Re: computational model of transactions

From: Brian Selzer <brian_at_selzer-software.com>
Date: Sun, 06 Aug 2006 15:39:49 GMT
Message-ID: <93oBg.5217$uo6.2900@newssvr13.news.prodigy.com>

"paul c" <toledobythesea_at_oohay.ac> wrote in message news:0a3Bg.321039$Mn5.154491_at_pd7tw3no...
> David Cressey wrote:

>> "Brian Selzer" <brian_at_selzer-software.com> wrote in message
>> news:AKTAg.1198$1f6.1097_at_newssvr27.news.prodigy.net...
>>> "J M Davitt" <jdavitt_at_aeneas.net> wrote in message
>>> news:FDSAg.63277$Eh1.44696_at_tornado.ohiordc.rr.com...
>>
>>>> I think GW triggered on *always* in the phrase, "Axioms are always
>>>> true..."  In this world, axioms are little more than things that
>>>> are said to be true because someone says they're true and we
>>>> sometimes encounter axioms which contradict each other.
>>> Thank you for pointing that out.  I didn't intend that sense of the 
>>> word;
>>> though, now that you mention it, I can see how that could be assumed.
>> What
>>> I did intend was the sense denoting a fundamental, self-evident truth 
>>> that
>>> is so obviously true that a counter-proof would be inconceivable.
>>>
>>>
>>
>> I'm going to recall a discussion some months ago, about whether what is
>> stored in the database is "fact" or "opinion".
>> A given assertion could be axiomatic within the contrived world of the
>> database,  but easily proven false in the real world.
>>
>> Illustration:
>>
>> Teller (looking at screen):  According to my database,  you're dead.
>> Client (exasperated):  But, as you can see, I'm not dead!
>> Teller:  I'm sorry, but I won't be able to help you until someone back at
>> headquarters fixes the database.
>> Client:  Is there someone else I can speak to?
>> ...
>
>

> Heh, obviously two worlds clashing here. Some assume the Bible contains
> fundamental truths but in a logical theory, surely an axiom is merely an
> assumption we make in order for the theory to operate as we desire it to,
> eg., sets that have no members or rows that have no columns.

>

> For some, another assumption/axiom is time but in stark logic I don't
> think we absolutely need it. We don't need it to 'read' a db even though
> we usually use a time shortcut to up-"date" one. Given the assumptions
> that have passed by in this thread, I'm probably throwing fuel on the fire
> here but I'll chance it. Surely what we "read" is a logical 'sum' of
> assertions and retractions in the sense not that that is what it has to be
> in the natural world but rather that it is what it has to be given the
> theory we want to use.

>

> We may choose to say those assertions and transactions must have gone
> 'before', otherwise we wouldn't be reading their sum 'now' and we usually
> do. For practical reasons a dbms usually acknowledges time, but I take
> this as a grudging acknowledgement, a shortcut that memorizes a logical
> sum for later. It doesn't mean time needs to be an axiom, unless an
> application has a requirement for that to be so. Ie., a logical system
> doesn't need to assume time. We could imagine a dbms where a program
> reads a sum calculated from all the other programs, not a stored sum. In
> a world without time, the calculation wouldn't take long!

>

> I find it very hard to use English for this, trying to avoid the many
> words like 'always' that have time built in (BTW, recently somebody on TV
> was saying that all human grammars have tense). Eg., if we say that a
> program is the logical sum of the set of all the programs that have gone
> 'before' we are assuming time, somehow that program comes 'later'. In a
> world without the time dimension we might choose to define 'before' as the
> set of programs/invocations that produce the same result as the db gives.
> Usually we think doing that might take too much time but that's only
> because computers are stuck in this world. Logically, I think time is
> optional.

>

Time may be optional, but I don't think you can ignore order. You speak of a logical "sum." Since we're dealing with propositions, I think that that "sum" must be conjunctive in nature, but is not logical conjunction exactly, because the order in which the propositions are "summed" is important. If the propositions to be "summed" form a set, then order is not important, but I don't think they form a set, but rather a list, and your reference to retractions above implies that. The truth of a set of propositions is the same regardless of the order, but the same is not true with a list of propositions. In a list, the same assertion can be stated more than once while still maintaining consistency, provided that there are intervening retractions. The same is not true if those assertions and retractions are taken together as a set. The conjunction, A ^ ~A ^ A is the same as A ^ ~A, because A ^ A = A; in other words A ^ ~A ^ A is a contradiction and thus can be ignored. The list of assertions (A, ~A, A), on the other hand, means A.

In addition, the act of stating an assertion changes the database. Assume that you have a database D that contains k assertions. If you assert a new fact F, then database D is transformed into database D' with k+1 assertions. So now you have two database states, D, the preceeding state, and D', the succeeding state. There is a definite relationship between D and D', and given D and D', you can determine F. If you ignore the existence of D, then you ignore the relationship between D and D', and therefore, you must state every assertion in D', you cannot just assert F.

Now, I'll grant you that if the database can't change, then order is optional.

> p
>
Received on Sun Aug 06 2006 - 10:39:49 CDT