Hi Jawit, please see comments below.
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Jawit Kien
Sent: Friday, February 12, 2010
8:11 AM
To: [ontolog-forum]
Subject: Re: [ontolog-forum]
Inconsistent Theories
Thanks for your interest. You wrote:
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
in depth.
JK
Yes,
there is a lot of material behind it, which will be better read first, before
resorting to reading my tortured mathematization! It will be far more
productive if you read the ‘923 patent, and the patent application at my web
site. The links for these two documents are:
www.englishlogickernel.com/Patent-7-209-923-B1.PDF
(the ‘923)
and
www.englishlogickernel.com//Pat20090070317.pdf
which
are both relevant to the math here. After reading those two short
documents, I think you will be somewhat more comfortable with the posts here.
The
first document is an issued patent (the ‘923) which describes how to extract
structural, class and pattern information from databases containing
unstructured text columns, possibly intermixed with structured columns.
The
second document is a patent application. It shows a method for applying
the technology of the ‘923 to the USPTO patent database. That database
has both structured and unstructured text and image columns, and was chosen, in
part, as a demonstration of the principles described in the ‘923, among other
reasons.
But your
continued interest is welcome – the more feedback the better! It would
just make our job of communicating easier if we spoke from the same two
starting documents. From there on out, we at least are able to talk more
effectively.
Thanks,
-Rich
On Mon, Feb 8, 2010 at 7:32 PM, Rich Cooper <rich@xxxxxxxxxxxxxxxxxxxxxx>
wrote:
Hi Chris,
All right, perhaps I was a
little too fluid in my presentation. I will try to mathematize it
appropriately, with terms carefully defined. See below, please, for my
comments clarified:
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel
DOT com
On Mon, 2010-02-08 at 11:54
-0800, Rich Cooper wrote:
> Example: Let the two
theories be:
>
> TrueS(F,x)
:= <expression1 of terminals x>;
> FalseS(F,x) :=
<expression2 of terminals x>;
I don't understand what it
means to say these are theories. They look like clauses in a BNF. I
suppose a BNF is a sort of theory, but it's a theory that describes the grammar
of a specific language. But the left sides here look like atomic
statements in a first order language, not a class of expressions.
> So that there are two
theories: TrueS(F,x) is the set of Things which are
> believed (with current
knowledge) to be in the set F for terminal vector x,
> while FalseS(F,x) is
the set of Things which are believed NOT to be in F(x).
How can you possible get
that from the above?
-chris
I defined it
that way, where the F[k] are Boolean membership functions. That is;
If you have a
theory T[j] which has not been fully and accurately completed; it is a Boolean
function of the (here goes) terminal linguistic symbols, whether each such
terminal symbol designates a constant, variable, function, phrase or _expression_
of the above.
So to use John Sowa's favorite sentence: A cat is on a mat.
I see that there are five words in alphabetical order:
1) "A"
2) "CAT"
3) "IS"
4) "MAT"
5) "ON"
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
yields this
(∃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" ?
T[j] is a theory
of how to use each symbol as information structured in linguistic patterns
containing features F[k] that repeat from time to time in samples.
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
T[j] is the jth
iteration of the theory of how to predict members
of a set you are
interested in.
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?
T[1]..T[j] is
the sequence showing how the calculation got there with successive
theories.
"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[1], T[2], T[3], 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?
Each theory T[j]
is a revision of the previous theory T[j-1] (except of course the 1st
theory T[1] which just lets everything through).
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
So each function
F[k](x) in the set vector F(x) is a Boolean function that returns True if the
sample x (a vector of symbols x[i] for i in [1,m]) is a member of the
set. So if we define
Whoa. F[k](x) is a matrix/single-dimension vector of
functions which take a vector of symbols ?
so F[1] is a function which is given the vector [ "a cat is on a mat"
] ?
or F[1] is a function which is given the vector ["a" ,
"cat" , "is" , "on" , "a" ,
"mat" ] ?
or what?
Okay, now you are making the F[1] (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?
as one possible
such Boolean member function (x[i] designates a Turkey), and
F[n] := IsA(x[7],Swan)
Why did you change from x[i] from x[7] ? 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)
JK
Is the nth such
Boolean member function of x where x[7] designates a Swan, constraining the
definition of theory T[j] by defining predicates at positions 1 and n, as
schematized below:
F(x) := [IsA(x[i],Turkey),
.., IsA(x[7],Swan)]
This _expression_
means that F(x) is hereby defined to contain the vector (of size n), each
element F[k] of F containing a function F[k](x) of the terminal symbols x in
sequence as experienced in a given sample, stored in a database text cell,
presently under consideration.
As hinted, x is
a vector (think of the state vector in a linear system of equations) and
represents (to me at least), a sequence of symbols which are being organized
into a proper theory (our old friend T[j]).
But to begin
with, call it time t=t0, T[j] only could think that a theory is correct as
stated. At t=t1 (scale t0:t1 any way you like), T[j] has encountered some
sample instances that are predicted by T[j] to be True members of the set, but
which have been found to actually, in the real world, not do so well as TrueS
in T[j]; they find themselves better categorized as FalseS in T[j]. They
are erroneous designations which, though correct according to the current
theory T[j], are found to be False in practice.
So T[j]
designates the set of correctly encountered instances conforming with the
theory T[j] versus ~T[j], which is hereby defined as the set of correctly
encountered instances that are known not to conform with T[j] though T[j]
predicts that they will so conform.
Questions,
comments, condemnations, qualifications?
-Rich
|
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (01)
|