Re: teaching relational basics to people, questions

On Dec 11, 1:29 pm, Kevin Kirkpatrick <kvnkrkpt...@xxxxxxxxx> wrote:
Hello Mr. Scott,
If I'm understanding your explanation properly, in a database with
only table:
BIG_US_CITIES {CITY_NAME, STATE_CODE}
(that is, lacking table STATES {STATE_CODE}) one must logically infer,
from the CWA, that states with no big cities, e.g. 'RI', do not exist?

On Dec 11, 1:36 pm, Gene Wirchenko <ge...@xxxxxxxx> wrote:
Effectively yes.

On Dec 11, 8:15 pm, "Mr. Scott" <do_not_re...@xxxxxxxxx> wrote:
There isn't anywhere to record the assertion that there is a
state with no big cities, so there can't be any.

It is more reasonable to say that the database is silent about the
existence of states and cities. But even if it did, the inference that
some state doesn't exist is wrong.

If the predicate is "the city named city_name in state state_code is
big", then what you know is that for every tuple <c, s> in
big_us_cities "city named c in state s is big", and that (by the cwa)
for every tuple <c, s> typed by but not in in big_us_cities "it is not
the case that: the city named c in state s is big". (Maybe there is
no such named city anywhere; or maybe there's one in one or more in
other states; and/or maybe they're just not big; or there's no such
state; or that city in s is small; etc.) (If it were the case, the
tuple would have been in the relation. The use of this interpretation
of relations, which is done in a relational dbms and the relational
algebra needs in order to answer queries, is "assuming a closed
world".) This particular database (ie relation variable plus
predicate) has nothing to say about the existence of states or cities.
There is no way to write a relation expression whose predicate
involves existence starting from only the given predicate.

Now, if the user is allowed to assume (which they would using the
everyday meaning of the predicate above) that "exists c: the city
named c in state s is big" implies "there is a state named s" then
they could reason from <c,s> being in big_us_cities that "there is a
state named s". But from <c,s> not in big_us_cities they still
couldn't infer that "s is not a state". (Maybe there's just no such
city; or it's small in state s; etc.)

Note that the database has no idea what the predicate is, let alone
what "big" means or what a "state" is or the consequences (like
"existence") of there being or not being a big city named c in state
s. With this relation and predicate you can write a query that tells
you whether (ie its predicate is) for some city c "there exists an s
such that the city named c in state s is big". But there is no query
that answers "is there a state s". (But I told you how to derive it).

This should not be surprising since if we change the predicate for
big_us_cities to "the number of characters in string city_name is not
the age of any dog whose tag says state_id" we wouldn't expect any
query to give a different answer for any given value of big_us_cities.
Regarding silence on existence, we also wouldn't expect any such
change if we do add explicit information about existence.

Also regarding non-existence: Suppose existence is made explicit by
the predicate being something like "state state_code exists and city
city_name exists in that state and that city is big". Then when <c, s>
is in big_us_cities you know "state s exists" because it follows from
"state s exists and ...". But if <c,s> is not in big_us_cities you
still don't know which (one or more) of the conjuncts is false to make
the whole thing false. You only know the whole predicate is fakse
using <c,s>. So you don't know that "state s doesn't exist".

philip
.

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