Re: Relational symmetric difference is well defined
From: V.J. Kumar <vjkmail_at_gmail.com>
Date: Fri, 15 Jun 2007 23:17:20 +0200 (CEST)
Message-ID: <Xns9950B034ADC1Fvdghher_at_194.177.96.26>
>> Jan Hidders <hidd..._at_gmail.com> wrote
>> innews:1181910061.495472.280190_at_c77g2000hse.googlegroups.com:
>>
>>
>>
>> > On 1 jun, 03:40, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:
>> >> Vadim Tropashko <vadimtro_inva..._at_yahoo.com> wrote
>> >> innews:1180628927.976321.267880_at_a26g2000pre.googlegroups.com:
>>
>> >> > On May 30, 8:52 pm, Marshall <marshall.spi..._at_gmail.com> wrote:
>> >> >> Can you clarify the difference between set containment join and
>> >> >> set equality join? The inverse of join is much on my mind these
>> >> >> days.
>>
>> >> > Set equality join
>>
>> >> > A(x,y)/=B(y,z) is {(x,z)| {y|A(x,y)}={y|A(y,z)} }
>>
>> >> > Set containment join
>>
>> >> > A(x,y)/=B(y,z) is {(x,z)| {y|A(x,y)}>{y|A(y,z)} }
>>
>> >> > where the ">" is "subset of".
>>
>> >> The above formulas obviously are no longer first-order
>> >> expressions. Along with the increased expressive power (e.g. it's
>> >> trivial to define a powerset), you will reap the usual drawbacks
>> >> of the higher order logic.
>>
>> > This was perhaps already clear, but it is the *formulation* of the
>> > semantics which is not first-order. The semantics themselves are
>> > clearly first order since they can be defined in first order logic
>> > or the flat relational algebra.
>>
>> This is very intriguing !
Date: Fri, 15 Jun 2007 23:17:20 +0200 (CEST)
Message-ID: <Xns9950B034ADC1Fvdghher_at_194.177.96.26>
Jan Hidders <hidders_at_gmail.com> wrote in news:1181919464.037821.176760_at_p77g2000hsh.googlegroups.com:
> On 15 jun, 16:00, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:
>> Jan Hidders <hidd..._at_gmail.com> wrote
>> innews:1181910061.495472.280190_at_c77g2000hse.googlegroups.com:
>>
>>
>>
>> > On 1 jun, 03:40, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:
>> >> Vadim Tropashko <vadimtro_inva..._at_yahoo.com> wrote
>> >> innews:1180628927.976321.267880_at_a26g2000pre.googlegroups.com:
>>
>> >> > On May 30, 8:52 pm, Marshall <marshall.spi..._at_gmail.com> wrote:
>> >> >> Can you clarify the difference between set containment join and
>> >> >> set equality join? The inverse of join is much on my mind these
>> >> >> days.
>>
>> >> > Set equality join
>>
>> >> > A(x,y)/=B(y,z) is {(x,z)| {y|A(x,y)}={y|A(y,z)} }
>>
>> >> > Set containment join
>>
>> >> > A(x,y)/=B(y,z) is {(x,z)| {y|A(x,y)}>{y|A(y,z)} }
>>
>> >> > where the ">" is "subset of".
>>
>> >> The above formulas obviously are no longer first-order
>> >> expressions. Along with the increased expressive power (e.g. it's
>> >> trivial to define a powerset), you will reap the usual drawbacks
>> >> of the higher order logic.
>>
>> > This was perhaps already clear, but it is the *formulation* of the
>> > semantics which is not first-order. The semantics themselves are
>> > clearly first order since they can be defined in first order logic
>> > or the flat relational algebra.
>>
>> This is very intriguing !
> > Not really. It is pretty obvious that in the above formulation of the > semantics of the joins you can replace the higher order expression > with a first order formula.
How ?
> > -- Jan Hidders > >Received on Fri Jun 15 2007 - 23:17:20 CEST