Semantic notions for a set of formulas:

\Sigma - satisfiable, examples.

Logical implication \Sigma \entails \alpha

complete -- \Sigma \entails \alpha (inclusive OR) \Sigma \entails (\neg \alpha)

\Sigma is satisfiable and complete then 
         \Sigma \entails \alpha (XOR) \Sigma \entails (\neg \alpha)

Maximum Satisfiability 
          In addition to being satisfiable, Sigma has the following property: 
          \neg( \Sigma \entails \alpha) \implies \Sigma \cup \{ \alpha\} is not satisfiable. 
