On Sun, 2 Mar 2008, Chris Menzel wrote:
> ...A system S is negation complete if, for any sentence A of
> the language of S, either A or its negation ~A is a theorem of S. Note
> that this is a purely proof theoretic notion. A *logic* L -- that is, a
> language + semantics + proof theory -- is semantically complete if every
> logical truth of the language of L is a theorem of L. Note that nothing
> we typically call a system of *logic* is negation complete. For
> example, in propositional logic, no propositional variable p or its
> negation ~p is a logical theorem. In predicate logic, neither (x)Px nor
> ~(x)Px, for example, is a theorem.  (01) 
I forgot to emphasize (as most folks here probably know): While neither
propositional nor predicate logic is negation complete (and that's a
very good thing!), both are *semantically* complete (that's also a very
good thing :-).  (02)
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