Re: a union is always a join!

From: Walter Mitty <>
Date: Mon, 16 Mar 2009 03:41:46 GMT
Message-ID: <_Tjvl.473$>

"Brian Selzer" <> wrote in message news:7mivl.20610$
> "Walter Mitty" <> wrote in message
> news:sQ7vl.237$
>> "Brian Selzer" <> wrote in message
>> news:9uVul.22264$
>>> "paul c" <> wrote in message
>>> news:wJDul.17957$PH1.5324_at_edtnps82...
>>>> Brian Selzer wrote:
>>>>> "paul c" <> wrote in message
>>>>> news:ZXlul.17783$PH1.16918_at_edtnps82...
>>>>>> Brian Selzer wrote:
>>>>>>> "Walter Mitty" <> wrote in message
>>>>>>> news:apltl.2309$
>>>>>>>> "Brian Selzer" <> wrote in message
>>>>>>>> news:eY2tl.9205$
>>>>>>>>> "paul c" <> 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?
> I'm not sure what you're driving at.

Now we're even! Received on Mon Mar 16 2009 - 04:41:46 CET

Original text of this message