Linear Logic Maybe?

From: Jan Burse (janburse_at_fastmail.fm)
Date: 02/10/05

  • Next message: Bart Demoen: "Re: Linear Logic Maybe?" 
    Date: Thu, 10 Feb 2005 00:40:52 +0100

    Dear All

    I am working on an algebra for some
    language processing. The language
    processing includes the combination
    of nouns, verbs and adjectives.

    So I came up first with the
    following connectives:

       A & B: Conjunction
       A v B: Disjunction

    And some rules, for example
    disjunctive normal form:

       A & (B v C) --> (A & B) v (A & C)
       etc..

    This works pretty well for some
    language phaenomena. For example
    "roof, window and door", kann be
    modeled by &, and so on.

    Now I was introducing the following
    two connectives:

        A ! B: Composition
        A ? B: Guard

    And the rules are as such:

        A ! (B ! C) --> (A ! B) ! C
        (A & B) ! C --> A ! C & B ! C (i)
        A ! (B & C) --> A ! B & A ! C (ii)
        etc..
        (A ? B) ! C --> (B ! A) & (B ! C) (iii)
        etc..

    This works pretty well for some
    language phaenomena. For example
    "the green door is open" can be
    modelled by (green?door)!open.

    But now, as I dont have any clue
    what algebra this might be, so that
    I can lookup up the algebras properties,
    many questions arise. For example

    1) Does the order of application
        of the rules (i) and (ii) make
        any difference in the normal form?
        (answer = yes, guess why?)

    2) Similar questions in the interaction
        between ? and !, not yet answered
        for my self.

    Any pointers welcome?

    Best Regards 

    ---
Spuntik III
  • Next message: Bart Demoen: "Re: Linear Logic Maybe?"

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