http://www-groups.dcs.st-and.a... - s get false, it too must get false in the model. We have thus found our falsifying model, and s could never have been proved using any sound system of rules....
http://www-groups.dcs.st-and.a... - provable. Alternatively, if s is not provable, we must exhibit a model where s is false. If s is not provable, then when we attempt to prove it using the rules...
http://www-groups.dcs.st-and.a... - ∀x.f is true wrt. environment e, we must show that for all m, f is true wrt. environment e(x := m). From the assumption, choosing e to be e(u := m),...
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http://www-groups.dcs.st-and.a... - (at least one of) P or Q gets false in the model, so P ∧ Q gets false in the model. Having shown soundness and completeness for our system, we can derive...
