Faithful and invariant conditionals in Lukasiewicz logic

To every consistent finite set circle minus of conditions, expressed by formulas (equivalently, by one formula) in Lukasiewicz infinite-valued propositional logic, we attach a snap P(circle minus) assigning to each formula psi a rational number P(circle minus)(psi) is an element of [0, 1] that represents "the conditional probability of psi given circle minus". The Value P(circle minus)(psi) is effectively computable from circle minus and psi. The map circle minus bar right arrow P(circle minus) has the following properties: (i) (Faithfillness): P(circle minus)(psi) = 1 if and only if circle minus proves psi, where proves is syntactic consequence in Lukasiewiez logic, coinciding with semantic consequence because circle minus is finite. (ii) (Additivity): For any two formulas phi and psi) whose conjunction is falsified by circle minus, letting chi be their disjunction we have P circle minus(chi) = P circle minus(phi) + P circle minus(psi). (iii) (Invariance): Whenever circle minus' is a finitely axiomatizable theory and (L) is an isomorphism between the Lindenbaum algebras of circle minus and of circle minus', then for any two formulas psi and psi' that correspond via (L) we have P circle minus(psi) = P circle minus(psi'). (iv) If 0 = 0(x(1),...,x(n)) is a tautology, then for any formula psi = psi (x(1),...,x(n)), the (now unconditional) probability P({)theta} (psi) is the Lebesgue integral over the n-cube of the McNaughton function represented by psi.