Can Uncertainty Management Be Realized In A Finite Totally Ordered Probability Algebra? [chapter]

Yang Xiang, Michael P. Beddoes, David Poole
1990 Machine Intelligence and Pattern Recognition  
In this paper, the feasibility of using finite totally ordered probability models under Aleliunas's Theory of Probabilistic Logic [Aleliunas, 1988] is investigated. The general form of the probability algebra of these models is derived and the number of possible algebras with given size is deduced. Based on this analysis, we discuss problems of denominator-indifference and ambiguity-generation that arise in reasoning by cases and abductive reasoning. An example is given that illustrates how
more » ... e problems arise. The investigation shows that a finite probability model may be of very limited usage. The semantics of TPL is given by 'possible worlds'. Each proposition P is associated with a set of situations or possible worlds S(P ) in which P holds. Given Q as evidence, the conditional probability p(P |Q), whose value ranges over the set P, is some measure of the fraction of the set S(Q) that is occupied by the subset S(P &Q). TPL provided minimum constraints for a rational belief model. For our particular domain we thought the following criteria were desirable: Consider the evaluation of p(f |s&a) in model M 8,4 with idempotent elements {e 1 , e 4 , e 7 , e 8 }. p(f |s&a) = p(s|f &a) * p(f |a)/p(s|a) = e 2 * e 5 /e 5 = e 5 /e 5 = [e 4 , e 1 ] Notice the solution in last step.
doi:10.1016/b978-0-444-88738-2.50011-7 fatcat:qq6jmgr4qzhaxlavyigqxhd32q