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## Re: [ontolog-forum] Validity of laws of predicate logic under CWA and NA

 To: ankesh@xxxxxxxxx, "[ontolog-forum]" Adrian Walker Fri, 20 Feb 2009 10:42:20 -0500 <1e89d6a40902200742h28f3a800mb48907a3abc3d14a@xxxxxxxxxxxxxx>
 Hi Ankesh --Good questions.Unfortunately, there is more than one model theoretic semantics for negation as failure. (Apt-Blair-Walker stratified model, stable model,...)Fortunately, I'd guess that all of your statements are indeed valid under most of the above.  If Pat Hayes is watching, I'd expect an erudite contribution from him real soon (:-)Hope this helps,  -- AdrianInternet Business LogicA Wiki and SOA Endpoint for Executable Open Vocabulary English over SQL and RDF Online at www.reengineeringllc.com    Shared use is freeAdrian WalkerReengineeringOn Fri, Feb 20, 2009 at 10:35 AM, Ankesh Khandelwal wrote: Dear Ontolog-members, I have a knowledge base and a set of rules written under closed world assumption that use negation only as negation as failure. Under these circumstances are the laws of quantifier movement valid? Laws of Quantifier movements: 1. '(all x.P(x)) --> Q' equivalent-to 'exists x.(P(x)-->Q)', provided x is not free in Q 2. '(exisits x.P(x)) --> Q' equivalent-to 'all x.(P(x)-->Q)', provided x is not free in Q 3. 'P --> (all x.Q(x))' equivalent-to 'all x.(P --> Q(x))', provided x is not free in P 4. 'P --> (exists x.Q(x))' equivalent-to 'exists x.(P --> Q(x))', provided x is not free in P And/ Or are the following laws valid? 1. 'not(all x. P(x))' equivalent-to 'exists x.(not P(x))', where not has the Negation as Failure semantics. 2. 'not(exists x. P(x))' equivalent-to 'all x.(not P(x))', where not has the Negation as Failure semantics. Thank you, Ankesh _________________________________________________________________ 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    (01)
 Current Thread [ontolog-forum] Validity of laws of predicate logic under CWA and NAF, Ankesh Khandelwal Re: [ontolog-forum] Validity of laws of predicate logic under CWA and NAF, Adrian Walker <= Re: [ontolog-forum] Validity of laws of predicate logic under CWA and NAF, Ed Barkmeyer Re: [ontolog-forum] Validity of laws of predicate logic under CWA and NAF, Christopher Menzel