# [FOM] AI Challenge

Dr. Cyrus F Nourani akdmkrd at mail.com
Mon Oct 16 03:14:46 EDT 2017

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Dear colleagues,

I found a few mintues to join that discussion to ease the scenario on what I wrote on AI and games briefs on circles that group can recognize Computers are best on processing millions alternative to suggest an option and with augmented intelligent models that has been improved. I published an alternative to chase game models at AAAI on the Deepblue vs Kasparov plays: Multiagent Chess Games:
ww.aaai.org/Papers/Workshops/1997/WS-97-04/WS97-04-010.pdf

That model considers a multiagent group for either player, with every chess piece being a player.   So the two person games on a computer are not really two person games.
On ASL I stated theorems on infinitary games  modeling two person games with multiagent to reach bounds based on the game size summing propositions to a theorem proof.

Nim is a mathematical game of strategy in which two players take turns removing objects from distinct heaps. On each turn, a player must remove at least one object, and may remove any number of objects provided they all come from the same heap.

Considering the following: from GeeksForGeeks

Combinatorial Game Theory | Set 2 (Game of Nim)

Combinatorial Game Theory | Set 1 (Introduction)[http://www.geeksforgeeks.org/introduction-to-combinatorial-game-theory/]
The Game of Nim is described by the following rules-
“ Given a number of piles in which each pile contains some numbers of stones/coins. In each turn, a player can choose only one pile and remove any number of stones (at least one) from that pile. The player who cannot move is considered to lose the game (i.e., one who take the last stone is the winner). ”
For example, consider that there are two players- A and B, and initially there are three piles of coins initially having 3, 4, 5 coins in each of them as shown below. We assume that first move is made by A. See the below figure for clear understanding of the whole game play.

Amongst the conclusions there is that : we can conclude that this game depends on two factors-

The player who starts first.The initial configuration of the piles/heaps.
In fact, we can predict the winner of the game before even playing the game !
Nim-Sum : The cumulative XOR value of the number of coins/stones in each piles/heaps at any point of the game is called Nim-Sum at that point.

“If both A and B play optimally (i.e- they don’t make any mistakes), then the player starting first is guaranteed to win if the Nim-Sum at the beginning of the game is non-zero. Otherwise, if the Nim-Sum evaluates to zero, then player A will lose definitely.”

The multiagent game trees on heaps modeling NIM played on competitive models can be NIM win game sequences that do not depend on the starting player.  This an research that has to be supported before it can be explained.

To view a set definition : Game definition Nim is a 2 player game. A game state consists of a multiset S of nonnegative integers together with whose turn it is. If S does not contain any positive integers, then whose turn it is loses (we will call this the normal play rule) or wins (mis`ere rule), depending on the version of the game. Otherwise, a move consists of strictly decreasing one of the positive elements S to another nonnegative integer, and then whose turn it is alternates to the other player. Unless said otherwise, we assume the normal play rule.

On complexity of NIM an article from UCSD 2006 : Chris Calbro:
Condition for a forced win : representing a game state simply as S and assume that player 1 goes first. Then we can say that S is losing iff every legal move on S leads to a winning state; (Notice that the universal quantifier obviates the need to define a base case since if there is no legal move, then certainly every legal move leads to a winning state.) otherwise, S is winning. Define the nim sum of a game S as g = the binary XOR of the numbers in S.
An actual winning move can be found in log space as well since this only requires computing the position of the most significant bit in the nim sum, finding an element of S with a 1 in that position, and computing the XOR of the remaining elements
The following are what I published recent on game trees and models:
Universal Logic: Federal University of Rio de Janeiro, Brazil
* https://www.uni-log.org/cont5.html
... of superminds. A response to Bringsjord's argument on infinitary logic" .... Cyrus F. Nourani  "Predictive competitive model game trees"

*1999 European Summer Meeting of the Association for ... - jstor
https://www.jstor.org/st[https://www.jstor.org/st]
able/pdf/421084.pdf
took place at the University of Utrecht in The Netherlands on August 1-6, 1999. The. Program ... 1999 EUROPEAN SUMMER MEETING OF THE ASL. Abstracts of invited ...... II (J. Donald Monk and R. Bonnet, editors), North-Holland, Ams. 1989, pp. 11-24 ...... CYRUS F. NOURANI, Infinite multiplayergame trees.

Spring Southeastern Sectional Meeting, Full Program
www.ams.org › Meetings › Sectional
Special Event or Lecture · Inquiries: meet at ams.org ...... (1087-65-15); 5:30 p.m.. Competitive Models, Descriptive Computing, and Nash Games. Cyrus F Nourani* & Oliver Schulte , SFU, Burnaby, Canada and Akdmkrd.tripod.com

The point is computers by themselves do no invent or process structures. To take that one point further that thought processes are reasoning jumps with guesses, I presented the ASL Summer colloquium MIM logik 1996 brief to a Morph Gentzen structural algebraic logic that can process structural guesses mimicking real thinking: More specifics are on a book I published on Intelligent Multimedia Computing, 2005, American Scientific publishers. Newer applications to structural learning and reasoning are published before since 1996: Slalom Tree Computing:   AI Communications.
Best regards.
Cyrus
Acdmkrd.tripod.com :Acdmkrd at gmail.com
MIT-NIM cyrusfn at alum.mit.edu

Sent: Sunday, October 01, 2017 at 8:34 AM
From: "Patrik Eklund" <peklund at cs.umu.se>
To: "Foundations of Mathematics" <fom at cs.nyu.edu>
Subject: Re: [FOM] AI Challenge
Thank you, Daniel, for underlining

On 2017-09-30 22:40, Daniel Schwartz wrote:
> I believe that if new logic-based applications in AI could be created,
> this
> would spur a resurgence in interest in formal logics.
> http://www.cs.nyu.edu/mailman/listinfo/fom[http://www.cs.nyu.edu/mailman/listinfo/fom]

Dear All,

Harvey Friedman promotes NIM as an application area. This is fine, and
time will tell how discussions will develop on that side.

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Before I give other and very different examples, let me underline the
importance of finding a solution to a problem, rather than finding a
problem to a solution. My strong credo is that application development
is successful only if we really go deep into the essense of a problem,
and not just a shallow description of a problem.

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Allow me to be as concrete as I possible can, and I will pick two
examples in health. I am not a medical or health care expert, so anyone
knowing more detail on examples I mention, please add and/or correct. If
by any change there is an oncologist or cardiologist is the FOM
audience, and I would see a reply like "Patrik, you really don't have a
clue.", I would actually be happy, because than I would at least know
that problems are even deeper than I have imagined, and I would take it
from there.

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1. Hypertension

This is quite specific, even if it can be made even more specific as to
the reasons why it develops, and as to other diseases affecting and
complicating it. My example detail relates to pharmacologic treatment of
hypertension. Roughly and naively speaking there are two main strategies
to lower the blood pressure, one being relaxing vessels not to contract
so much, another being reducing blood volume. The relaxing bit has a
focus on angiotensin causing 'vasoconstriction', e.g. by applying
angiotensin receptor blockers ("ARBs"), such a relaxing can be achieved
and pressure goes down. This means pressure goes down also in very small
vessels like those appearing in kidneys and other parts of the body, so
a drug prescriber must ensure e.g. that kidney insufficiency is not
present. The blood volume bit is about too much water in the blood so we
simply suggest to take away some of that water by using diuretics. This
affects other part of the body, and indeed relates to transportation of
water within the body, and eventually out of it. Decades ago, while
cholesterol hysteria was still around and almost everybody (this was
indeed the strategy of the pharmaceutical industry) were eating statins,
diuretics was the number one choice for treating hypertension. This has
now changed so that focus number one, in case of no other complications
to be considered, is on that hormone (angiotensin), and what it really
is doing on vessel walls.

PS Beta blockers also relax but the mechanism is different and these
blockers are no longer considered as first line treatment for
uncomplicated hypertension. They are applied, if I recall correctly, if
there is heart insufficiency, or arrhythmias involved, like atrial
fibrillation. Anyway, beta blockers are "old" but "still going strong",
and there are many different types of beta blockers, functioning
differently.

Now to the logical problem, and naively focusing only on "less hormone"
(angiotensin receptor drugs) and "less water" (diuretics).

Modern consensus guidelines on hypertension treatment suggest first to
start with a smaller dose on the "relaxing vessels" side, and then, if
pressure does not come down sufficiently, to continue with a small dose
of diuretics, and then to take it from there. Often, several drugs must
be applied, and the patient becomes a "test patient", because there are
side-effects and such things which vary from individual to individual,
so too much side-effect may raise the need to change prescriptions.
There are also "ACE" drugs where that A also is about angiotensin, but
not on the walls of vessels but related to converting enzymes in that
cycle involving several organs. ACE inhibitors decrease that "conversion
activity", which lowers the pressure. Some guidelines say ACE before ATR
and if one of them is not enough, go for diuretics. Others say ATR
before ACE and then diuretics. Other guidelines are still beta blocker
fans, so beta blockers appear a bit higher in the hierarchy.

Now, is the order important? Suppose we would have two perfectly
identical patients, one for which we first relax, say during 6 months,
and then continue with also to remove, and for the other patient we do
the other way around. Who lives longer? Evidence-Based Medicine (EBM) is
unable to answer this question, I would claim. Why? Because the
mathematics of EBM is baby mathematics.

Can MATH or math (No, Hendrik, I don't know the difference. Do you?)
provide more insight, in particular if it really is so that the order
matters. Mathematics could contribute to more life years gained?! Or at
least, mathematics could help medicine to formulate problems more
deeply, so that clinical trials aiming at understanding the effect of
that order could be designed and executed. Even more so, math and logic
could help medicine and cardiology associations to formulate guidelines
logically more precisely. Those of you interested could have a look at
JNC 6, 7 and 8 guidelines for hypertension treatment, and make a
"logical comparison". I see it so that that JNC 6 and 7 are comparable
wrt "logical depth", but JNC 8 departs from that and becomes logically
even more shallow.

It sounds simple, but I fear it involves at least the whole
angiotensin-renin systems, and probably much more to really understand
water retention in the body, the role of sodium, potassium and calcium,
and many other things affecting the way cells communicate and hormones
are produced.

Medicine is good at finding disease and either treating them or treating
related symptoms, but medicine is less focused on explaining disease
(pathogenesis).

1a. Can logic help in describing pathogenesis???
1b. Can logic help organizations like Cochrane to better understand the
logical meaning of "evidence" (probabilities in EBM) and "evidence
levels" (requires many-valued logic).

On evidence levels we have some small papers, e.g., related to the use
of non-commutative quantales to generally describe the relation between
disease severity and success of interventions. It's very general, and
medically still very shallow, but it's an effort, and it aims mainly to
underline the importance of managing non-commutativity of logical
connectives. We also say it maight explain that many-valuedness does not
start from two but from three.

2. Cancer

This is more general, as there are so many different cancer types, so I
will try to describe Melanoma, skin cancer. We have nothing in writing
on this example.

Skin is about several layers, and lots of cell types in those layers,
melanocytes producing melanin being one of them. "Overproduction" is
obviously orchestrated by something, like UV from lying on the beach or
playing to much golf, but it is not clear where and how. Oncogenetics
look at mutations in some specific part of DNA, and protein bindings and
interactions in cell communication is another root of the problem. Once
this get started, pigments may turn into lesions, and lesions into
carsinoma. Once going into metastatis, skin cancer turn into cancer, and
a dermatology problem turns into a challenge for oncology, surgery and

How could we logically represent all these things, all this information?
Of course, there is work on mathematical modelling of protein folding
and thousands of other things, Markovian views on genes, and so on, many
of you may know much more than I do, but we really do not have a number
one huge success story of mathematical modeling in these respects, do
we?

Suppose it's all about logic, and we haven't played that card at all.

2a. Can logic help in describing pathogenesis???
3b. Can logic help in describing progression and care pathways? Look for
instance into OMG's standards. UML is fine, and in particular its Class
Diagram is much about standard logic, but the Baheviour Diagram less so.
OMG's BPMN is poorly understood from logic point of view, and OMG's DMN
is just awful and simple and naive relational logic, like description
logic.

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A word of caution:

Those of you who never did these things, but have been thinking about
doing these things, please do so, but please reserve enough time. Don't
expect to solve it in 2 years, because you might end up needing more
than 20 years, maybe even 200, and then you have to organize your
research work in a completely different way.

A wor(l)d of hope:

I mention description logic, DL. "Web ontology" is logically mostly
about DL, and unfortunately health ontology believes "ontology logic"
must be the same as in web ontology, so from SNOMED's adoption of DL
there are influences even up to WHO-FIC (World Health Organization
Family of International Classifications) also to adopt DL. This nonsense
must be stopped! If we logicians and mathematicians, all of you much
more prominent and skillful than I am, neglect this totally, the logic
of health remains in the hands of amateur logicians, and "Logic-Based
Medicine" (whatever that is) never enters the scene to complement EBM.

I believe that logic and even FOM can contribute to gaining more life
years.

Time will tell how discussions will develop on this side.

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