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@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 - 10:42:10 CDT