I wrote about this in my "Teenage Theory of Mind and Universe", Part 4, section 21", first published in early 2004.
(C) Todor Arnaudov 2004 (in Bulgarian)
English translation (C) 2011
21. Fuzzy logic and is it really fuzzy? [Also Truth, comparison … ], p.21 - p.25 in the formatting linked above.
This is one of the answers in a thread in the AGI List (I may add the responses here also now or later, stay tuned):
This section explains about principles of recognition and generalization in generalizing sensori-motor hierarchies, including inter-modal matching - somatosensory-proprioceptive-visual-gustatory - for finding stable patterns in the inputs.
21. Fuzzy logic and is it really fuzzy?
[Also Truth, comparison … ]
Fuzzy logic is based on, they say so, partially
true and partially false statements, whose truth
is defined in fractions, instead of binary
true/false in classical logic.
However is fuzzy logic really fuzzy?
Let's start from the concept of “truth”. In Part 3 it
was defined like this:
From “Universe and Mind” - Part 3:
50. The truth is a match – if the knowledge (or
confidence, belief, persuasion [, desire])
matches something that is perceived somewhere
else later, then the new one is true, compared to
the old; on the other hand, if the new one is
different, it's “a lie” (false) or it becomes truth
and the old truth turns into full or partial false,
depending on how the new truth is different
from the old one. The more the newly evaluated
for “truth” input piece of knowledge [pattern]
matches a piece of knowledge [pattern] from the
memories of mind, the more it's “truth” and
“actual”, according to mind. Therefore,
determining a “truth” is a determination of
difference between past and wanted present.
(“Wanted” was missing in the Part 3 writing,
added here in Part 4).
[“Truth” in Bulgarian is “Istina”]
Interestingly, in Serbian “isto” means “same” -
it has morphological association to “same”,
because the statement that a given feature is
“truth” means also that:
TRUTH: The feature [specifics, detail] that is
being evaluated matches the pattern/template - it
is the same as in the pattern, at a given
resolution of perception. (*That's a definition of mine.)
The difference between fuzzy and binary logic
is that the first uses higher resolution of
perception when searching for matches. Fuzzy
logic works with more degrees of freedom,
representing the existence or miss of a match.
Fuzzy logic uses also “latent variables” which
determine whether a statement is true or not
true.
In the most simple form of classical formal
logic, there are no latent variables and the
degrees of freedom for expressing presence or
lack of ta match are only two.
Fuzzy logic uses numbers with any precision,
while formal logic uses only 1-bit. However,
many sequential 1-bit logical elements can be
connected together to construct parallel (multibit)
logical units – this topic was discussed in
Part 2.
Thus “Fuzzy” logic is a derivation of the
Classical, that is using redundancy of
information. For example, this is how usually
human recognize images [objects, by vision]:
If the image possesses at least one feature of the
remembered features for any object, and no
other object has this feature, then the image is of
this object.
For example, how do we recognize that a
bitten apple is still an apple?
Behavior always depends on specific memories
of the control unit.
If a little child bites an apple for the first time,
he would get to know, that the image of the
inside of the apple is also an image of an apple,
because the object that he's holding in his hand,
after biting a piece of, is remaining the same.
This is learned earlier the following way:
If one eats a slice of bread, when biting from it
or breaking off pieces, then the remaining keeps
being the remaining of the same thing – slice of
bread, unless an action to move out the data
recorded in hand memory is performed: to free
it from holding the slice of bread, or to input
new data to the same hand – to catch and hold
something else. If one didn't left what he was
holding and didn't get something else, but he is
keeping to feel something with his fingers and
to see it, then this should be the remaining of the
slice of bread.
Then, “remaining of a slice of bread” is a subset
of “a slice of bread” and it's a representation of
an object that is built by the tissue [the matter;
visually also the texture] of the slice of bread in
its initial state, where the Initial state is the
perception of the slice of bread in the moment
when one takes it to his hand and sees it for the
first time.
Therefore the bitten apple is a state of [the
concept of] “apple” that the child remembers. If
in the previous moment the apple was in his
hand and he knew, that he's about to bite a piece
of it, then he's still having the information that
he keeps holding an apple, because in the
previous cases, after similar action he has
discovered that he was still eating an apple.
[How do we know that? Easily: ]
We know that after a bite the thing in our hand
is still an apple, because the taste of the pieces
that we bite afterward are close enough to the
taste of the previous ones. Since the taste was
the same and since we know that after holding
an object in hand it would keep existing and
staying in our hand, unless we leave it or stop
feeling its impact [on fingers, hand; weight;
warmth etc., related to permanency of
existence], therefore [we conclude] that the
object keeps being in our hand, implying that
the object – a bitten apple – is still an apple.
The representation of an object is a set of all
its states a mind has memories of. (…)
If an object has attributes allowing to
discriminate it as a sub-type of a concept – a
type of apple, bike, wheel – then it's going to be
recognized.
The representation of an object is remembered
as examples of that object. The general and the
specific is extracted from the examples.
“The paradox” of the liar:
Goodlier from the village of Good Lierville
once said, that all of his fellow villagers and him
are liars, and then he asked is he lying if he says
this?
If he lies, then he's not a lier, therefore he
doesn't lie. However, he's from Good Lierville,
therefore he's a lier. What a “paradox”, I'm
totally confused!? Really?!
I'm sorry, but I wouldn't even really call this a
“paradox”, but a play of words and “pseudo
wisdom”. What I'd answer to this Goodlier
character is:
- I don't know do you lie or not, there is not
enough input data.
I'd say him also that he's a liar anyway, no
matter is he lying in this very moment, because
probably he's trying to trick me that he's wise
(sorry, he failed).
One or two sentences in this or similar
“paradox” cases are not enough to imagine a
definite non-ambiguous what this is all about.
For example, many people would believe that
they know what a “liar” means once they hear
the word.
Well, what does a liar means? [Unfortunately],
The practical value of general concepts in
execution of direct [immediate, specific] actions
is... fuzzy in such cases.
Which one of all possible meanings and
happenings [events, stories, memories,
interpretations] that our mind has for a “liar” the
story teller meant in this particular case?
What does it mean to be “from Good
Liarsville”?
Was Goodlier born there or he lives
there, or he's a fan of the football team of the
village? Or he has relatives there? Or he is
originally from a village in this commune. It is
possible that liars are the ones for whom one of
this is true, but not all, and anyway - being a liar
[in common sense] does not mean that you're
lying in every single sentence.
Therefore it's impossible to conclude is
Goodliar lying in this very situation or not, as
it's impossible to say definitely in more realistic
cases from the daily live, where there are no
[artificially] tangled premises and consequences
[causes and effects].
In reality there are many causes and man
possibilities to explain what's happening [and
why].
Sometimes input data is not enough to
find a [persuasive] proof only on their basis.
According to my current understanding, mind
works with specific concepts, and not general;
in specific concepts everything is as precisely
defined as possible, while with the general
concepts, there are too many undefined which
easily lead to “paradoxes”, i.e. to insufficiency
of input data for determining whether a
statement belongs to a group [set/class].
Said otherwise, the description of the story is
black and white, but we're asked what color is it.
Or there are many colors on a picture, evenly
spread, and we're asked to specify of what color
is the picture: only one single color.
Overall, in the above conditions the asking unit
has too low resolution of perception and not
enough memory in order to think us precise as
the evaluating unit – us. [The answer of the
question requires to lower the resolution of the
input and to loose details].
The one asking the questions does not
understand [discriminate, recognize, perceive]
all details we do, and in order to communicate
with it, we should act according to its model.
We see the indefiniteness and the simultaneous
“truth” and “false” [error, mismatch] of each
possible actions, according to our own
resolution of perception, but we should select
from the offered possibilities.
In case we're asked to select only one feature of
all and there is no “I don't know” option, then
mind would create a model for selection of
some of all, based on other, lateral data; of data
which did not come from this specific situation.
Since the device proposing us the possibilities
lacks brains to differentiate black-and-white and
color image or a motley and one-colored
picture, then this device is forced to lower the
resolution of perception and to delete part of its
memories [records] that otherwise we would
have [possessing higher resolution of
perception].
This device can call a motley picture with one
color and can have it's defined reasons, but
apparently it would not be able to make
inferences about many colors placed on one
canvas.
Read More
(C) Todor Arnaudov 2004 (in Bulgarian)
English translation (C) 2011
21. Fuzzy logic and is it really fuzzy? [Also Truth, comparison … ], p.21 - p.25 in the formatting linked above.
This is one of the answers in a thread in the AGI List (I may add the responses here also now or later, stay tuned):
This section explains about principles of recognition and generalization in generalizing sensori-motor hierarchies, including inter-modal matching - somatosensory-proprioceptive-visual-gustatory - for finding stable patterns in the inputs.
21. Fuzzy logic and is it really fuzzy?
[Also Truth, comparison … ]
Fuzzy logic is based on, they say so, partially
true and partially false statements, whose truth
is defined in fractions, instead of binary
true/false in classical logic.
However is fuzzy logic really fuzzy?
Let's start from the concept of “truth”. In Part 3 it
was defined like this:
From “Universe and Mind” - Part 3:
50. The truth is a match – if the knowledge (or
confidence, belief, persuasion [, desire])
matches something that is perceived somewhere
else later, then the new one is true, compared to
the old; on the other hand, if the new one is
different, it's “a lie” (false) or it becomes truth
and the old truth turns into full or partial false,
depending on how the new truth is different
from the old one. The more the newly evaluated
for “truth” input piece of knowledge [pattern]
matches a piece of knowledge [pattern] from the
memories of mind, the more it's “truth” and
“actual”, according to mind. Therefore,
determining a “truth” is a determination of
difference between past and wanted present.
(“Wanted” was missing in the Part 3 writing,
added here in Part 4).
[“Truth” in Bulgarian is “Istina”]
Interestingly, in Serbian “isto” means “same” -
it has morphological association to “same”,
because the statement that a given feature is
“truth” means also that:
TRUTH: The feature [specifics, detail] that is
being evaluated matches the pattern/template - it
is the same as in the pattern, at a given
resolution of perception. (*That's a definition of mine.)
The difference between fuzzy and binary logic
is that the first uses higher resolution of
perception when searching for matches. Fuzzy
logic works with more degrees of freedom,
representing the existence or miss of a match.
Fuzzy logic uses also “latent variables” which
determine whether a statement is true or not
true.
In the most simple form of classical formal
logic, there are no latent variables and the
degrees of freedom for expressing presence or
lack of ta match are only two.
Fuzzy logic uses numbers with any precision,
while formal logic uses only 1-bit. However,
many sequential 1-bit logical elements can be
connected together to construct parallel (multibit)
logical units – this topic was discussed in
Part 2.
Thus “Fuzzy” logic is a derivation of the
Classical, that is using redundancy of
information. For example, this is how usually
human recognize images [objects, by vision]:
If the image possesses at least one feature of the
remembered features for any object, and no
other object has this feature, then the image is of
this object.
For example, how do we recognize that a
bitten apple is still an apple?
Behavior always depends on specific memories
of the control unit.
If a little child bites an apple for the first time,
he would get to know, that the image of the
inside of the apple is also an image of an apple,
because the object that he's holding in his hand,
after biting a piece of, is remaining the same.
This is learned earlier the following way:
If one eats a slice of bread, when biting from it
or breaking off pieces, then the remaining keeps
being the remaining of the same thing – slice of
bread, unless an action to move out the data
recorded in hand memory is performed: to free
it from holding the slice of bread, or to input
new data to the same hand – to catch and hold
something else. If one didn't left what he was
holding and didn't get something else, but he is
keeping to feel something with his fingers and
to see it, then this should be the remaining of the
slice of bread.
Then, “remaining of a slice of bread” is a subset
of “a slice of bread” and it's a representation of
an object that is built by the tissue [the matter;
visually also the texture] of the slice of bread in
its initial state, where the Initial state is the
perception of the slice of bread in the moment
when one takes it to his hand and sees it for the
first time.
Therefore the bitten apple is a state of [the
concept of] “apple” that the child remembers. If
in the previous moment the apple was in his
hand and he knew, that he's about to bite a piece
of it, then he's still having the information that
he keeps holding an apple, because in the
previous cases, after similar action he has
discovered that he was still eating an apple.
[How do we know that? Easily: ]
We know that after a bite the thing in our hand
is still an apple, because the taste of the pieces
that we bite afterward are close enough to the
taste of the previous ones. Since the taste was
the same and since we know that after holding
an object in hand it would keep existing and
staying in our hand, unless we leave it or stop
feeling its impact [on fingers, hand; weight;
warmth etc., related to permanency of
existence], therefore [we conclude] that the
object keeps being in our hand, implying that
the object – a bitten apple – is still an apple.
The representation of an object is a set of all
its states a mind has memories of. (…)
If an object has attributes allowing to
discriminate it as a sub-type of a concept – a
type of apple, bike, wheel – then it's going to be
recognized.
The representation of an object is remembered
as examples of that object. The general and the
specific is extracted from the examples.
“The paradox” of the liar:
Goodlier from the village of Good Lierville
once said, that all of his fellow villagers and him
are liars, and then he asked is he lying if he says
this?
If he lies, then he's not a lier, therefore he
doesn't lie. However, he's from Good Lierville,
therefore he's a lier. What a “paradox”, I'm
totally confused!? Really?!
I'm sorry, but I wouldn't even really call this a
“paradox”, but a play of words and “pseudo
wisdom”. What I'd answer to this Goodlier
character is:
- I don't know do you lie or not, there is not
enough input data.
I'd say him also that he's a liar anyway, no
matter is he lying in this very moment, because
probably he's trying to trick me that he's wise
(sorry, he failed).
One or two sentences in this or similar
“paradox” cases are not enough to imagine a
definite non-ambiguous what this is all about.
For example, many people would believe that
they know what a “liar” means once they hear
the word.
Well, what does a liar means? [Unfortunately],
The practical value of general concepts in
execution of direct [immediate, specific] actions
is... fuzzy in such cases.
Which one of all possible meanings and
happenings [events, stories, memories,
interpretations] that our mind has for a “liar” the
story teller meant in this particular case?
What does it mean to be “from Good
Liarsville”?
Was Goodlier born there or he lives
there, or he's a fan of the football team of the
village? Or he has relatives there? Or he is
originally from a village in this commune. It is
possible that liars are the ones for whom one of
this is true, but not all, and anyway - being a liar
[in common sense] does not mean that you're
lying in every single sentence.
Therefore it's impossible to conclude is
Goodliar lying in this very situation or not, as
it's impossible to say definitely in more realistic
cases from the daily live, where there are no
[artificially] tangled premises and consequences
[causes and effects].
In reality there are many causes and man
possibilities to explain what's happening [and
why].
Sometimes input data is not enough to
find a [persuasive] proof only on their basis.
According to my current understanding, mind
works with specific concepts, and not general;
in specific concepts everything is as precisely
defined as possible, while with the general
concepts, there are too many undefined which
easily lead to “paradoxes”, i.e. to insufficiency
of input data for determining whether a
statement belongs to a group [set/class].
Said otherwise, the description of the story is
black and white, but we're asked what color is it.
Or there are many colors on a picture, evenly
spread, and we're asked to specify of what color
is the picture: only one single color.
Overall, in the above conditions the asking unit
has too low resolution of perception and not
enough memory in order to think us precise as
the evaluating unit – us. [The answer of the
question requires to lower the resolution of the
input and to loose details].
The one asking the questions does not
understand [discriminate, recognize, perceive]
all details we do, and in order to communicate
with it, we should act according to its model.
We see the indefiniteness and the simultaneous
“truth” and “false” [error, mismatch] of each
possible actions, according to our own
resolution of perception, but we should select
from the offered possibilities.
In case we're asked to select only one feature of
all and there is no “I don't know” option, then
mind would create a model for selection of
some of all, based on other, lateral data; of data
which did not come from this specific situation.
Since the device proposing us the possibilities
lacks brains to differentiate black-and-white and
color image or a motley and one-colored
picture, then this device is forced to lower the
resolution of perception and to delete part of its
memories [records] that otherwise we would
have [possessing higher resolution of
perception].
This device can call a motley picture with one
color and can have it's defined reasons, but
apparently it would not be able to make
inferences about many colors placed on one
canvas.
