Re: a union is always a join!

From: Brian Selzer <>
Date: Sun, 15 Mar 2009 21:57:22 -0400
Message-ID: <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. I'm not trying to answer philisophical questions about change, nor do I seek to wax metaphysical. I merely accept that it is not only the micro-world that a database is supposed to represent that can vary over time, but also the things in that micro-world. Received on Mon Mar 16 2009 - 02:57:22 CET

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