|From:||Jawit Kien <jawit.kien@xxxxxxxxx>|
|Date:||Fri, 12 Feb 2010 10:11:26 -0600|
I must say, Rich, that your more formal presentation is quite accomplished, but I'm not|
sure I understand it. Likewise, I find it surprising that no one has commented on it to date.
I will attempt to do so, but clearly, you have a lot more thought behind this than I can examine
On Mon, Feb 8, 2010 at 7:32 PM, Rich Cooper <rich@xxxxxxxxxxxxxxxxxxxxxx> wrote:
So to use John Sowa's favorite sentence: A cat is on a mat.
I see that there are five words in alphabetical order:
Are these the "terminal linguistic symbols" ?
Alternately, Using the grammar:
<sentence> := <NP> <VERB> <NP>
<NP> := <ADJ> <NOUN>
<NP> := <PREP> <ADJ> <NOUN>
<VERB> := "is"
<PREP> := "on"
<NOUN> := "cat" | "mat"
<ADJ> := "a"
there are phrases: (again in alphabetical order)
1) "a cat"
2) "a cat is on a mat" : alternately "(1) is (4)"
3) "a mat"
4) "on a mat" : alternately "on (2)"
Are these your "terminal linguistic symbols" ?
John Sowa's analysis
(∃x:Cat)(∃y:Mat)on(x,y).ie: ThereExists X such X is a Cat
ThereExists Y such that Y is a Mat
the function "on" holds between that X and that Y.
Are any of these your "terminal linguistic symbols" ?
I understand a theory as a collection of axioms and theorems or alternately a set of facts and rules.
The subject of each of your theories is a boolean function of a terminal linguistic symbols?
So for our "a cat on a mat" statement is your theory applied to the sentence as a whole
ie: you have T["a cat on a mat"] ? what does it mean to have a boolean result of a sentence?
and is it a logical statement that is the result, and you
or is the result of your T[j] the
What are you trying to predict them to be? since it is supposed to be a boolean function, are you trying to predict that they are true or false?
"got there" implies you are using a metaphor/analogy here.
Perhaps that the calculation is "moving along some path" and each "milestone" along the path is the value of T, T, T, up to milestone T[j].
Could you elaborate more about this movement? What does it mean to make a "step" along the path? Since paths have surfaces, what does the surface look like? What is the "stuff" that the path consists of? What is it that is moving along the path? Does the movement only happen when the calculation completes (halts) ? Is the milestones consistent "snapshots" of the calculations? What exactly is getting calculated?
So now you are using a different metaphor/analogies. On the one hand, you have the T[j] being a more "refined" object that T[j-1], somehow purer, or more focused, or more accurate, or more polished, or more "good" using some measure. The "revision" process is a succession of sub-processes, the first of which makes no "changes" at all, and each of the following ones
Whoa. F[k](x) is a matrix/single-dimension vector of functions which take a vector of symbols ?
so F is a function which is given the vector [ "a cat is on a mat" ] ?
or F is a function which is given the vector ["a" , "cat" , "is" , "on" , "a" , "mat" ] ?
Okay, now you are making the F (which you now say is a function and not a theory as you said before), only get a single symbol in your sample x as input. If it is a theory, wouldn't it have statements about each of the values of x[i] ? Does your := mean that you are adding this statement to the theory or does it comprise the entire Theory?
Why did you change from x[i] from x ? How do you know i=7 ?
I'm going to stop right now, I have a meeting, but you have quite a theory you have
worked up, but I don't quite understand it, and will send this e-mail so I can find
out if I am chasing a wild swan, wild turkey, or wild goose here.
(maybe I should be drinking that wild turkey)
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