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:
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[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