it is well-known that “casual conditional” in islamic logics has been used with two meanings: “specific conditional” and “general conditional”. however, viewing the works of the muslim logicians, we find out that these two meanings of “casual conditional” have been interpreted in two various ways: each of the general and specific conditionals is sometimes interpreted as the condition of “non-ne...

we prove that the limit of a sequence of pettis integrable bounded scalarly measurable weak random elements, of finite weak norm, with values in the dual of a non-separable banach space is pettis integrable. then we provide basic properties for the pettis conditional expectation, and prove that it is continuous. calculus of pettis conditional expectations in general is very different from the c...

A considerable amount of studies have been established on conditional reasoning supporting mental model theory of propositional reasoning. Mental model theory proposed by Johnson- larid and Byrne is an explanation of someone's thought process about how something occurs in the real world. Conditional reasoning as a kind of reasoning is the way to speak about possibilities or probabilities. The a...

We consider the problem of using simulation to efficiently estimate the win probabilities for participants in a general random knockout tournament. Both of our proposed estimators, one based on the notion of “observed survivals” and the other based on conditional expectation and post-stratification, are highly effective in terms of variance reduction when compared to the raw simulation estimato...