20 lines
490 B
Plaintext
20 lines
490 B
Plaintext
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Thm : \Sigma is Maximum Satisfiability
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iff
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\Sigma is satisfiable and complete.
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Proof of above theorem.
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Claim: \Sigma \entails \alpha Iff \Sigma \cup \{ \neg \alpha\} is Not satisfiable.
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Finite models theorem: (FMT)
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A set \Sigma \entails some wff \alpha
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implies
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there is a finite subset of \Sigma which \entails \alpha.
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Proof of FMT using claim above.
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Claim : \Sigma is maximally satisfiable Iff
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\Sigma has a unique valuation.
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Left as an exercise.
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