Quantum logic as a fragment of independence-friendly logic

Journal of Philosophical Logic 31 (3):197-209 (2002)
Abstract
The working assumption of this paper is that noncommuting variables are irreducibly interdependent. The logic of such dependence relations is the author's independence-friendly (IF) logic, extended by adding to it sentence-initial contradictory negation ¬ over and above the dual (strong) negation ∼. Then in a Hilbert space ∼ turns out to express orthocomplementation. This can be extended to any logical space, which makes it possible to define the dimension of a logical space. The received Birkhoff and von Neumann "quantum logic" can be interpreted by taking their "disjunction" to be ¬(∼A & ∼ B). Their logic can thus be mapped into a Boolean structure to which an additional operator ∼ has been added
Keywords quantum logic  independence-friendly logic  negation  Boolean structures
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

    No references found.

    Citations of this work BETA
    Jaakko Hintikka (2004). Independence-Friendly Logic and Axiomatic Set Theory. Annals of Pure and Applied Logic 126 (1-3):313-333.
    Similar books and articles
    Analytics

    Monthly downloads

    Added to index

    2009-01-28

    Total downloads

    32 ( #45,914 of 1,089,047 )

    Recent downloads (6 months)

    3 ( #30,948 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.