Logicandapplications2023/class_08_22082023/summary.txt

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2023-08-29 14:58:24 +05:30
Thm : \Sigma is Maximum Satisfiability
iff
\Sigma is satisfiable and complete.
Proof of above theorem.
Claim: \Sigma \entails \alpha Iff \Sigma \cup \{ \neg \alpha\} is Not satisfiable.
Finite models theorem: (FMT)
A set \Sigma \entails some wff \alpha
implies
there is a finite subset of \Sigma which \entails \alpha.
Proof of FMT using claim above.
Claim : \Sigma is maximally satisfiable Iff
\Sigma has a unique valuation.
Left as an exercise.