Re: Godel's Incompleteness and Nonmonotonic Logic

From: Student (jagasian_at_mailinator.com)
Date: 08/24/04

  • Next message: Student: "Re: Godel's Incompleteness and Nonmonotonic Logic" 
    Date: 24 Aug 2004 14:41:03 -0700

    > Does "Answer Set Logic" have anything to do with negation by failure?
    > To get the kind of paradox you're after, one would at least imagine
    > provability to have to be decidable.

    Decidability is a separate issue. The problem is that an inconsistent
    logic will allow for incorrect answers.

    > How to stitch this together with second order logics to which Goedels
    > incompleteness theorems refer escapes me.

    Godel's two famous theorems apply to first-order predicate logic. See
    Kleene's "Introduction to Metamathematics", Kleene's "Mathematical
    Logic", or Girard's "Proof Theory and Logical Complexity : Volume I",
    if you cannot get your hands on the Godel's original work (or a
    translation thereof).

    > Closed world assumption, which is a more mainstream representative of
    > the kind of nonmonotonic logics you seem to be talking about,
    > guarantees "Hilbert completeness" only wrt ground atomic formulae.

    Well, the answer set style logics work with non-ground formula by
    assuming a possibly infinite grounding. See "Knowledge
    Representation, Reasoning, and Declarative Problem Solving" by Chitta
    Baral.

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