New Implicit approach to fuzzy logic

[Roger Bagula]

Some time back I realized that competition in populations behaved very
much like the classical pH and pOH equation in chemistry for titration
curves:
pH+pOH =14
http://www.ausetute.com.au/titrcurv.html
The Neanderthal - modern human population densities by area behave in
this manner.

Suppose that the implicit curves of fuzzy logic behaved the same way:
Log[x]+Log[y]=constant
It was the diagram on page 136 of Fuzzy Thinking by Bart Kosko that made
me think this approach might work :
http://www.amazon.com/Fuzzy-Thinking-New-Science-Logic/dp/078688021X/ref=sr_11_1/104-0029617-0633535?ie=UTF8&qid=1174578060&sr=11-1

This morning I did curves in Mathematica for implicit Fuzzy logics that
seem to work:
( these plots give analogs of the iterative plots and work better in
Mathematica than the iteratives do)
Kosko-Grim type:
Clear[x, y, a, b]
x'=1 - Abs[x - y]
y'=1 - Abs[x + y - 1]
f[x_, y_] = (1 - Abs[x - y])*(1 - Abs[x + y - 1])
ContourPlot[ f[x, y], {x, -0.5,
1.5}, {y, -0.5, 1.5}, PlotPoints -> {300, 300},
ImageSize -> 600,
ColorFunction -> (Hue[2#] &)]

Zadeh type:
x'=x*y
y'=x+y-x*y
Clear[x, y, a, b]
f[x_, y_] = x*y*(x + y - x*y)
ContourPlot[ f[x, y], {x, -2, 2}, {y, -2, 2}, PlotPoints -> {300, 300},
ImageSize -> 600,
ColorFunction -> (Hue[2#] &)]

My half dual iteration type:
( this type of fuzzy logic like the zero centered version was developed
for getting better Julias , pictures as output)
x'=0.5 - Abs[-x + y - 0.5]
y'=0.5 - Abs[x + y - 0.5]
Clear[x, y, a, b]
f[x_, y_] = (0.5 - Abs[-x + y - 0.5])*(0.5 - Abs[x + y - 0.5])
ContourPlot[ f[x, y], {x, -0.5, 0.5}, {y, 0, 1.}, PlotPoints -> {300, 300},
ImageSize -> 600,
ColorFunction -> (Hue[2#] &)]

The code search gives:
http://www.google.com/codesearch?q=fuzzy+logic+lang%3Amathematica&hl=en&btnG=Search+Code

The engineering versions ( Zadeh, Kosco) of fuzzy logic is a little
different than the mathematics and
the philosophical versions ( Grim).
The engineering version is more about making "categories" than about the
philosophical idea of truth and lies.
Mathematical versions are more about making an algebra that is more
general than Boolean.
Another area that is close is the Bayesian probability approach (
dependent logic).
Another related area from topology is the Hausdorff measure/ space approach.
Another related area is the sigmoids of population theory.
The applications of this more abstract fuzzy logic are to things like
election theory and moral/ ethics theory.

It has been said that future wars will be fought over the right of
people to believe and behave in "gray"
areas. Not Republican or Democrat or religiously moral of reprobate
but in between.
A for instance is that in the United States people are allowed their own
religious beliefs, but in cleric controlled Islamic countries Christians
are often persecuted and imprisoned for nothing more than going to church.
So the terrorist war is meant to "correct" the Christian countries for
allowing atheists, Jews and agnostics to live
in peace; for allowing lifestyles that include both alcohol and other
immoral behavior by their
ideas.
So in a very real way the current war is a fuzzy logic war.

[Roger Bagula]

Brain Injury Said to Affect Moral Choices

http://www.nytimes.com/2007/03/22/science/22brain.html?ex=1332216000&en=f5bb061d194af5fa&ei=5088&partner=rssnyt&emc=rss
By BENEDICT CAREY
Published: March 22, 2007

Damage to an area of the brain behind the forehead, inches behind the
eyes, transforms the way people make moral judgments in life-or-death
situations, scientists reported yesterday. In a new study, people with
this rare injury expressed increased willingness to kill or harm another
person if doing so would save others' lives.
Skip to next paragraph
Multimedia
Brain Injury and Moral JudgementGraphic
Brain Injury and Moral Judgement

The findings are the most direct evidence that humans' native revulsion
to hurting others relies on a part of neural anatomy, one that evolved
before the higher brain regions responsible for analysis and planning.

The researchers emphasize that the study was small and that the moral
decisions were hypothetical; the results cannot predict how people with
or without brain injuries will act in real life-or-death situations. Yet
the findings, appearing online yesterday, in the journal Nature, confirm
the central role of the damaged region, the ventromedial prefrontal
cortex, which is thought to give rise to social emotions, like compassion.

Previous studies showed that this region was active during moral
decision making, and that damage to it and neighboring areas from severe
dementia affected moral judgments. _/*The new study seals the case by
demonstrating that a very specific kind of emotion-based judgment is
altered when the region is offline.*/_ In extreme circumstances, people
with the injury will even endorse suffocating an infant if that would
save more lives.

"I think it's very convincing now that there are at least two systems
working when we make moral judgments," said Joshua Greene, a
psychologist at Harvard who was not involved in the study. "There's an
emotional system that depends on this specific part of the brain, and
another system that performs more utilitarian cost-benefit analyses
which in these people is clearly intact."

The finding could have implications for legal cases. Jurors have reduced
sentences based on brain-imaging results showing damage. The new study
focused on six patients who had suffered damage to the ventromedial area
from an aneurysm or a tumor. The cortex is the thick outer wrapping of
the brain, where the distinctly human, mostly conscious functions of
thinking and language reside. "Ventral" means "underneath," and "medial"
means "near the middle." The area in adults is about the size of a large
plum.

People with this injury can be lucid, easygoing, talkative and
intelligent, but socially awkward, seemingly numb to the ebb and flow of
subtle social cues and emotions. They also have some of the same moral
instincts that others do.

The researchers, from the University of Iowa and other institutions, had
people with the injury respond to moral challenges. In one, they had to
decide whether to divert a runaway boxcar that was about to kill a group
of five workmen. To save the workers they would have to flip a switch,
sending the car hurtling into another man, who would be killed.

They favored flipping the switch, just as the group without injuries
did. A third group, with brain damage that did not affect the
ventromedial cortex, made the same decision.

All three groups also strongly rejected doing harm to others in
situations that did not involve trading one certain death for another.
They would not send a daughter to work in the pornography industry to
fend off crushing poverty, or kill an infant they felt they could not
care for. But a large difference in the participants' decisions emerged
when there was no switch to flip -- when they had to choose between
taking direct action to kill or harm someone (pushing him in front of
the runaway boxcar, for example) and serving a greater good.

Those with ventromedial injuries were about twice as likely as other
participants to say they would push someone in front of the train (if
that was the only option), or suffocate a baby whose crying would reveal
to enemy soldiers where the subject and family and friends were hiding.

The difference was very clear for all the ventromedial patients, said
Dr. Michael Koenigs, a neuroscientist at the National Institutes of
Health who led the study while at the University of Iowa. After
repeatedly endorsing killing in these high-conflict situations, Dr.
Koenigs said, one patient told him, "Jeez, I've turned into a killer."

The other authors included Dr. Daniel Tranel of Iowa; Dr. Marc Hauser of
Harvard; and other neuroscientists.

The ventromedial area is a primitive part of the cortex that appears to
have evolved to help humans navigate social interactions. The area has
connections to deeper, unconscious regions like the brain stem, which
transmit physical sensations of attraction or discomfort; and the
amygdala, a gumdrop of neural tissue that registers threats, social and
otherwise. The ventromedial area integrates those signals with others
from the cortex, including emotional memories, to help generate familiar
social reactions.

"This area, when it's working, will give rise to social emotions that we
can feel, like embarrassment, guilt and compassion, that are critical to
guiding our social behavior," said Dr. Antonio Damasio, a co-author of
the study and a neuroscientist at the University of Southern California.

Those sensations put a finger on the brain's conscious, cost-benefit
scale weighing moral dilemmas, Dr. Damasio said, creating a tension that
even trained snipers can feel when having to pull the trigger on an
enemy. This tension between cost-benefit calculations and instinctive
emotion in part reflects the brain's continuing adjustment to the vast
social changes since the ventromedial area of the cortex first took shape.

The area probably adapted to help the brain make snap moral decisions in
small kin groups -- to spare a valuable group member's life after a
fight, for instance. As human communities became increasingly complex,
so did the cortical structures involved in parsing ethical dilemmas. But
the more primitive ventromedial area continued to anchor it with
emotional insistence on an ancient principle: respect for the life of
another human being.

"A nice way to think about it," Dr. Damasio said, "is that we have this
emotional system built in, and over the years culture has worked on it
to make it even better."

[Roger Bagula]

http://www.amazon.com/Philosophical-Computer-Exploratory-Essays-Modeling/dp/0262071851/ref=pd_bbs_sr_1/104-0029617-0633535?ie=UTF8&s=books&qid=1174589059&sr=8-1
*The Philosophical Computer: Exploratory Essays in Philosophical
Computer Modeling (Hardcover) *
by Patrick Grim
<http://www.amazon.com/exec/obidos/search-handle-url/104-0029617-0633535?%5Fencoding=UTF8&search-type=ss&index=books&field-author=Patrick%20Grim>
(Author), Gary Mar
<http://www.amazon.com/exec/obidos/search-handle-url/104-0029617-0633535?%5Fencoding=UTF8&search-type=ss&index=books&field-author=Gary%20Mar>
(Author), Paul St
<http://www.amazon.com/exec/obidos/search-handle-url/104-0029617-0633535?%5Fencoding=UTF8&search-type=ss&index=books&field-author=Paul%20St>
(Author)
Editorial Reviews
Review
"This is a delightful introduction to the philosophical research tool
hiding underneath your word processor."
-- Brian Skyrms, Distinguished Professor of Philosophy, University of
California, Irvine

Peter Gibbins,The Times Higher Education Supplement, September 11, 1998
"The book explores the computer as a philosophical tool, and not just as
a metaphor to which philosophers appeal... the first systematic such
journey I know of to be packaged and presented as a new paradigm of how
to do philosophy... it is essential reading for anyone wishing to use
computers as a philosophical tool. By exploiting the iterative
capability of computers and their capacity to help us visualise
processes by throwing them on a screen the book makes an impressive
start in supporting a new paradigm in philosphy: executable
metaphysics... Strongly recommended."

[Roger Bagula]

http://www.sunysb.edu/philosophy/faculty/pgrim/index.html
http://www.tzingaro.com/artelectric/index.html

[Roger Bagula]

http://www.benoit.com/music/solo.html
http://www.benoit.com/sounds/fl-fuzzy.mp3
http://www.benoit.com/sounds/fl-snap.mp3
http://www.benoit.com/sounds/fl-suv.mp3
http://www.benoit.com/sounds/fl-dream.mp3

Fuzzy Logic (close-up of album cover)
Date: February 5, 2002• Length: 44:06 minutes

Fuzzy Logic


1. Snap! (mp3)
2. Fuzzy Logic (mp3)
3. Someday Soon
4. Then The Morning Comes
5. Reflections


6. Coming Up For Air
7. You Read My Mind
8. War of the S.U.V.s (mp3)
9. Tango In Barbados
10. One Dream At A Time (mp3)