On Sun, September 19, 2010 2:06, Alex Shkotin said: (01)
> It seems that in FOL we do not have a definition at all:
>
> suppose we have binary predicate R (primary or defined) and we introduce
> new
> predicate R_ and two axioms with it: (02)
> "R(x,y) hence R_(x,y)"
> and (03)
> "R_(x,z) and R(z,y) hence R_(x,y)" (04)
> We can't say that we have *definition* for R_ (05)
Not yet, another rule is needed: (06)
"R_(x,y) hence
either R(x,y)
or thereExists z such that R_(x,z) and R(z,y)" (07)
-- doug foxvog (08)
> as we need to add "the
> smallest..." as for transitive closure (
> http://en.wikipedia.org/wiki/Transitive_closure).
>
> What do you think?
>
> Alex
>
>
> 2010/9/18 Rich Cooper <rich@xxxxxxxxxxxxxxxxxxxxxx>
>
>> Ferenc,
>>
>>
>>
>> How about
>>
>>
>>
>> If _x is an ancestor of _z
>>
>> And _z is the father of _y
>>
>> Or _z is the mother of _y
>>
>> Then _x is an ancestor of _y.
>>
>>
>>
>> The basis relations include:
>>
>> _ is the father of _
>>
>> _ is the mother of _
>>
>>
>>
>> And the term defined with recursion, is
>>
>> _ is an ancestor of _
>>
>>
>>
>> Each expansion of the Horne clause during the query must be instantiated
>> with some variable or constant in order to continue expanding the search
>> backward. If at any point, the database runs out of father and mother
>> facts, then recursion stops. But that fact doesn’t show up in FOL as
>> clearly as in the software function that interprets it, and which must
>> specifically figure out how to stop the recursion when there is no more
>> fodder for the query.
>>
>>
>>
>> -Rich
>>
>>
>>
>> Sincerely,
>>
>> Rich Cooper
>>
>> EnglishLogicKernel.com
>>
>> Rich AT EnglishLogicKernel DOT com
>>
>> 9 4 9 \ 5 2 5 - 5 7 1 2
>> ------------------------------
>>
>> *From:* ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:
>> ontolog-forum-bounces@xxxxxxxxxxxxxxxx] *On Behalf Of *FERENC KOVACS
>> *Sent:* Saturday, September 18, 2010 8:17 AM
>> *To:* ontolog-forum@xxxxxxxxxxxxxxxx
>> *Subject:* [ontolog-forum] PROF Swartz ON DEFINITIONS
>>
>>
>>
>> IN THE SAME DOCUMENT
>>
>> *Recursive Definitions*
>> (Advanced material) By a "direct ancestor" we mean one's "parents,
>> grandparents, great-grandparents, etc." More formally, we might write:
>>
>> "*x* is a direct ancestor of *y*" =df "*x* is a parent of *y*; or *x* is
>> a
>> parent of a parent of *y*; or *x* is a parent of a parent of a parent of
>> *
>> y*; etc."
>>
>>
>>
>> *My comments: is it not the referent that the definition is about?C
>> ompare
>> with the statement in the front above: quote*
>>
>> * *
>>
>> *For example, the term, "pain", is defined, but pain itself is not
>> defined. We define only terms, never their referents*. end of quote
>>
>> **
>>
>> *Ferenc*
>>
>>
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>
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> (09)
=============================================================
doug foxvog doug@xxxxxxxxxx http://ProgressiveAustin.org (010)
"I speak as an American to the leaders of my own nation. The great
initiative in this war is ours. The initiative to stop it must be ours."
- Dr. Martin Luther King Jr.
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