fom
Posts:
1,026
Registered:
12/4/12
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Re: fom - 03 - connectivity algebra
Posted:
Dec 7, 2012 5:30 PM
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On 12/7/2012 4:14 PM, Graham Cooper wrote:
> On Dec 7, 8:24 pm, fom <fomJ...@nyms.net> wrote:
>>>>
>>>> NOR (NOR,NOR) = OR
>>
>> ((p NOR q) NOR (p NOR q)
>>
>> T..F..T...T...T..F..T
>> T..F..F...T...T..F..F
>> F..T..F...F...F..T..F
>> F..F..T...T...F..F..T
>>
>> p q | p OR q
>> ------|--------
>> T T | T
>> T F | T
>> F F | F
>> F T | T
>>
>
>
>
> OK, here are the 16 predicates..
>
>
>
> p(n,A,B,_)
>
> p(1,0,0,0).
> p(1,0,1,0).
> p(1,1,0,0).
> p(1,1,1,0).
>
> p(2,0,0,0). AND
> p(2,0,1,0).
> p(2,1,0,0).
> p(2,1,1,1).
>
> p(3,0,0,0).
> p(3,0,1,0).
> p(3,1,0,1).
> p(3,1,1,0).
>
> p(4,0,0,0).
> p(4,0,1,0).
> p(4,1,0,1).
> p(4,1,1,1).
>
> p(5,0,0,0).
> p(5,0,1,1).
> p(5,1,0,0).
> p(5,1,1,0).
>
> p(6,0,0,0).
> p(6,0,1,1).
> p(6,1,0,0).
> p(6,1,1,1).
>
> p(7,0,0,0).
> p(7,0,1,1).
> p(7,1,0,1).
> p(7,1,1,0).
>
> p(8,0,0,0). OR
> p(8,0,1,1).
> p(8,1,0,1).
> p(8,1,1,1).
>
> p(9,0,0,1).
> p(9,0,1,0).
> p(9,1,0,0).
> p(9,1,1,0).
>
> p(10,0,0,1).
> p(10,0,1,0).
> p(10,1,0,0).
> p(10,1,1,1).
>
> p(11,0,0,1).
> p(11,0,1,0).
> p(11,1,0,1).
> p(11,1,1,0).
>
> p(12,0,0,1).
> p(12,0,1,0).
> p(12,1,0,1).
> p(12,1,1,1).
>
> p(13,0,0,1).
> p(13,0,1,1).
> p(13,1,0,0).
> p(13,1,1,0).
>
> p(14,0,0,1).
> p(14,0,1,1).
> p(14,1,0,0).
> p(14,1,1,1).
>
> p(15,0,0,1).
> p(15,0,1,1).
> p(15,1,0,1).
> p(15,1,1,0).
>
> p(16,0,0,1).
> p(16,0,1,1).
> p(16,1,0,1).
> p(16,1,1,1).
>
>
>
> I might run a program
>
> pn(pm,ps)
>
> on all 4 inputs and check the result
> against the 4 inputs, if there is a duplicate
> it can be reduced.
>
> e.g.
>
> and(if(A,B),if(B,C))
>
> the result is the same as
>
> if(A,C)
>
> so I could detect B is eliminated
> and a reduction exists.
>
>
> Herc
>
yes
that is how the list was generated
but, the purpose of the list is a step
required to transform uninterpreted
symbols purported to be constants
into symbols interpretable as
functions
the axioms assert the identity
statements that establish that
situation
take a quick look somewhere at
universal algebras and varieties
(or even equational classes since
that is how Birkhoff introduced
the notion)
the compositionality underlying
the generation of wffs is a property
that can be expressed without
truth tables
but, the ideas lie with Church and
Curry, since it Church used it to
introduce the lambda calculus and
Curry used it to describe logistic
systems built on applicative systems
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