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ALL(F):N->R is 2OL! NOT 1OL!!!!!!
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More options Nov 14 2012, 11:43 pm
Newsgroups: sci.logic, sci.math, sci.physics, comp.ai.philosophy, comp.lang.prolog
From: Graham Cooper <grahamcoop...@gmail.com>
Date: Wed, 14 Nov 2012 20:43:54 -0800 (PST)
Local: Wed, Nov 14 2012 11:43 pm
Subject: Re: ALL(F):N->R is 2OL! NOT 1OL!!!!!!

F is just a LIST!

f(1) = 0.322323...

LIST ITEM 1  =  REAL#1  =  0.322323...

> > > > > I believe that was his conclusion.

> > > > > I don't know how to write in that language yet.  Does this make

> > > > > sense:

> > > > > EXISTS(G):F(N),N->R ALL(F):N->R ALL(m):N ALL(n):N F(n)=/=SUM(G(F(m),m))

> > > > G is just NXR->R

I'm just saying your TYPE of G is not well formulated.

If you are summing the digit positions into d1/10 + d2/100 + d3/1000
+ ....

that's fine!

If you want to put ALL FUNCTION at the start you are talking about a
bona-fide function here not my countable LIST:N->R of domain N.

Lot's of students don't remember lectures very well for various
reasons!  ;-)

Not really I am posting this to GG aswell as part of a high level
argument of misusing SETS for FUNCTIONS and calling 2OL 1OL.

You seem to be referring to another of my meta-argument.

---8<----------

There was only one problem...  PROLOG was a single logic value
language,  1 RECORD FOUND using backward chaining and the Theorem
Provers of the time were Resolution Based 2 valued logic where
Theorems were TRUE and Assumptions were reversed otherwise!  Set
Theory adopted a construction system of Predicates,  true or false,
as
long as they were well formed, functions were formulas, no sets, more
than infinity of them at any rate, don't try listing a function now-
a-
days... axioms were replaced as the theorem provider with |= missing
theorems from somewhere else, and every thing started with first
order
logic!

f(0).
t(1).
t(X) :- f(f(X)).
wff(X) :- t(X).
wff(X) :- f(X).
what(X,true) :- t(X).
what(X,false) :- f(X).

t(if(X,Y)) :- t(X), t(Y).
t(if(X,Y)) :- f(X), f(Y).
t(if(X,Y)) :- f(X), t(Y).
t(or(X,Y)) :- t(X).
t(or(X,Y)) :- t(Y).
t(and(X,Y)) :- t(X),t(Y).
t(iff(X,Y)) :- t(X),t(Y).
t(iff(X,Y)) :- f(X),f(Y).
t(xor(X,Y)) :- t(X),f(Y).
t(xor(X,Y)) :- f(X),t(Y).

f(if(X,Y)) :- t(X),f(Y).
f(or(X,Y)) :- f(X),f(Y).
f(and(X,Y)) :- f(X).
f(and(X,Y)) :- f(Y).
f(iff(X,Y)) :- t(X),f(Y).
f(iff(X,Y)) :- f(X),t(Y).
f(xor(X,Y)) :- t(X),t(Y).
f(xor(X,Y)) :- f(X),f(Y).

RESOLUTION
or(R,Q) :- if(L,R), or(L,Q).
or(R,Q) :- if(L,R), or(Q,L).
or(Q,R) :- if(L,R), or(L,Q).
or(Q,R) :- if(L,R), or(Q,L).

MODUS PONENS
t(R) :- if(L,R), t(L).
t(R) :- or(f(L),R), t(L).
t(R) :- or(R,f(L)), t(L).

INFERENCE RULE
if( if(t(S),f(R)) , if(t(R),f(S)) ).
if it's sunny then it's not raining
ergo
if it's raining then it's not sunny

--------8<------

This is PROLOG PROGRAMMING.

I am taking a *different approach*.

Rather than CONSTRUCTING ANY WFF that is TRUE OR FALSE.

I work out which is true and which is false by the very construction.

So I have WFFT and WFFF.

That way I can do LOGIC in PROLOG.  Actual LOGIC!  And Backtrack from
Normal Clauses to Horn Clauses, theorem proving capability PLUS axiom
back tracking derivation capability in the 1 system.  Normal Clauses
OVER Horn Clauses.  This is just MY Method but it looks like it would
have general Utility.

Herc

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More options Nov 15 2012, 1:44 am
Newsgroups: sci.logic, sci.math, sci.physics, comp.lang.prolog, comp.ai.philosophy
From: Hercules ofZeus <herc.is.h...@gmail.com>
Date: Wed, 14 Nov 2012 22:44:42 -0800 (PST)
Local: Thurs, Nov 15 2012 1:44 am
Subject: Re: ALL(F):N->R is 2OL! NOT 1OL!!!!!!
On Nov 15, 4:24 pm, forbisga...@gmail.com wrote:

> ALL(A)[(EXISTS(w)(weA) AND EXISTS(x) ALL(w)(weA->w<=z))->
> EXISTS(x) ALL(y)([All(w)(weA->w<=y)]<->x<=y)]

> where <= is being used as "less than or equal to".
> I'm leaving the brackets in place because it appears
> some use it as a transform from true to 1 and false to 0.
> I dont get it in this context.  It seems to mix some
> programming languages' coding for the comparison operators
> with their logical value.

Most people here use  A(x) E(x) or Ax Ex

I *emphasised*  ALL(F):
merely to imply the reading "ALL FUNCTIONS", since that was my point

<=  is definable using Peano Arithmetic

A(n)  0 <= n
A(m) A(n) s(m)<=s(n) -> m<=n

e.g.

s(0) <= s(s((0)) ?

m=0  n=s(0)

s(m)<=s(n)  -> m<=n     2nd Axiom

0 <= s(0)     1st Axiom

Herc

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More options Nov 15 2012, 2:39 am
Newsgroups: sci.logic, sci.math, sci.physics, comp.lang.prolog, comp.ai.philosophy
From: Graham Cooper <grahamcoop...@gmail.com>
Date: Wed, 14 Nov 2012 23:39:14 -0800 (PST)
Local: Thurs, Nov 15 2012 2:39 am
Subject: Re: ALL(F):N->R is 2OL! NOT 1OL!!!!!!

> <=  is definable using Peano Arithmetic

> A(n)  0 <= n
> A(m) A(n) s(m)<=s(n) -> m<=n

Other way around...
m<=n -> s(m)<=s(n)

I was thinking of PROLOG
s(m)<=s(n) :- m<n

FORWARD CHAINING

0 <= s(0)     FROM AXIOM 1
0<=s(0) -> s(0)<=s(s(0))   FROM AXIOM 2

L & L->R -> R    MODUS PONENS
L =   0<=s(0)
R =   s(0)<=s(s(0))
==============
s(0)<=s(s(0))

Herc

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More options Nov 15 2012, 3:05 am
Newsgroups: sci.logic, comp.ai.philosophy, comp.lang.prolog
From: Graham Cooper <grahamcoop...@gmail.com>
Date: Thu, 15 Nov 2012 00:05:06 -0800 (PST)
Local: Thurs, Nov 15 2012 3:05 am
Subject: Re: ALL(F):N->R is 2OL! NOT 1OL!!!!!!
On Nov 15, 5:39 pm, forbisga...@gmail.com wrote:

the set of all permutations of <1,2,3...> is considered un-countable
itself and isn't usually taken into consideration.

I devised a set of all computable orderings (of all functions).

> ...

> > That way I can do LOGIC in PROLOG.  Actual LOGIC!  And Backtrack from
> > Normal Clauses to Horn Clauses, theorem proving capability PLUS axiom
> > back tracking derivation capability in the 1 system.  Normal Clauses
> > OVER Horn Clauses.  This is just MY Method but it looks like it would
> > have general Utility.

> My issue is your use of WFF.  It's non-standard.  A formula is
> well formed by its form not its logical state or lack there of.
> By not using the standard definition your conclusions are off
> and this reduces the utility of your work.

I don't use the term WFF as I utilise it in PROLOG.

wff(X) :- t(X).
wff(X) :- f(X).

a formula is WFF is it is either t(...formula...) or f(...formula...)

wff is superfluous in my system.

in Predicate Calculus..

if F is a formula -->  NOT(F) is a formula

this is a wasted opportunity definition, by keeping WFF-T separate to
WFF-F it allows you to decompose the truth values of any formula!

> I've been trying to relearn prolog as well so I can address some
> of the issues.  I've had to move here because google doesn't allow
> cross posts any more and you don't read comp.ai.philosophy even though
> you add a cross post to it.

You can go back to old Google groups from the Options menu.

> As it turns out I learned prolog on a (now defunct) Bordland product
> that appears to be somewhat related to Visual Prolog.  That version
> of Prolog had string functions.  I could parse BNFhttp://en.wikipedia.org/wiki/Backus%E2%80%93Naur_Form
> to define a language's syntax then bind elements as needed to lists or
> functions.  It was a lot of work and the limitations of my patience
> lead me to move on.  Unix programmers have created lots of useful
> scripting languages to aid LALR compiler generation.

TRY
www.microPROLOG.com

[LIST]

[vert [pnt 1 2] [pnt 1 4]]?

--------------------

However that's as far as I got!!

I designed a new PROLOG ENGINE  =  ITERATIVE UNIFY

This wil be my 4th redesign, so give me a couple weeks!

Basically I'm going to parse all the Predicates into a SET of discreet
terms.

vert ( pnt( 1,2 ) pnt( 1,4 ) )

This will be

ID  REF   FIELD   TYP
=================
1   11     vert       H
1   12     pnt        P
1   13     pnt        P

1   121   1          T
1   122   2          T
1   131   1          T
1   132   4          T

Now there is NO RECURSION REQUIRED to unify 2 fomulas!

That is the set of facts when you make a QUERY.

All it has to do is UNIFY all those terms with the PROLOG RULE!

THE PROLOG RULE - Listed at microPROLOG!

vert ( pnt( X,Y ) pnt( X,Z ) )

ID  REF   FIELD   TYP
=================
21   11     vert       H
21   12     pnt        P
21   13     pnt        P

21   121   X          V
21   122   Y          V
21   131   X          V
21   132   Z          V

So all the PROLOG ENGINE has to do is check term against term!

Herc
--
--
if( if(t(S),f(R)) , if(t(R),f(S)) ).
if it's sunny then it's not raining
ergo
if it's raining then it's not sunny

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