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

 To: "[ontolog-forum]" "doug foxvog" Sun, 19 Sep 2010 02:36:09 -0400 (EDT) <57408.75.148.142.41.1284878169.squirrel@xxxxxxxxxxxxxx>
 ```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 > >> 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 doesnâ€™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 >> >> > > _________________________________________________________________ > 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 >    (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. =============================================================    (011) _________________________________________________________________ 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    (012) ```
 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