Systems of logico-probabilistic reasoning characterize inference from conditional assertions that express high conditional probabilities. In this paper we investigate four prominent LP systems, the systems _O, P_, _Z_, and _QC_. These systems differ in the number of inferences they licence _. LP systems that license more inferences enjoy the possible reward of deriving more true and informative conclusions, but with this possible reward comes the risk of drawing more false or uninformative conclusions. In the first part of the paper, we (...) present the four systems and extend each of them by theorems that allow one to compute almost-tight lower-probability-bounds for the conclusion of an inference, given lower-probability-bounds for its premises. In the second part of the paper, we investigate by means of computer simulations which of the four systems provides the best balance of reward versus risk. Our results suggest that system _Z_ offers the best balance. (shrink)

. Syllogisms like Barbara, “If all S is M and all M is P, then all S is P”, are here analyzed not in terms of the truth of their categorical constituents, “all S is M”, etc., but rather in terms of the corresponding proportions, e.g., of Ss that are Ms. This allows us to consider the inferences’ approximate validity, and whether the fact that most Ss are Ms and most Ms are Ps guarantees that most Ss are Ps. It (...) turns out that no standard syllogism is universally valid in this sense, but special ‘default rules’ govern approximate reasoning of this kind. Special attention is paid to inferences involving existential propositions of the “Some S is M” form, where it is does not make sense to say “Almost some S is M”, but where it is important that in everyday speech, “Some” does not mean “At least one”, but rather “A not insignificant number”. (shrink)