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Re: Review of Direct Semantics (ACTION 314)

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Tue, 07 Apr 2009 20:30:14 -0400 (EDT)
Message-Id: <20090407.203014.166245011.pfps@research.bell-labs.com>
To: schneid@fzi.de
Cc: public-owl-wg@w3.org
From: "Michael Schneider" <schneid@fzi.de>
Subject: RE: Review of Direct Semantics (ACTION 314)
Date: Tue, 7 Apr 2009 23:56:02 +0200

>>> * General: The definitions in the document, in particular those in
>>>2.5, are of the form "A if B". While this is a typical convention
>>>under mathematicians, our documents are targeted to a broader
>>>audience. In order to avoid confusion, I suggest to always say "if
>>>and only if" (or "iff", and say once that this means "if and only
>>>if").

>>I've had extensive discussions about this with many people (notably
>>Uli), and they insisted that the latter form is rather ugly. I'd prefer
>>leaving things as they are.

> I cannot really be ok with this answer, since this is not a matter of
> ugliness, but a matter of correctness. I had a related review comment
> for the RDF-Based Semantics, but there, it was only about replacing the
> term "iff" by "if and only if" for clarity. Just for the record: In the
> RDF-Based Semantics, I won't agree to change the definitions there to
> "if", if "if and only if" is actually meant. However, given that an "if"
> in definitions is a widespread convention, I won't further request any
> changes, unless someone else in the WG concurs.
> 
> Weakly (and conditionally) accepted.


From http://en.wikipedia.org/wiki/If_and_only_if and similar also to
what I learned in fifty-two or so years of speaking English and four
years of honours mathematics (although my professors used "if" in
definitions even in logic-ish courses---of course, they were
logical mathematicians and not even mathematical logicians).


Definitions

In philosophy and logic, "iff" is used to indicate definitions, since
definitions are supposed to be universally quantified biconditionals. In
mathematics and elsewhere, however, the word "if" is normally used in
definitions, rather than "iff". This is due to the observation that "if"
in the English language has a definitional meaning, separate from its
meaning as a propositional conjunction. This separate meaning can be
explained by noting that a definition (for instance: A group is
"abelian" if it satisfies the commutative law; or: A grape is a "raisin"
if it is well dried) is not an equivalence to be proved, but a rule for
interpreting the term defined. (Some authors, nevertheless, explicitly
indicate that the "if" of a definition means "iff"!)


Of course, the use if "iff" is not all that old, as it apparently first
appears in print in 1955.  I wonder that philosophers and logicians used
before "iff" was available.  

So one could say that it is definitions with "iff" that are confined to
the philosophical ghetto, and that if we are writing to a general
audience then we should be using definitions with "if".

peter
Received on Wednesday, 8 April 2009 00:28:07 GMT

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