🚀 go-pugleaf

In article <Bw0r39.G2I@cs.bham.ac.uk>, ard@cs.bham.ac.uk (Antoni Diller) writes:
|> In article <rkaivola.718902434@mits> rkaivola@mits.mdata.fi (Risto Kaivola) writes:

	[ stuff about translating conditionals deleted ]

Here are the usual translations found in logic texts for the material
(and similar) conditional and biconditional:

     --------------------------------------------

     P -> Q

     if P then Q
     if P, Q
     Q if P
     Provided that P, Q
     Q provided that P
     On condition that P, Q
     Q on condition that P
     P only if Q
     P only on condition that Q

     ---------------------------------------------

     P <-> Q

     P if and only if Q
     P just in case Q
     P when and only when Q
     P exactly on condition that Q

     -------------------------------------------

There are probably other common translations as well, but I
cannot recall at the moment.

For some reason 'only' tends to confuse people (I suspect it
is because they don't really know how it works in English).
Sometimes it is easier to get the correct sense of an 'only'
expression by considering a quantified version, as in

	Only a dog is a labrador retriever.

	(x is a labrador retriever) -> (x is a dog)

	Bob is a labrador retriever only if he is a dog.

On the other hand, in my experience, many people find this
even *more* confusing.  In reading 'P->Q' as 'P only if Q'
it helps to emphasize the 'only':  P *only* if Q.  (If you
say the 'only' loudly enough you start to get the idea.)

-- 
Gary H. Merrill  [Principal Systems Developer, C Compiler Development]
SAS Institute Inc. / SAS Campus Dr. / Cary, NC  27513 / (919) 677-8000
sasghm@theseus.unx.sas.com ... !mcnc!sas!sasghm