“…only a convention”

April 1, 2009

Welcome to the first post in my “logic malpractice” category. In this category, I will document various actions and words by nominally (and seriously) qualified logicians that are so wacked out as to constitute malpractice (if anyone comes to harm). I’ll usually document such words when they could cause confusion in the logic laity. Our first entry comes from a post by Pat Hayes:

Most conventional logical notations segregate relations from the things (“individuals”) they are relations on. OWL-DL and the OBO Foundry logics follow this ‘segregated’ convention. However, this is only a convention, and there is no fundamental logical requirement why this must be done: OWL-Full, RDF and Common Logic all do not make any strong distinction between relations and other entities.

Full disclosure: I am not speaking with Pat since he publicly accused me and some others of falsifying an academic paper in order to “destroy RDF”. Note that Pat was wrong on the technical point (check the rest of the thread) and does not retract his appalling remark.

Sad, isn’t it. That doesn’t mean I can’t document his malpractices of course!

So what’s wrong with this quote? Critically, it presents the standard sorting of first order logic as a “mere convenience” which has little to no serious implications for the logic (“there is no fundamental logical requirement why this must be done”). This is well-known to be utterly false. While you can lift the sorting of the user defined vocabulary, there are several different ways to do it and they radically different effects. If you also lift the sort distinction between user defined vocabulary and the logical vocabulary, things get even messier (see OWL Full).

Of course, it depends on how you do it. In OWL 2, we allow “punning” which breaks the sorting without and semantic implications at all. That is, we allow the sort of an occurrence of a term to be determined by its syntactic position. Thus, by simple syntactic analysis, we can rewrite each name in the logical theory to incorporate its sort (e.g., C_a_unary_predicate vs. C_a_logical_constant and then separate the terms in the normal way. Going beyond this is tricky. For a nice analysis of some key liftings, see Boris Motik’s paper on metamodeling in OWL. (He includes a discussion on punning.)

To suggest otherwise is serious malpractice. To phrase your malpractice in weasel words (i.e., no fundamental logical requirement) lifts it from culpable negligence to, at best, criminal negligence with a strong suggestion of malice. (The weasel words are there, IMHO, so that when challenged on this point, Hayes can backpedal with “What I say is technically TRUUUUUEEEE!!!!!! The problems aren’t fundamental since you CAN work around them and still have an “essentially” first order logic. Thus they aren’t a REQUIREMENT either!?111.” But this is malpractice. Even expert logicians, steeped in the field, might well find Pat’s suggestion surprising. But they are in a position to check and evaluate the various ways of breaking the basic sorting. The general public isn’t. The connotation of Hayes’ line is that the sorting is piddling and rather unimportant. That’s so not true.) The suggestion to the logical novice that this is an easy peasy thing that has been relaxed many times without problem and what ho! see OWL Full and Common Logic is really off the charts. At the moment, it’s still unknown if OWL Full is consistent. That’s not a trivial matter.

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