Interpret the Fagin Halpern conditional in terms of the rese

Interpret the Fagin Halpern conditional in terms of the resemblance-based rule of conditioning.

Solution

the axioms for probability used in the logic of Fagin, Halpern and Meggido :

P1 µ(X) 0 for all X X

P2 µ(S) = 1

P3 µ(X) = µ(X Y ) + µ(X Y^\' )

Acceptability rules, and in a sense reveal why P3 is a consequence of notion of acceptability of gambles.

Fagin, Halpern and Meggido, have formulated probabilistic logics that use measure-theoretic semantics, and have complete inference procedures; we designate them by LF HM . They consider only the case where the underlying logic is propositional logic, but in this case, their probabilistic logics are more expressive than ours. In the case where our probabilistic logic L uses measuretheoretic semantics and uses propositional logic as its underlying logic, it can be regarded as a relatively small fragment of one of Fagin, Halpern, and Meggido’s logics, but it is still of some interest, because it enables complete inference about relatively elementary probability statements (including those considered by Nilsson and by Frisch and Haddawy) without the greater complexity of Fagin, Halpern, and Meggido’s logics. Halpern and Pucella consider upper probability measures, and in they add reasoning about