Re: knowledge and belief

[bob@MEGALITH.RATTLESNAKE.COM]

   I will not attempt to resume discussion of how to express fuzzy levels of
   truth.  This is one of those areas where a summary of where the last
   overly technical discussion ended up would be useful to those of us who
   never quite followed most of it.

Here is an attempt to rise to the challenge, with a certainty factor of about
0.3 that I will succeed.... :-)

The scales use four cmavo, for four concepts:

    ja'a      NA    bridi affirmer
                      bridi logical affirmer; scope is an entire bridi

    je'a      NAhE  scalar affirmer
                      scalar affirmer; denies scalar negation: Indeed!


    ju'o      UI5   certainty
                      attitudinal modifier: certainty - uncertainty -
                      impossibility

    la'a      UI3   probability
                      discursive: probability - improbability


For example,

 * True in the espistemology:

    i. ja'a la djan. pu klama la paris. .e la rom.
    Definately, it is true that John went to both Paris and Rome.

 * 0.8 truth value in a fuzzy truth espistemology where the
   binary opposites are true and false:

    i. ja'a xipibi la djan. pu klama la paris. .e la rom.
    In fuzzy truth terms, it is about 0.8 true
        that John went to both Paris and Rome.

 * Subtly different kind of 0.8 truth value, suggesting that the
   binary opposites are alternatives of a different sort than true and
   false (perhaps John went to London and Copenhagen).

    i. la djan. je'a xipibi pu klama la paris. .e la rom.
    In fuzzy truth terms, there is about a 0.8 sense that
        John went to both Paris and Rome, rather than some alternative.


Truth values are different from certainty factors, which indicate your
judgement of the quality of your assertion.  The difference is between
being 100% sure you are seeing *either* a dog or a wolf in the
distance and being 80% certain that what your are seeing is really and
truly a wolf.

In previous postings I have discussed a scale that enables you to
`add' two `strongly suggestive' estimates of your certainly to get a
`very strongly suggestive' estimate (you never get 100% certainty).

 * Certainty:

    i. ju'o mi viska ca'o lo labno
    I am certain that I am now seeing what is truly a wolf.

 * 0.8 certainty

    i. ju'o xipibi mi ca'o viska lo rebla pe lo labno
    I feel strongly confident (0.8 on a certainty factor scale)
    that I am seeing a tail of a wolf.

    i. ju'o xipixa mi ca'o viska lo mebri pe lo labno
    I feel somewhat confident (0.6 on a certainty factor scale)
    that I am seeing the brow of a wolf.

    i. ju'o xipisore mi viska ca'o lo labno
    I feel very strongly confident (0.92 on a certainty factor scale)
    that I am seeing a wolf.


The rule for adding two positive certainty factors is:

    CFcombine (CFa CFb) = CFa + CFb(1 - Cfa)
                .92     =  .6 + .8(1 - .6)

I.e., reduce the influence of the second certainty factor by the
remaining uncertainty of the first, and add the result to the
certainty of the first.

Finally, probabilities are expressed in a familiar fashion:

    i. la'a xipinore mi ba viska lo labno ca le bavlamdei
    There is a 2% probability I will see a wolf tomorrow.

--

    Robert J. Chassell               bob@rattlesnake.com
    P. O. Box 693                    bob@ai.mit.edu
    Stockbridge, MA 01262-0693 USA   (413) 298-4725