A qualitative probability satisfies some axioms:

• QP1
• QP2
• QP3

Lemma "=>" a qualitative probability =>

• Forall B in A, O"=>"B
• forall B,C in A, B Subset C => B "<" C
• forall B,C,D,E in A, B intersect C = empty set, D intersect E= empty set, B"=>"D, C"=>"E => A union B "=>" C union D