Valid argument schemas can use semantics and try to find counterexamples. If argument finds none, it is proof {semantic proof}. For first-order logic, semantic validity is also syntactic validity {soundness theorem, semantic proof}. For first-order logic, if one can find semantic counterexample, syntactic calculus cannot prove argument. Second-order, monadic, modal, and temporal logics use semantic argument proofs.
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Date Modified: 2022.0224