- From: Pat Hayes <phayes@ai.uwf.edu>
- Date: Thu, 27 Sep 2001 22:40:21 -0500
- To: "Seth Russell" <seth@robustai.net>
- Cc: www-rdf-logic@w3.org
- Message-Id: <p0510101cb7d99e06401a@[205.160.76.184]>
>It seems to me that if the law of identity does not hold in a context, What law of identity are you referring to, exactly? >then the Law of the Excluded Middle (LEM) and the Law of Non >Contradiction (LNC) are irrelevant and cannot be used in that >context. Why? I don't see the connection. (Presume you mean LEM = P or (not P) LNC = not (P and (not P)) right? These amount to the same thing in classical logic.) > For example: If we have two different computers hooked up to the >semantic web and in one's database an apple is only known as 'apple' >and the other it is only known as 'orange', Wait. How could you know that? That is, A is talking about things called A#apple, and B is talking about things called B#orange. How could you (or anyone) know they are supposed to be the same things? > then logical consequences that are inferred from the combination of >those two databases in that regard might be erroneous. If you only make valid inferences, they will never be erroneous (unless you make them from erroneous premises, of course, but the logic can't check that for you.) However, in general, one might be able to infer something from (A and B) that cannot be inferred from either A or B alone, so combining information from disparate sources is a risky business. It also suggests opportunities, though. ( Rather like life, right?) However, I can't quite see how one could get errors from your example. The problem seems more to be the other way round: If A says A#apples are red, you ought to be able to infer that B#oranges are red too, but you can't. Your inferential abilities are too weak, not too strong. > In KIF I think this would be expressed something like: > > (=> > (holdsIn contextX IDENTITY) > (and > (holdsIn contextX LNC) > (holdsIn contextX LEM) > ) > Not sure what that is supposed to mean. >I have expressed this in the following mentograph: ><http://robustai.net/mentography/lawsOfLogic.gif>http://robustai.net/mentography/lawsOfLogic.gif > >Don't you think that a model theory for RDF should take this basic >assumption about when to apply strong logic into consideration? > The model theory just says how RDF graphs can be interpreted, and thereby how to infer valid conclusions. Not sure what you mean by strong logic, but validity of entailment *always* applies. Pat Hayes -- --------------------------------------------------------------------- IHMC (850)434 8903 home 40 South Alcaniz St. (850)202 4416 office Pensacola, FL 32501 (850)202 4440 fax phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes
Received on Thursday, 27 September 2001 23:40:26 UTC