Re: deductive databases
From: Jan Hidders <jan.hidders_at_REMOVETHIS.pandora.be>
Date: Sat, 21 May 2005 10:39:33 GMT
Message-ID: <FdEje.97223$4s4.5634188_at_phobos.telenet-ops.be>
>
> Then we haven't yet arrived at a precise formulation of the matter
> at issue. Your earlier formulation was
>
> In a structure with the two binary relations R and S. The formula should
> be true for precisely those structures in which S is the transitive
> closure of R.
>
> but from your comments above, this is not in fact what you had in
> mind.
Date: Sat, 21 May 2005 10:39:33 GMT
Message-ID: <FdEje.97223$4s4.5634188_at_phobos.telenet-ops.be>
Torkel Franzen wrote:
> Jan Hidders <jan.hidders_at_REMOVETHIS.pandora.be> writes:
>
>>Note that Mikito was asking about the case where you also had PA in your >>logic, so the structure also includes the constant 0 and the succesor >>function.
>
> Then we haven't yet arrived at a precise formulation of the matter
> at issue. Your earlier formulation was
>
> In a structure with the two binary relations R and S. The formula should
> be true for precisely those structures in which S is the transitive
> closure of R.
>
> but from your comments above, this is not in fact what you had in
> mind.
I immedeately admit that my formulation was sloppy here but it seemed obvious to me that if we are talking about a logic including PA then the signature also contains the functions that are necessary for doing PA. By now I think you have enough information to know what the exact problem is. So for the sake of clarity: the structure consists of D, R, S, 0 and succ, and nothing else.
- Jan Hidders