As a survey of many technical results in probability theory and probability logic, this monograph by two widely respected scholars offers a valuable compendium of the principal aspects of the formal study of probability. Leblanc and Roeper explore probability functions appropriate to propositional, quantificational, intuitionistic and infinitary logic and investigate the connections among probability functions, semantics and logical consequence. They offer a systematic justification of constraints for various types of probability functions, in particular, an exhaustive account of probability functions adequate for first-order quantificational logic. The relationship between absolute and relative probability functions is fully explored and the book offers a complete account of the representation of relative functions by absolute ones. The volume is designed to review familiar results, to place these results within a helpfully broad context, and to extend the discussions in new and interesting ways. Authoritative, articulate and accessible, it should interest mathematicians and philosophers at both professional and post-graduate levels.