HDTenEightyP/NetNews huggingface dataset:
From: hau4@ellis.uchicago.edu (sven  hauptfeld)
Subject: Re: "Solvability" in Chess
Reply-To: hau4@midway.uchicago.edu
Organization: University of Chicago Computing Organizations
Date: Sat, 26 Sep 1992 07:37:38 GMT

In article <1992Sep26.003838.14329@cbnewsl.cb.att.com> ed@cbnewsl.cb.att.com (edward.m.hummel) writes:
>In article <1992Sep25.185626.14074@ugle.unit.no> andreas@idt.unit.no (Andreas Lothe Opdahl) writes:
>>In article <1992Sep25.013439.1019@cbnewsl.cb.att.com> ed@cbnewsl.cb.att.com (edward.m.hummel) writes:
>>>The graph may be finite, but how do you assign a value to the loops?
>>>As far as I can see, they have undetermined value. 
>>
>>This is important, thank you for pointing it out.
>> ...
>>  Obviously, a "pure" game-theoretic evaluation can not make such 
>>an assumption about players behaviour (i.e. claiming a draw.)
>>
>>What is your reason why it can not be *proven* that closed loops have
>>the value of a draw?  
>
>It is easy enough to create a counter example.  I made up one for a
>simple game (only five nodes for the whole game tree) and could
>find no contradictions with the rules.
>
>>Perhaps we must add the *axiom* that closed loops 
>>are drawn to make chess solvable? 
>
>Yep.  That would do it, but it admits defeat.
>
>Another thought:  Can it even be proved that all undetermined loops
>have the same value?  I haven't worked this one out in any great detail
>but it is not obvious to me.  If it turns out that there are an infinite
>number of different undetermined values (to the infinite number of loops)
>then chess is not solvable.  If there are a finite number of values,
>then chess is solvable, but we can't determine the "optimal" strategy
>or assign a value to the initial position.
>
>

Would the people who talk about 'undetermined loops' be so kind to provide an
example, as I haven't the slightest idea what they mean. If at any point in
a loop one side can exit the loop and get on a winning path, then the loop is
a win for the side that can do it first. If neither side can do it, i.e. all
exits from the loop are draws, it is a draw.

And please don't respond 'philosophically'. If you claim that there are 
'undetermined' loops, give an example!

	Sven
From: torbenm@diku.dk (Torben AEgidius Mogensen)
Newsgroups: sci.logic
Subject: Re: Church's Heresy and the Unsolveability of chess
Date: 6 Oct 92 11:28:19 GMT
Organization: Department of Computer Science, U of Copenhagen

markh@csd4.csd.uwm.edu (Mark) writes:

>   The strong version of Church's Heresy: the set of all functions that have
>been, are being, ever will be, or ever could be computed is a finite subset
>of the recursive functions bounded above in size by 2-to-the-256.

>Corollary: Every computable function can be represented uniquely by 32 bytes.
>Theorem:   This 32-byte coding is not computable, but is finite and recursive.

No. It is only the size of the functions that can be represented in 32
bytes. The functions themselves needs 2^256 bytes.

	Torben Mogensen (torbenm@diku.dk)
Newsgroups: sci.logic
From: hbe@sonia.math.ucla.edu (H. Enderton)
Subject: UCLA Logic Colloquium, Oct 16
Organization: UCLA Mathematics Department
Distribution: ca
Date: Tue, 6 Oct 92 17:23:50 GMT

                    UCLA LOGIC COLLOQUIUM
                   Friday, October 16, 1992
                           4:00 p.m.
                   Mathematical Sciences 6627
                             UCLA
                                                  
                          KECHENG LIU 
                         (U.C. Irvine)

           "COFINALITIES OF (ELEMENTARY) SUBALGEBRAS
                  OF ALGEBRAS ON ALEPH_OMEGA"
From: fulk@cs.rochester.edu (Mark Fulk)
Newsgroups: sci.logic
Subject: Re: A question in Recursion Theory
Date: 29 Sep 92 21:03:11 GMT
Organization: Computer Science Department University of Rochester

In article <1aaaouINN9vp@usenet.INS.CWRU.Edu> cxm7@po.CWRU.Edu (Colin Mclarty) writes:
>
>In a previous article, chinnici@ghost.dsi.unimi.it (roberto riccard chinnici) says:
>> (read earlier article for problem.)
>	to find gn for n in J, start evaluating psi for each m in I.
>Of course you can not just start with the first m in I and evaluate 
>psi for it, since psi might be undefined for it.  So take a few steps 
>on the first element of I, then a few on the second, then a few more 
>on the first, a few more on the second and a few on the third, then a
>few more on the first....  This way we would eventually find the value 
>of psi for each element of I where it is defined.  Since psi maps I 
>onto J we will eventually finish evaluating psi on some element of I 
>that gives n.  Define gn to be that element.  

This argument requires that I be r.e.  Otherwise, one could not
carry out the first step: ``start evaluating psi for each m in I''.
A little thought indicates that failing to exclude N-I from the
computation can lead to failure.  In fact, it is easy to construct
co-r.e. I satisfying chinnici's conjecture; see my earlier post.

Mark
-- 
Mark A. Fulk			University of Rochester
Computer Science Department	fulk@cs.rochester.edu
Newsgroups: sci.logic
From: fulk@cs.rochester.edu (Mark Fulk)
Subject: Re: A question in Recursion Theory -- OOPS!
Keywords: recursion
Organization: Computer Science Department University of Rochester
Date: Wed, 30 Sep 1992 14:21:59 GMT

In article <1992Sep30.140356.9401@cs.rochester.edu> fulk@cs.rochester.edu (Mark Fulk) writes:
>My previous post on this matter was poorly worded, and contained some
>mistakes in the presentation of the proof.  Herewith an improvement:

Wherein I still left a gap.

>Let f be the left projection function for some pairing function.
>Let J be the set of natural numbers.
>
>We construct I by deleting elements from N; note that this makes I co-r.e.
>In the construction, we will refer to certain requirements R_i:
>
>R_i: range phi_i is finite or there is y in N such that phi_i(y) not in I.
>
>We will also restrain some numbers into I for requirements R_i.  These
>restraints can be broken for higher-priority (lower-numbered) requirements,
>but the standard finite-injury argument will establish that every requirement
>gets met.  The point of these restraints is that the range of f restricted
>to I (f|I) will still be N; this forces any section of f|I to have an
>infinite range, since a section must be in injection.
>
>Stage s:
>
>   Search for s steps for all i such that: requirement i is not met,
>   and there are x,y such that phi_i(x) = y, f(y)=x, and y is not
>   restrained into I for any requirement i'<i.
>
>   Let i0 be the least such i found; let x0 and y0 be corresponding
>   values of x and y.
>
>   Delete y0 from I.
>
>   find y'>y0 such that y' has not yet been deleted from I, and such that
>   f(y') = f(y0) = x0, 

and restrain y' into I for requirement i0.

>
>   Mark requirement i0 as being met.
>
>   For all requirements i>i0 that are marked as met, remove the mark
>   (that is, start treating them as unmet).
>
>End stage s.
>
>I will leave the verification up to the reader.  The basic structure of
>the proof is that every requirement will be met, either by default
>(phi_i has finite range) or by being met in the construction.  The
>latter will happen to each requirement at most a finite number of times
>(2^(i-1) will do it).  Then note that meeting every requirement is enough
>to establish that f|I has no section.
>
>Mark
-- 
Mark A. Fulk			University of Rochester
Computer Science Department	fulk@cs.rochester.edu
Newsgroups: sci.logic
From: holmes@opal.idbsu.edu (Randall Holmes)
Subject: Re: The Mathematical Universe
Keywords: inconsistent multiplicities
Organization: Boise State University
Date: Tue, 6 Oct 1992 15:59:30 GMT

In article <BvpECx.41I@unx.sas.com> sasghm@theseus.unx.sas.com (Gary Merrill) writes:
[...]
>
>Well, I'm still trying to get a grip on what this means -- particularly
>since I thought you were holding a realist or Platonist position arrayed
>against the sort of anti-realist position I have espoused.  At this point,
>I'm having trouble distinguishing your position from my own.
>
>
>
>-- 
>Gary H. Merrill  [Principal Systems Developer, C Compiler Development]
>SAS Institute Inc. / SAS Campus Dr. / Cary, NC  27513 / (919) 677-8000
>sasghm@theseus.unx.sas.com ... !mcnc!sas!sasghm

Probably the point is that I am not really a "possible worlds realist"
in the sense you are describing.  I think that there is only one
actual total (logical) universe.

Where I do find talk of possible worlds reasonable is in the
discussion of the physical world that we live in.  Since I think that
the physical world is a subset of the logical universe, I find it
reasonable to suppose that alternate physical worlds (all possible
ones) _actually exist_ (in exactly the same sense that ours does).
Such worlds provide an actual model for Kripke's semantics for modal
logic, for discussions restricted to the physical world; in the
internal language of this model, they are "possible worlds".  It is
probably an abuse of terminology to call them "possible worlds"
without reference to this model.  I don't think that one of them is
especially worthy of notice, except for the fact that I (and all of
_us_) are in it.

In an absolute sense (relative to the _logical_ universe) I am _not_ a
possible worlds realist; I think that there is one actual logical
universe.  However, there are various ways to describe the actual
universe, and it is also possible to "model" alternate logical
universes (in some suitable sense) within the actual one; in this
sense, it is possible to talk about counterfactual "possible logical
universes", but I do not ascribe reality to these (only to their
models).

My working logic is classical logic (not modal logic) and I am a
mathematical realist; thus, I think that there are models of the
Kripke semantics for modal logic.  In relation to the physical world,
I think that there are models of various versions of Kripke semantics
for talk of the physical world in which the other "possible worlds"
have the same status as our own.  In this context, I am a realist with
respect to possible worlds.  In the case of the entire logical
universe, I am not.
-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu
Newsgroups: sci.logic
From: nik@csgi49.dcs.leeds.ac.uk (Nik Silver)
Subject: Re: cardinality
Organization: School of Computer Studies, University of Leeds
Date: Mon, 28 Sep 1992 18:31:01 GMT

In article <26319@castle.ed.ac.uk>, sandy@festival.ed.ac.uk (Sandy Nicholson) writes:
>In article <1992Sep25.113936.19246@news.nd.edu>, nik@csgi48.dcs.leeds.ac.uk
>(Nik Silver) writes (much deleted):
>
>|> On the other hand, when we consider the (countably) infinite numbers w and
>|> w+1 we find that they are ordinally different (w+1 comes after w) but
>|> have the same cardinality. They have the same cardinality because we can
>|> define a bijection f from w+1 to w as follows:
>|> 	f(n)   = n+1 for n finite,
>|> 	f(w)   = w,
>|> 	f(w+1) = 0.
>
>I presume this was a momentary lapse---clearly the (von Neumann) ordinal w+1
>is not a member of the ordinal w+1, any more than w is a member of w.
>The bijection should be something along the lines of:
>
>      f(n) = n+1  for all finite n
>      f(w) = 0

Sandy Nicholson is quite correct, here, and I apologise for any confusion
I may have caused. (When I read the correction, I had to pause for quite
some time before seeing my mistake.) What has happened is that I had
confused the set X with the set of ordinals up to and including X (where X is
w or w+1).

Was it a momentary lapse, or really a lack of understanding on my part? I
thank you for the benefit of the doubt :-).

-- 
Nik ``nik@scs.leeds.ac.uk'' Silver
Newsgroups: sci.logic,sci.math,rec.games.chess
From: wbralick@afit.af.mil (Will Bralick)
Subject: Re: "Solvability" in Chess
Organization: Self-similar
Date: Mon, 28 Sep 1992 03:01:30 GMT

In article <xeno.717639078@pv34ad.vincent.iastate.edu> xeno@iastate.edu (Gary L Snethen) writes:
>
>If all moves lead to a forced loss, claim a draw.
>   reasoning:  We cannot assume our opponent will make a mistake.  Our best
>               option is therefore to claim a draw.

Huh?  If _all_ moves lead to a forced loss then our opponent cannot
possibly make a mistake.  Resign.

Regards,

-- 

Will Bralick					wbralick@afit.af.mil

Standard disclaimers apply.  Void where prohibitted by law.
Newsgroups: sci.logic,sci.math,rec.games.chess
From: "Ian Sutherland" <p00117@psilink.com>
Subject: Re: "Solvability" in Chess
Organization: Key Software, Inc.
Date: Sun, 27 Sep 1992 17:43:45 GMT
X-Mailer: PSILink (3.2)

edward.m.hummel writes:
>Take a look at FIDE rules 10.5 and 10.8.
>They clearly state

etc.

If you're posting something on this thread which has nothing to do with 
mathematical logic (as Mr. Hummel's post didn't; it was about scoring 
rules for chess), please remove "sci.logic" from the "Newsgroups" line.  
Thanks.

Newsgroups: sci.logic
From: sbloch@silver.cs.umanitoba.ca (Stephen Bloch)
Subject: Re: The Mathematical Universe
Keywords: inconsistent multiplicities
Organization: Computer Science, University of Manitoba, Winnipeg, Canada
Date: Tue, 6 Oct 1992 20:29:38 GMT

holmes@opal.idbsu.edu (Randall Holmes) writes:
>|> No, my view is that there is only one universe, and this includes all
>|> of the "possible worlds", _all_ of which are actual.  I am a possible

and sasghm@theseus.unx.sas.com (Gary Merrill) replies:
>But certainly there *is* a distinguished world (which we normally refer
>to as the "actual" one).  You may say that *all* of the possible worlds
>are actual (or real, or whatever), but if you wish to retain a distinction
>between what *is* and what *might be*, then *some* distinction must be
>made.  No?  If not, I don't see how to distinguish between fact and fiction.

Imagine I live in a suburban neighborhood containing lots of nearly
indistinguishable houses (in fact, to avoid being able to say "the house
at the northwest corner," let's suppose this suburb extends infinitely
in at least one dimension.  God, how depressing!)  I can still refer to
"the house," and everyone who hears me will understand that I mean
"the one I'm in."  If somebody else, living in a different house, says
"the house", she means the one's SHE's in.  The statement "A cat lives
in the house" may be fact in one and fiction in another.

This entire "neighborhood" of possible physical worlds is a subset of
The Logical Universe (comprising "things that could be").

Of course, I could be wrong :-)
-- 
					Stephen Bloch
				sbloch@silver.cs.umanitoba.ca
Newsgroups: sci.logic,sci.math,rec.games.chess
From: frank@Cookie.secapl.com (Frank Adams)
Subject: Re: "Solvability" in Chess
Date: Mon, 28 Sep 1992 15:56:40 GMT
Organization: Security APL, Inc.

In article <1992Sep25.014035.1269@cbnewsl.cb.att.com> ed@cbnewsl.cb.att.com (edward.m.hummel) writes:
>I think this argument rest on the assumption that chess is a zero sum game.
>How do you prove that?  Suppose the value of an infinite game is less than
>a draw for each player (but more than a loss), then neither player
>would choose a draw *with best play*.

As noted, this was intended to read "more than a draw for each player (but
less than a win)".  However, it is actually closer to correct as written:
the value of an infinite game *is* less than a draw; not as specified by the
rules, but in fact: no one wants to spend the rest of their life playing a
single game of chess.  This isn't *in* the rules for chess; it is *assumed*
by them.
Newsgroups: sci.logic
From: sbloch@silver.cs.umanitoba.ca (Stephen Bloch)
Subject: Re: A set cannot contain itself as a member
Keywords: recursion
Organization: Computer Science, University of Manitoba, Winnipeg, Canada
Date: Tue, 6 Oct 1992 20:13:30 GMT

sa114984@longs.lance.colostate.edu (Steven Arnold) writes:
>	Suppose X is an arbitrary set which contains itself as a
>member.  All other members within the set can be symbolized as
>'g'; therefore,
>
>		X = {g,X}		(1)

As somebody else did, I'll take it Steven meant "X = g U {X}".

>	Eq. 1 can be expanded as follows:
>
>		X = {g, X'}
>		        /\
>		       {g,X''}
>		          /\
>			 {g,X'''}
>...
>	The number of X's below X'' is infinite; nonetheless, it
>is certainly true that X' contains X'' as well as all the X's
>contained by X'';

What does "contains" mean?  If "X contains Y" means "Y is an element
of X", then I'll simply point out that "is an element of" is NOT
transitive (consider the sets {a}, {{a}}, and {{{a}}}).  If on the
other hand he means "there is a finite chain of 'is-an-element-of'
relationships from Y to X" (a nonstandard definition) we can go on.

>therefore X' contains one more X than X''!

This comment only makes sense for "sets with multiplicity" (i.e. the
set {a,b} is different from the set {a,b,b,b,b}).  If this nonstandard
definition is what he means, we can go on.

The statement "X' contains one more X than X''!" is no contradiction,
since both numbers are infinite (as Steven had already pointed out).
So let's go on.

>It
>follows that X' != X'', for X' contains an X not contained in X''. 

But I thought all these X's were assumed to be identical.  To prove
X'!=X by this method, you'd need to be able to point out one object
that's in one but not in the other.

Yes, there are several flaws in the argument.  And each of them is
interesting in a way; they point out several of the ways standard set
theory violates the intuitions one develops by dealing with finite
(not to mention well-founded!) sets.

-- 
					Stephen Bloch
				sbloch@silver.cs.umanitoba.ca
Xref: sparky sci.logic:1572 sci.math:12287 rec.games.chess:8149
From: ed@cbnewsl.cb.att.com (edward.m.hummel)
Newsgroups: sci.logic,sci.math,rec.games.chess
Subject: Re: "Solvability" (long & pedantic)
Date: 27 Sep 92 16:42:47 GMT
Organization: AT&T

In article <1992Sep26.190032.62552@uvmark.uucp> jim@uvmark.uucp (Jim Todhunter) writes:
>  Here we are specifically
>  addressing the argument that if you disallow certain drawing rules the
>  game is infinite and hence unsolvable.

Just for the record -- you have this backwards.  If you ignore certain
rules you can force the games to be finite.  When you include the full
rules, as approved by FIDE, you have to allow for infinite games.
I also don't think that just because infinite games are allowed, chess
is unsolvable.

>    It should also be apparent the three fold repetition
>  should be treated as a drawing condition.  (Remember, we define
>  solvability in terms of best play that produces a known result.  Thus,
>  any position which repeats thrice should be treated as a draw since
>  a decisive line, if one does exist, is reachable via a shorter path.)

This is not a proof.  How do you prove that "best play" must lead to a
"known result"?  By definition?  That's very convenient.  It also isn't
very convincing.
From: maj@waikato.ac.nz
Newsgroups: sci.logic
Subject: One or many universes
Date: 30 Sep 92 09:16:10 +1200
Organization: University of Waikato, Hamilton, New Zealand

If one sees the universe as one in an infinitly branching
sea of possible universes there is no difficulty in
seeing 'the' set-theoretic universe in the same light.

It may have a solid core which is the same in most real
universes, but shade off into a vague highly real-universe-
dependent part.

This is a personal, idiosyncratic view of things, which
somewhat lowers the technical plane of these discussions.
Fortunately, in most real universes, I don't actually
post this note.
-- 
Murray A. Jorgensen [ maj@waikato.ac.nz ]    University of Waikato
Department of Mathematics and Statistics     Hamilton, New Zealand      
__________________________________________________________________
'Tis the song of the Jubjub! the proof is complete,
if only I've stated it thrice.'
Newsgroups: sci.logic,sci.math,rec.games.chess
From: cuffell@spot.Colorado.EDU (CUFFELL TIMOTHY MICH)
Subject: Re: "Solvability" in Chess
Organization: University of Colorado, Boulder
Date: Mon, 28 Sep 1992 02:58:46 GMT

In article <1992Sep25.205258.25317@cs.rochester.edu> fulk@cs.rochester.edu (Mark Fulk) writes:
>Actually, the FIDE rules go a bit farther: if there have been 50 moves
>without a capture, the game is drawn unless one player can demonstrate a
>forced mate (this allows the use of the KBN vs. K mate).

Isn't there another modification of the 50 move rule, for K+N+N v. K+P, where
the pawn doesn't have time to promote, but prevents the stalemate in K+N+N v. 
K?

Anyone have specifics?
From: sasghm@theseus.unx.sas.com (Gary Merrill)
Subject: Re: Textbooks for Set Theory and Logic
Originator: sasghm@theseus.unx.sas.com
Date: Fri, 2 Oct 1992 14:50:43 GMT
Organization: SAS Institute Inc.
Keywords: set theory, logic


In article <chomicki.717970449@antares.cis.ksu.edu.cis.ksu.edu>, chomicki@cis.ksu.edu (Jan Chomicki) writes:

|> I intend to cover naive and axiomatic set theory, and propositional
|> and predicate logic. Specific topics include: cardinal and ordinal
|> numbers, transfinite induction, ZFC, proof systems (Hilbert- and
|> Gentzen-style, possibly resolution), soundness and completeness of
|> proof systems, some basic model theory.

You are going to do this in *one* course for students with no prior
work specifically in formal logic?  With all due respect I believe
you are out of your mind -- unless you plan to simply gloss virtually
every topic you have mentioned.  If so I would recommend that you do
not use a book at all.  Develop course notes and teach the course at
the "conceptual" level.
-- 
Gary H. Merrill  [Principal Systems Developer, C Compiler Development]
SAS Institute Inc. / SAS Campus Dr. / Cary, NC  27513 / (919) 677-8000
sasghm@theseus.unx.sas.com ... !mcnc!sas!sasghm
Newsgroups: sci.logic
From: sjv@doc.ic.ac.uk
Newsgroups: sci.logic
Subject: Re: FAQ
Date: 1 Oct 1992 16:24:37 GMT
Organization: Imperial College
Distribution: world
NNTP-Posting-Host: dse-mac-l1-85.doc.ic.ac.uk

In article <1992Sep30.195747.15980@husc3.harvard.edu> zeleny@husc9.harvard.edu
(Michael Zeleny) writes:
>... at this moment TeX has the advantage of being the
>de facto worldwide math typesetting standard in the academic circles.  So
>on the net which is fairly biased towards an academic audience, it is well
>suited to doing the work of lingua franca for mathematically oriented
>newsgroups.

A non-sequitur here - most news postings never get typeset.

That doesn't mean that TeX notation has no place in human-readable Ascii, but
there's no point in slavishly sticking to TeX if there is a visually clearer
non-Tex alternative (e.g. "->" for "\rightarrow"). The original posting was
about a proliferation of "\"s. They could normally be dropped (e.g. "Go"del" or
"G"odel", "x in X") with an improvement in readability and with the meaning no
less clear.

Steve Vickers.

Xref: sparky sci.logic:1590 sci.math:12332 rec.games.chess:8204