On Feb 25, 2010, at 3:57 PM, sean barker wrote:
> ...
> If we define a concept C, which is defined using an axiom Q, and replace Q
> with an axiom P such that Q implies P but not vice versa (P is "stronger
> than" Q), then any process that had Q as a postcondition may produce invalid
> answers. (01)
Niggling point: You are turning around the usual understandings of "stronger"
and "weaker". If Q implies P (Q=>P) but not vice versa, then Q is stronger
than P and P weaker than Q. Thought of model theoretically, Q has fewer models
and hence "says more" than P. (02)
Less niggling point: Perhaps I am misunderstanding what you have in mind by an
"answer", but if postcondition Q of a process A is replaced by an axiom P such
that Q=>P but not vice versa, then every "answer" generated through the use of
P rather than Q could have been generated by the use of Q. So if the use of P
produces invalid answers, so does the use of Q. Seems to me the danger in
question arises only if you replace Q with an axiom R such that R=>Q but not
vice versa. For then the possibility arises of new answers that could not be
generated through the use of Q  answers that are perhaps "invalid" in some
relevant sense. (03)
> If we replace Q with a weaker axiom R, such that R implies Q but not vice
> versa, then any process which uses Q as a precondition can no be used, as
> the preconditions may be violated. (04)
Parallel comments here. (05)
Chris Menzel (06)
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