21 lines
676 B
Plaintext
21 lines
676 B
Plaintext
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Class 17 : Consistency, Satisfiability and Maximal consistency
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Consistency of \emptyset using soundness
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Theorem : \Sigma is satisfiable ==> \Sigma is consistent
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Example (1) \Sigma_1=\{p\}
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Example (2) \Sigma_2=\{p_1,p_2,...\}
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Example (3) \Sigma_3=\{ p_i -> p_j | for all i,j\}
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Consistency of \Sigma іn the above examples using Theorem.
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Maximally Consistent Set (\Sigma):
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(1) \Sigma is Consistent
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(2) \Sigma \derives \alpha OR \Sigma \union \{\alpha} is inconsistent
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Example (4) \Sigma_1 is consistent but not MCS
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Example (5) \Sigma_1 is consistent. Discussion of difficulty in
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proving it's maximal consistency. Motivation for the converse
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direction of above theorem.
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