 Compactness and completeness: Compactness is a property of a logic where a set of formulas is satisfiable if every finite subset is satisfiable. Propositional probability logics lack the compactness property, as every finite subset of \(\{P(p)&gt;0\}\cup\{P(p)\leq a\,|\,a&gt;0\}\) is satisfiable, but the entire set is not.