloads

    Added to index

    2010-06-09

    Total downloads

    49 ( #27,976 of 1,089,047 )

    Recent downloads (6 months)

    2 ( #42,773 of 1,089,047 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature


    Discussion
    Start a new thread
    Order:
    There  are no threads in this forum
    Nothing in this forum yet.