Class 17 : Consistency, Satisfiability and Maximal consistency 

Consistency of \emptyset using soundness

Theorem : \Sigma is satisfiable ==> \Sigma is consistent

Example (1) \Sigma_1=\{p\}
Example (2) \Sigma_2=\{p_1,p_2,...\}
Example (3) \Sigma_3=\{ p_i -> p_j | for all i,j\}
Consistency of \Sigma іn the above examples using Theorem.

Maximally Consistent Set (\Sigma): 
(1) \Sigma is Consistent
(2) \Sigma \derives \alpha OR \Sigma \union \{\alpha} is inconsistent

Example (4) \Sigma_1 is consistent but not MCS
Example (5) \Sigma_1 is consistent. Discussion of difficulty in
proving it's maximal consistency. Motivation for the converse
direction of above theorem.