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Re: Self-evidently I am not my grandpa

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If the X_i are distinct from each other and distinct from I.

 >    father(I, X_1)
 >    father(X_1, X_2)
 >    :
 >    father(X_n, I)

Its quite difficult to satisfy for n>1:

grand_father(X,Y) :- father(X,Z), father(Z,Y).

Maybe you have ancestor/2 in mind? How would you define it?

Moebius schrieb:
> Am 02.05.2024 um 02:59 schrieb Mild Shock:
> 
> Ok, I have to admit that I unconsciously assumed that the database does 
> not allow for father(a,a) entries. Hence I missed the solutions with 
> domain size = 1, sorry.
> 
> Of course if this restriction does not exist, there's a solution with 
> database entry father(I,I) too. :-)
> 
> In general we get a solution (for all n e IN) with database entries
>    father(I, X_1)
>    father(X_1, X_2)
>    :
>    father(X_n, I)
> and I, X_1, ... X_n pairwise distinct.
> 
> In this cases: grand_father(I,I) [with domain size = n+1].
> 
>> Yeah you find such a solution also among
>> the answers that the model finder generates:
>>
>> % ?- counter(1).
>> % father(0,0)-1
>> % grand_father(0,0)-1
>> % 1true
>> % father(0,0)-1 father(0,1)-0 father(1,0)-0 father(1,1)-0
>> % grand_father(0,0)-1 grand_father(0,1)-0
>> grand_father(1,0)-0 grand_father(1,1)-0
>> % 2true
>> % father(0,0)-1 father(0,1)-1 father(1,0)-0 father(1,1)-0
>> % grand_father(0,0)-1 grand_father(0,1)-1
>> grand_father(1,0)-0 grand_father(1,1)-0
>> % 3true
>> % father(0,0)-1 father(0,1)-0 father(1,0)-1 father(1,1)-0
>> grand_father(0,0)-1 grand_father(0,1)-0
>> grand_father(1,0)-1 grand_father(1,1)-0
>> % 4true
>> https://swish.swi-prolog.org/p/mace4.swinb
>>
>> The first solution, is from a domain with size N=1,
>> and it basically says a counter model is when
>> there is an individual 0, which is its own father.
>>
>> The fourth solution, is from a domain with size N=2,
>> and it basically says a counter model is when
>> there are two individuals 0 and 1, which are each others father.
>>
>> Problem 1 is defined as:
>>
>> /* I am my own grandpa? */
>> problem(1, (
>>    @[X]: @[Y]:(#[Z]:(father(X,Z) & father(Z,Y)) <=> grand_father(X,Y)) =>
>>    ~ #[X]:grand_father(X,X))).
>>
>> I have also toyed around with Problem 2:
>>
>> /* Is every monoid commutative? */
>> problem(2, (
>>     (@[X]:(0*X = X) &
>>     @[X]:(X*0 = X) &
>>     @[X]: @[Y]: @[Z]:((X*Y)*Z = X*(Y*Z))) => (a*b = b*a))).
>>
>> But Problem 3 is quite hard, takes 12 minutes:
>>
>> /* Is every group commutative? */
>> problem(3, (
>>     (@[X]:(0*X = X) &
>>     @[X]:(i(X)*X = 0) &
>>     @[X]: @[Y]: @[Z]:((X*Y)*Z = X*(Y*Z))) => (a*b = b*a))).
>>
>> McCune claims it takes < 1 second with his mace4.
>>
>> Don't know yet how to speed up Problem 3.
>>
>> Moebius schrieb:
>>> "Problem 1: I am my own grandpa?
>>>
>>> Is this possible from terminological definition:
>>> grand_father(X,Y) :- father(X,Z), father(Z,Y)."
>>>
>>> Of course. Where's the problem?
>>>
>>> If X = Y = I
>>> and Z = Nobody
>>>
>>> and in the datebase:
>>> father(I, Nobody)
>>> father(Nobody, I)
>>>
>>> then clearly
>>>
>>> grand_father(I,I)
>>>
>>> holds. No?
>>>
>>>
>>
> 

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Self-evidently I am not my grandpa Mild Shock <janburse@fastmail.fm> - 2024-04-27 14:44 +1000
  Re: Self-evidently I am not my grandpa Mild Shock <janburse@fastmail.fm> - 2024-05-02 10:35 +1000
    Re: Self-evidently I am not my grandpa Moebius <invalid@example.invalid> - 2024-05-02 02:49 +0200
    Re: Self-evidently I am not my grandpa Moebius <invalid@example.invalid> - 2024-05-02 02:50 +0200
      Re: Self-evidently I am not my grandpa Mild Shock <janburse@fastmail.fm> - 2024-05-02 10:59 +1000
        Re: Self-evidently I am not my grandpa Moebius <invalid@example.invalid> - 2024-05-02 03:44 +0200
          Re: Self-evidently I am not my grandpa Mild Shock <janburse@fastmail.fm> - 2024-05-03 11:46 +1000
            Re: Self-evidently I am not my grandpa Moebius <invalid@example.invalid> - 2024-05-03 10:07 +0200

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