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## Re: [ontolog-forum] PROF Swartz ON DEFINITIONS

 To: "'[ontolog-forum] '" "Rich Cooper" Sun, 19 Sep 2010 14:03:39 -0700 <20100919210346.6212F138D20@xxxxxxxxxxxxxxxxx>
 Hi Alex,   The term “ancestor” in English means ALL those people who made babies in closure sequence that led to the subject x’s birth by parents y1 and y2, so the “smallest” ancestor would only give those responses that are equally small – y1 and y2.     For example, our ancestors may go all the way back to most of Turkana Boy’s ancestors two million years ago, so as an upper limit, 2^N ancestors for N generations (but there was also interbreeding, so the actual number must be way less than 2^N by a large factor) over long terms.     But I am not really certain I comprehend the point you are trying to make.  Perhaps you can use Parent(x,y) and Ancestor(x,y) instead of R(x,y) and R_(x,y).  The symbols are construed by the interpretER (me in this case) possibly differently than you meant them.     -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 Alex Shkotin Sent: Saturday, September 18, 2010 11:07 PM To: [ontolog-forum] Subject: Re: [ontolog-forum] PROF Swartz ON DEFINITIONS   Hi Rich, 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: "R(x,y) hence R_(x,y)" and "R_(x,z) and R(z,y) hence R_(x,y)"   We can't say that we have definition for R_ 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 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 _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
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 Current Thread [ontolog-forum] PROF Swartz ON DEFINITIONS, FERENC KOVACS Re: [ontolog-forum] PROF Swartz ON DEFINITIONS, Peter Yim Re: [ontolog-forum] PROF Swartz ON DEFINITIONS, Rich Cooper Re: [ontolog-forum] PROF Swartz ON DEFINITIONS, Alex Shkotin Re: [ontolog-forum] PROF Swartz ON DEFINITIONS, doug foxvog Re: [ontolog-forum] PROF Swartz ON DEFINITIONS, Rich Cooper <= Re: [ontolog-forum] PROF Swartz ON DEFINITIONS, Alex Shkotin Re: [ontolog-forum] PROF Swartz ON DEFINITIONS, Christopher Menzel Re: [ontolog-forum] PROF Swartz ON DEFINITIONS, John F. Sowa Re: [ontolog-forum] PROF Swartz ON DEFINITIONS, Alex Shkotin Re: [ontolog-forum] PROF Swartz ON DEFINITIONS, John F. Sowa Re: [ontolog-forum] PROF Swartz ON DEFINITIONS, Christopher Menzel Re: [ontolog-forum] PROF Swartz ON DEFINITIONS, John F. Sowa Re: [ontolog-forum] PROF Swartz ON DEFINITIONS, Patrick Durusau Re: [ontolog-forum] PROF Swartz ON DEFINITIONS, Christopher Menzel Re: [ontolog-forum] PROF Swartz ON DEFINITIONS, Alex Shkotin