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Thomas B. Passin wrote,
> I do not think that ordinary business applications today come close
> to using full FOL. Mostly things run on ordinary assertions (this
> would cover relational databases), and sometimes on rulesets.
> Ordinary markup languages are EC - Existential Conjunctive - only one
> sector of FOL - and they are almost always enough for these kinds of
> uses.
I disagree.
Actually, I'll go further. Even full first-order logic is too
restrictive to express many trivial inferences straightforwardly. For
example,
There's a 5% surcharge on primary coloured widgets
x is a red widget
red is a primary colour
therefore,
There's a 5% surcharge on x
This is easy to express in second-order logic, or in first-order logic
plus set theory (the "plus set theory" bit means that you can forget
about decidability). Not so easy in plain first-order logic.
Expressive power, decidablity ... pick one.
Cheers,
Miles
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