- From: Pat Hayes <phayes@ihmc.us>
- Date: Fri, 25 Mar 2011 08:47:19 -0500
- To: Michael Brunnbauer <brunni@netestate.de>
- Cc: Michael Schneider <schneid@fzi.de>, semantic-web@w3.org
On Mar 25, 2011, at 5:00 AM, Michael Brunnbauer wrote: > > re > > On Fri, Mar 25, 2011 at 12:00:52AM +0000, Michael Schneider wrote: >> since skolemization retains equisatisfiability. But skolemization does /not/ >> lead to logically equivalent graphs. > > I don't think this is of practical relevance. In logic skolemized statements > are not logically equivalent to the original ones because you have introduced > new symbols *in the whole system* and the truth of the original statement is > independend of these symbols. If you look at statements and their skolemized > versions as *different axiom systems* it should be possible to construct a > model for the skolemized versions out of a model of the original versions > and vice versa. the systems are somehow equivalent. I cannot substantiate that > because I am not a logician. You do OK :-) The technical relationship is exactly preserving satisfiability, as you say here. If you skolemize S to get sk(S), then S does not entail sk(S) because they have different vocabulaires, but sk(S) is satisfiable if and only if S is: you can take any model of S and extend it to a model of sk(S), over the same universe and with all the old names still denoting what they did in the first model. Pat > > Regards, > > Michael Brunnbauer > > -- > ++ Michael Brunnbauer > ++ netEstate GmbH > ++ Geisenhausener Straße 11a > ++ 81379 München > ++ Tel +49 89 32 19 77 80 > ++ Fax +49 89 32 19 77 89 > ++ E-Mail brunni@netestate.de > ++ http://www.netestate.de/ > ++ > ++ Sitz: München, HRB Nr.142452 (Handelsregister B München) > ++ USt-IdNr. DE221033342 > ++ Geschäftsführer: Michael Brunnbauer, Franz Brunnbauer > ++ Prokurist: Dipl. Kfm. (Univ.) Markus Hendel > > ------------------------------------------------------------ IHMC (850)434 8903 or (650)494 3973 40 South Alcaniz St. (850)202 4416 office Pensacola (850)202 4440 fax FL 32502 (850)291 0667 mobile phayesAT-SIGNihmc.us http://www.ihmc.us/users/phayes
Received on Friday, 25 March 2011 13:48:04 UTC