Re: WWW/Internet 2009: 2nd CFP until 21 September

"paul c" <toledobythesea_at_oohay.ac> wrote in message news:utehm.41210$PH1.31779_at_edtnps82...
> Mr. Scott wrote:
> ...
>> The table {X,A,B,C,D,E} has one predicate. All of the attributes apply
>> to all orders even if their values are at present unknown.
>>
>> The predicate is "being an order that has order number X for customer E
>> that was placed on date D with delivery e-mail address A and delivery
>> snail-mail address B and delivery contact phone number C where X is an
>> element of the domain of all order numbers and E is an element of the
>> domain of all customers and D is an element of the domain of all dates
>> and A is an element of the domain of all e-mail addresses and B is an
>> element of the domain of all snail-mail addresses and C is an element of
>> the domain of all phone numbers" where X, A, B, C, D and E are free. A
>> row in the table consists of values that are to be substituted for free
>> variables in the predicate. The row {x1,a1,b1,c1,d1,e1} would mean after
>> substitution "the order with order number x1 for customer e1 that was
>> placed on date d1 with delivery e-mail address a1 and snail-mail address
>> b1 and delivery contact phone number c1." A row with a null snail-mail
>> address and a null delivery contact, {x2,a2,d2,e2} means after
>> substitution "the order that has order number x2 for customer e2 that was
>> placed on date d2 with delivery e-mail address a2 and delivery snail-mail
>> address B and delivery contact phone number C where B is an element of
>> the domain of all snail-mail addresses and C is an element of the domain
>> of all phone numbers."
>> ...
>
> How can four values be substituted into a predicate with six
> place-holders?

I think the process is called currying. A n-ary predicate is a function of n variables that maps into the domain of truth values. Each row in a table is a function application that under the closed world assumption maps to the positive truth value. An incomplete row (a row with nulls) is a partial application that due to entity integrity still maps to the positive truth value. What remains is not a predicate but a formula with free variables that is known to be true. Received on Fri Aug 14 2009 - 20:20:40 CEST