Re: A Logical Model for Lists as Relations

From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Thu, 11 May 2006 21:09:14 GMT
Message-ID: <_JN8g.6435$A26.164800@ursa-nb00s0.nbnet.nb.ca>

Vadim Tropashko wrote:

> mAsterdam wrote:
>

>>Let's have a name for this way of describing a list as a relation.
>>Is "numbered items" ok?
>>
>>>The other possibility is to represent list with refereences like this:
>>>
>>>table EmpList (
>>>   nodeId   integer,
>>>   nextNodeId   integer,
>>>   ...  -- list element content
>>>)
>>
>>Would "successive items" be a good one for this way?
>>
>>So, we have several ways to describing a list as a relation, at
>>least "numbered items" and "successive items".

>
> The difference between the two essentially reduces to the way how we
> represent the order. The first method is intensional. It encodes the
> elements of a list with integer numbers which are (totaly) ordered. The
> second method is extensional. The order is represented explicitly by
> binary relation.
>

>>To me it isn't clear what discrete piece of information content
>>is carried by an individual "number" or "successor" attribute.

>
> This question is meaningless without understanding what "information
> content" is.
>
> To reply to another thread where Bob raised the utility question, it is
> undoubtful that sequences appear all over the math. Arguably, sequence
> is even more frequently occuring concept than set. There is even a
> dedicated website dedicated to integer sequences:
> http://www.research.att.com/~njas/sequences/

Keep in mind that the sets in question are sets of axioms. I have doubts regarding the prevalence of sequences of axioms.

In the math, sequences and series are very often parameterized so that one can construct statements or descriptions regarding the ith or jth element/term. Since statements and descriptions are no different than axioms, it only makes sense similarly to use sets of axioms regarding the parameterized elements.

One might argue that not all sequences are so parameterized. However, in these cases, the sequences must have some other distinction among the elements, which is all we need to make statements about them using sets of axioms.

By sticking with sets of axioms, we retain the full use of the predicate calculus. If we switch to something else, naturally we would want some benefit exceeding our loss. Received on Thu May 11 2006 - 16:09:14 CDT