14 lines
483 B
Plaintext
14 lines
483 B
Plaintext
Class 16 : DT, Soundness, consistency
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Completion of proof of deduction theorem
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Example proof of \derives (\neg \neg \alpha) --> \alpha
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Soundness theoreom : \Sigma \derives \alpha \implies \Sigma \entails \alpha
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Consistency defn 1 : There does not exists a formula \alpha such that
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\Sigma \derives \alpha and \Sigma \derives (\neg \alpha))
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Consistency defn 2 : There exists an alpha which is not derivable assuming \Sigma.
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Thm: Equivalence of two notions of consistency.
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