Re: a union is always a join!

"Brian Selzer" <brian_at_selzer-software.com> wrote in message news:9uVul.22264$Ws1.16416_at_nlpi064.nbdc.sbc.com...
>
> "paul c" <toledobythesea_at_oohay.ac> wrote in message
> news:wJDul.17957$PH1.5324_at_edtnps82...
>> Brian Selzer wrote:
>>> "paul c" <toledobythesea_at_oohay.ac> wrote in message
>>> news:ZXlul.17783$PH1.16918_at_edtnps82...
>>>> Brian Selzer wrote:
>>>>> "Walter Mitty" <wamitty_at_verizon.net> wrote in message
>>>>> news:apltl.2309$%u5.1252_at_nwrddc01.gnilink.net...
>>>>>> "Brian Selzer" <brian_at_selzer-software.com> wrote in message
>>>>>> news:eY2tl.9205$%54.7793_at_nlpi070.nbdc.sbc.com...
>>>>>>> "paul c" <toledobythesea_at_oohay.ac> wrote in message
>>>>>>> news:beZsl.15959$Db2.2243_at_edtnps83...
>>>>>>>> Walter Mitty wrote:
>>>>>>>>
>>>>>>>>> ... I'm also going to suggest that what
>>>>>>>>> Brain S. calls "oversimplification" is almost exactly what others
>>>>>>>>> call
>>>>>>>>> "abstraction". I'm also going to suggest that without abstraction
>>>>>>>>> you don't
>>>>>>>>> get any independence, and without independence, you don't get much
>>>>>>>>> of any
>>>>>>>>> bang for the buck. That may be of zero theoretical importance,
>>>>>>>>> but it's of
>>>>>>>>> interest to me.
>>>>>>>>> ...
>>>>>>>> Walter, I'm with the many people who think phyaical and logical
>>>>>>>> independence are of high importance, both theoretically and
>>>>>>>> practically. But I'd say many of the nuances and implications of
>>>>>>>> those haven't been explored much in print. Brain S as you call him
>>>>>>>> regularly enters the realm of mysticism. I point this out not to
>>>>>>>> correct him, but to warn newcomers here that he is not exactly
>>>>>>>> swimming in the main stream of relational theory (to be fair, not
>>>>>>>> many are, because the theory is often confused with past practice).
>>>>>>>> I have a number of mystic acquaintances and I like them all, partly
>>>>>>>> because they don't involve themselves in db theory and there is
>>>>>>>> much in life for which mysticism offers the only comfortable clues.
>>>>>>>>
>>>>>>> Mysticism. If accepting that the universe of discourse contains
>>>>>>> things and that at different times a thing can differ in appearance
>>>>>>> yet still be the same thing means that I'm a mystic, then I'm guilty
>>>>>>> as charged.
>>>>>> What difference does it make whether it's the same thing or a
>>>>>> different thing?
>>>>> If an employee worked 50 hours on a project and his labor rate is $20
>>>>> per hour, then it cost $1000 to have him work on the project, right?
>>>>> WRONG! The employee's labor rate /is/ $20 per hour, but that doesn't
>>>>> mean that it /had been/ $20 per hour during the time that he worked on
>>>>> the project. At that time his labor rate might have been $18 per hour
>>>>> or may even have changed part way through the project. So the record
>>>>> of cost must not contain just which project, which employee and how
>>>>> many hours, but also at which labor rate or rates the work was
>>>>> performed. But the employee is still the same employee even though
>>>>> his labor rate changed from $18 to $20. Other cost records may exist
>>>>> for projects that he worked on after the rate increase, and one should
>>>>> expect that a query of which projects he worked on would return all of
>>>>> the projects, regardless of the labor rate.
>>>>>
>>>>> So something can appear different at different times yet still be the
>>>>> same thing.
>>>>>
>>>>> This poses a problem because keys are not necessarily permanent
>>>>> identifiers. (I'm having trouble articulating my thought here because
>>>>> there is more than one usage of the term, "key." I'm disinclined from
>>>>> using "key value" because under an interpretation, a key value is a
>>>>> mapping to a particular thing in the universe, that thing being the
>>>>> output of the valuation function for the set of symbols for the
>>>>> components in a tuple of the set of attributes that is the candidate
>>>>> key, and it's possible for that same set of symbols to map to
>>>>> different things at different times, or for different sets of symbols
>>>>> to map to the same thing at different times. But it's unwieldy to say
>>>>> "sets of symbols for the components in a tuple of the set of
>>>>> attributes that is the candidate key" instead of just "keys.") The
>>>>> problem stems from how things in the universe of discourse are
>>>>> identified, and that the scope of the definition of a candidate key is
>>>>> any database and not all databases. While a key may uniquely identify
>>>>> something in the context of its containing database, that doesn't
>>>>> necessarily mean that that same key uniquely identifies that same
>>>>> something at all databases in which it appears.
>>>> I wish, at least once, you would give an answer that was shorter than
>>>> the question.
>>>
>>> Ask me a question that has a simple answer, and I'll simply answer it.
>>>
>>>
>>
>> That's a cute riposte in that it grants my wish as far as my last
>> question is concerned. But how about the simple answer to Walter M's
>> question (which is "none", ie., the attributes that are chosen for
>> relations determine the consequences)?
>
> As my voluminous reply indicated, I don't think that it is "none."
>
>> The example of the employee whose hourly cost changes is bogus because it
>> confuses employee cost with project hourly costs, obviously the latter
>> would be an attribute of some project relation in any workable system.
>>
>
> But it is clear that at each interval during which the employee was
> working on the project, the employee's hourly cost and the project's
> hourly cost (at least as far as the employee was concerned) were
> identical. That fact cannot be denied even though the database doesn't
> maintain an explicit record of the employee's rate changes.
>
>>
>> One of the flaws of the mystic persuasion as far as db's are concerned
>> and as we see it in your posts, is that it denies, in what usually
>> appears to me to be in a willful and haphazard way, that mechanical db's,
>> so far in history, don't actually relect reality, only an abstraction of
>> reality. This has got to be understood in any mention of
>> 'interpretation'. At some point maybe you will come to see that.
>
> Abstraction is a good thing. I don't deny it. The universe of discourse,
> or as Codd put it, "the micro-world that the database is supposed to
> represent," for most if not all databases is itself an abstraction of just
> a subset of reality. But what you appear to be trying to do is apply
> mechanisms that only work for static mathematical objects to things that
> can change over time. That's not abstraction: that's just illogical.
>
> There is a huge difference between a relation for an operator defined on a
> domain of mathematical objects and a relation defined on a domain of
> things that that can change over time. In particular, there can only ever
> be one extension of the relation for the operator, whereas there are as
> many possible extensions of the other as there are legal combinations of
> tuples. The relation for the operator is true at all possible worlds at
> all times under all interpretations, so the mechanism of its
> interpretation is moot since the outcome is always the same. But for
> things that can change over time, the mechanism of interpretation becomes
> critical because whether or not a tuple appears in a relation depends
> solely upon whether the assertion it represents has been assigned a
> positive truth value under an interpretation.
>
>> I wouldn't criticize if you could describe a formal model that could
>> embody the very extraneous notions you bring up, but the usual assumption
>> of any reader here is that the RM is the starting point but your starting
>> point doesn't which makes it very hard for any reader to guess what the
>> dickens your context is. Nothing wrong with additional abstractions
>> beyond Codd's, as long as the perpretators recognize that they need to
>> explain them to the rest of us.
>
> There really isn't room here for a detailed explanation, but perhaps what
> follows will at least clarify what my context is.
>
> The way I see it, the Relational Model is equivalent to a formal logical
> system based on a first-order modal tense logic. Modal because the set of
> all domain constraints, relation constraints and database constraints
> together specifies the set of all possible databases, which is the
> equivalent of the set of all possible worlds, and tense because a database
> is the equivalent of an assertion that states not just what is the case
> but rather what has been the case since the last update, and a transition
> is the equivalent of an assertion that states in the context of what has
> been the case (or more precisely, what had been the case during the
> interval from the last update up to this point) what is different and
> exactly how.
>
> The simple terms of a formal language of that system include, like any
> formal first-order language, a set of individual names, a set of
> individual variables, and a set of relation names of various degrees. An
> atomic formula is of the form P(x1,...,xn) where P is a relation name and
> (x1,...,xn) are a set of zero or more individual variables. Complex
> formulae are formed by combining atomic formulae with logical operators,
> connectives and quantifiers. Constraints are sentences (closed formulae)
> that together specify which models are legal under the intended
> interpretation. A model is an extension of each formula in each possible
> world, a mapping of each term to something in the universe of discourse,
> and a mapping of each formula in each extension to a truth value, which as
> a consequence states which member of the set of all possible worlds is the
> actual world. Constraints fall into four categories: a set of named
> constraints partitions the set of individual names; another set of
> constraints specifies the set of all legal extensions for each formula; a
> third set specifies the legal combinations of extensions that together
> constitute the set of all possible worlds, and a fourth set defines which
> possible worlds are accessible from another. Under the Unique Name and
> Closed World Assumptions, these sets of constraints are the equivalents of
> domain definitions, relation constraints, database constraints and
> transition constraints in the Relational Model.
>
> If you're interested in other abstractions beyond Codd's, you might want
> to investigate Edward Zalta's theory of abstract objects. In particular,
> his paper "The Modal Object Calculus and its Interpretation," published in
> /Advances in Intensional Logic/, 1996, describes in detail the mechanism
> of interpretation--including the assignment of meaning to terms in the
> formal language and the assignment of truth values to formulae.
>

Don't you think Heraclitus said all of this much more clearly, some 2500 years ago?

http://www.spaceandmotion.com/philosophy-metaphysics-heraclitus.htm Received on Sun Mar 15 2009 - 14:58:48 CET