Re: A Logical Model for Lists as Relations
From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Sat, 13 May 2006 15:42:10 GMT
Message-ID: <m7n9g.7229$A26.183202_at_ursa-nb00s0.nbnet.nb.ca>
>
>
> I'm suspicious as well, but my suspicions are at the semantic level. The
> above is not a list of Prime ministers,
> but a list of governments. We are using the PM as a token of the government
> that the PM led.
>
> In the US, if you are building a list of US presidents, Grover Cleveland
> appears once in the list. If you are building a list of presidencies,
> Cleveland appears twice.
>
> Off topic: Isn't it in "The Mikado" where there's a song "I have a little
> List"?
Date: Sat, 13 May 2006 15:42:10 GMT
Message-ID: <m7n9g.7229$A26.183202_at_ursa-nb00s0.nbnet.nb.ca>
David Cressey wrote:
> "JOG" <jog_at_cs.nott.ac.uk> wrote in message
> news:1147467334.905572.107190_at_y43g2000cwc.googlegroups.com...
>
>>Bob Badour wrote: >> >>>JOG wrote: >>> >>> >>>>Marshall Spight wrote: >>>> >>>> >>>>>JOG wrote: >>>>> >>>>> >>>>>>Marshall Spight wrote: >>>>>> >>>>>> >>>>>>>But a list can be described as a relation. Most simply, an infinite >>>>>>>list is a relation from the natural numbers to the target set, >>>>>>>and a finite list is a relation from some finite contiguous subset >>>>>>>[0..n] of the naturals to the target set. Generalizing, we could >>>>>>>describe an n-ary list as a relation with an index attribute and >>>>>>>zero or more other attributes. >>>>>> >>>>>>Do you not find this unsatisfying though? >>>>> >>>>>Actually, I find it quite satisfying, since it means I can, for >>>>>example, >>>>>use the full power of the relational algebra for selection on lists. >>>>> >>>>> >>>>> >>>>>>By doing this one is altering >>>>>>information that is ordinal in nature to being cardinal. >>>>> >>>>>I don't understand this statement. Can you expand? >>>> >>>> >>>>"The order of the primeministers were Blair, major, thatcher" = >>>>"Blair was prime minister after Major." >>>>"Major was prime minister after Thatcher." >>>> >>>>Hence A satisfying relation (to me ;) representing this list is: >>>>{ (Blair, Major), (Major, Thatcher) } >>>> >>>>This ordinal representation does not need to include cardinal indeces, >>>>and to my eyes that's a good thing as where did they exist in the >>>>original propositions? >>> >>>You will run into problems when you get to things like: >>> >>>{ (MacDonald, Laurier), (Laurier, MacDonald), (MacDonald, Laurier) } >> >>Indeed. This makes me think something suspicious is going on if we view >>lists, where repetition of elements is somehow acceptable, as a >>fundamental construct. Either we have to invent indeces or we seem to >>have a problem with set representation.
>
>
> I'm suspicious as well, but my suspicions are at the semantic level. The
> above is not a list of Prime ministers,
> but a list of governments. We are using the PM as a token of the government
> that the PM led.
>
> In the US, if you are building a list of US presidents, Grover Cleveland
> appears once in the list. If you are building a list of presidencies,
> Cleveland appears twice.
>
> Off topic: Isn't it in "The Mikado" where there's a song "I have a little
> List"?
If we are not interested in the full order of the prime ministers, why do we need a list in the first place? Received on Sat May 13 2006 - 17:42:10 CEST