- From: pat hayes <phayes@ai.uwf.edu>
- Date: Sat, 17 May 2003 10:59:11 -0500
- To: Jeremy Carroll <jjc@hpl.hp.com>, Ian Horrocks <horrocks@cs.man.ac.uk>
- Cc: www-webont-wg@w3.org
(Sending this quickly, more comments later. -Pat ) section 4.1.2. model/satisfying interpretation (Neither the RDF nor OWL documents uses 'model' in this technical sense.) 2nd 'consistent' is potentially misused (referring to an interpretation), suggest consistent with the constraints ... /satisfies all the constraints .... 4.2.2 Im still not happy with the way that conformance is stated. Discussion. The problem is that 'complete' means something different when applied to inconsistency and consistency checking. OK, you don't want to have two kinds of conformance, but there must be a way to get this stated which isn't so misleading. Here is the standard account. An inconsistency checker is complete if, given any inconsistent input, it will eventually return 'Inconsistent'. That is the standard definition of 'complete' used ever since Goedel's first theorem and throughout the logical literature, the sense in which resolution is complete and FOL has a complete proof theory. The analogous statement for consistency is false in these cases, because the task of determining consistency is one recursion class higher than for inconsistency, in general (so following your definition, and the observation that inconsistency of (A and not B) is the same as A entailing B, would lead to the assertion that there was no complete inference system for first-order logic, for example, which sounds like a denial of the central theorem of FOL proved by Goedel in 1938.) However, for subcases which are *decideable* - such as DLs - then termination of a complete inconsistency checker without finding inconsistency amounts to determining consistency. That is, you can in effect use negation-by-failure reasoning when you know (1) it is complete and (2) we know the problem is decideable. The trouble with your 'complete and terminating' phrase is that it is natural to read this is a conjunction of two properties, viz. complete and terminating, and then to ask what it be to be complete and non-terminating. Since the sense of 'complete' that you use only lines up with the standard notion in the case where it is terminating, there is a constant danger of this being misread as meaning exactly what it seems to say, rather than your meaning. The cheapest way around this would be to add a remark when you give the definition of 'complete' to indicate that this sense is not the standard sense. For example "This is stronger than the usual sense of completeness used in describing logical inference systems, which refers only to the detection of inconsistency." A better way, IMHO, would be to use a different term. How about 'decideable', would that be less likely to stick in Ian's craw? It is slightly nonstandard (the word is usually applied to the problem than to the algorithm) but clear in its meaning, fits well onto the useage for the DL case (on a decideable subcase, a complete correct algorithm is a decision procedure) and fits naturally: one can have a decideable consistency checker just when the problem of deciding consistency is a decideable problem. This has the merit of not mis-using an established terminology in a misleading way, it uses a conventional word, and it is shorter than "complete and terminating". My preference would be to use 'decideable' (or any word or phrase that does not misuse the word 'complete') and be (reluctantly) willing to go with the current wording but only if it is protected at the point of definition (6th para of 4.2.2) with a suitable warning. Pat -- --------------------------------------------------------------------- IHMC (850)434 8903 or (650)494 3973 home 40 South Alcaniz St. (850)202 4416 office Pensacola (850)202 4440 fax FL 32501 (850)291 0667 cell phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes s.pam@ai.uwf.edu for spam
Received on Saturday, 17 May 2003 11:58:04 UTC