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In article <1992Apr11.130906.796@gacvx2.gac.edu>, logic@gacvx2.gac.edu writes:
> In article <1992Apr10.161709.5397@vax.oxford.ac.uk>, loader@vax.oxford.ac.uk (R Loader) writes:
>> In article <1992Apr8.100146.689@gacvx2.gac.edu>, logic@gacvx2.gac.edu writes:
>>> In article <1992Apr7.124948.5325@vax.oxford.ac.uk>, loader@vax.oxford.ac.uk (R Loader) writes:
>>> 
>>>> S4 and S5 (and most other common modal logics), are subsystems of classical
>>>> (non-modal) logic extended with the axiom: A iff \box A.
>>> 
>>> Other stuff deleted....
>>> 
>>>> Ralph Loader,
>>>> Mathematical Institute, Oxford.
>>> 
>>> S4 and S5 are supersystems, not subsystems, of classical logic..  Neither
>>> contain the axiom "A iff \box A", both contain the axiom "if \box A then A".
>>> 
>>> Al Hart
>> 
>> Sorry, My original posting was ambiguous: I meant ". . . are subsystems
>>   of the logic obtained by adding A iff \box A to classical logic"
>> --
>> Ralph Loader, Oxford.
> 
> I see the ambiguity now - missed it during my first post..  however, not having
> extracted your first post, i'm not sure i see the point.  extending classical
> logic with the axiom A iff \box A obviously makes \box completely superfluous.
> 
> confused,
> al hart


He is obviously wrong, as two of us already pointed out (I did in # 1463).
"A iff \box A" does not belong to S4 or S5.

Marek Suchenek