Re: computational model of transactions

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.

>> I did intend was the sense denoting a fundamental, self-evident truth that
>> is so obviously true that a counter-proof would be inconceivable.
>>
>>

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.

p Received on Sat Aug 05 2006 - 17:53:32 CEST