Saturated Conditional Independence with Fixed and Undetermined Sets of Incomplete Random Variables
نویسندگان
چکیده
The implication problem for saturated conditional independence statements is studied in the presence of fixed and undetermined sets of incomplete random variables. Here, random variables are termed incomplete since they admit missing data. Two different notions of implication arise. In the classic notion of V -implication, a statement is implied jointly by a set of statements and a fixed set V of random variables. In the alternative notion of pure implication, a statement is implied by a given set of statements alone, leaving the set of random variables undetermined. A first axiomatization for V -implication is established that distinguishes purely implied from V -implied statements. Axiomatic, algorithmic and logical characterizations of pure implication are established. Pure implication appeals to applications in which the existence of random variables is uncertain, for example, when independence statements are integrated from different sources, when random variables are unknown or shall remain hidden.
منابع مشابه
Saturated Conditional Independence with Fixed and Undetermined Sets of Incomplete Random Variables
The implication problem for saturated conditional independence statements is studied in the presence of fixed and undetermined sets of incomplete random variables. Here, random variables are termed incomplete since they admit missing data. Two different notions of implication arise. In the classic notion of V -implication, a statement is implied jointly by a set of statements and a fixed set V ...
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