 \(\Cn\) is assumed to be supraclassical, i.e. if \(p\) can be derived from \(A\) by classical truth-functional logic, then \(p \in \Cn(A)\). \(A\) is a belief set if and only if \(A = \Cn(A)\). In what follows, \(K\) will denote a belief set. \(X \vdash p\) is an alternative notation for \(p \in \Cn(X)\), and \(X \not\vdash p\) for \(p \not\in \Cn(X)\). \(\Cn(\varnothing)\) is the set of tautologies.