Adams, E.W. and H.P. Levine, On the Uncertainties Transmitted from Premises to Conclusions in Deductive Inferences, Synthese 30 (1975) 429--460.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Hailperin [97, 98, 100] also obtained several new results and proposed extensions of probabilistic satisfiability, discussed below. Due to its basic character probabilistic satisfiability was often independently rediscovered, sometimes in particular cases or variants, i.e. by Adams and Levine [8], Kounias and Marin [130] Nilsson [144] Chesnokov [51] Gelembe [84] and probably others. 1.3 Extensions 1.3.1 Probability Intervals (or Imprecise Probabilities) Several significant extensions of probabilistic satisfiability have been proposed. Hailperin [97] noted that the use of intervals ....

....undetermined if S 2 is false. Such conditional events, implicit in Boole [26] were defined by de Finetti [67, 68, 69] and rediscovered recently by many authors. Proposals for building an algebra of conditional events were made, more or less systematically, by Reichenbach [156] Schay [160] Adams [8], Hailperin [98, 100] Dubois and Prade [76] Bruno and Gilio [34] Calabrese [39, 40, 41, 42] Goodman, Nguyen and Walker [92] Several definitions, often justified on intuitive grounds, were given for conjunction and disjunction operations. Difficulty is largely due to the fact that as shown by ....

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Adams, E.W. and H.P. Levine, On the Uncertainties Transmitted from Premises to Conclusions in Deductive Inferences, Synthese 30 (1975) 429--460.

....among its existing formulas. Amarger, Dubois and Prade 1 Nilsson s [26] retrospective on the paper mentions some of the subsequent research on this topic. 2 For an earlier investigation of probabilistic entailment for both propositional and first order logic see the article by Adams and Levine [1]. 2] extend Quinlan s approach with rules for the derivation of conditional probabilities, as well as means of introducing new nodes. However, the new nodes are limited to conjunctions and disjunctions of other nodes. The main contribution of this paper is to describe an alternative approach to ....

....P(OE) we have the problem h Psi; OE j T )i, and we simply write h Psi; OEi. In either case, the second element of the pair is called the target of the probabilistic entailment problem. To precisely formulate the probabilistic entailment problem, momentarily suppose that for every set S [0 1] we can write sentences of the form P(OE j ) 2 S with the obvious truth conditions. Given h Psi; OE j )i, Psi is as before, a set of L PL sentences whose probabilistic components are closed intervals) the probabilistic entailment problem is that of finding the smallest set S such that P(OE j ....

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E. Adams and H. Levine. On the uncertainties transmitted from premises to conclusions in deductive inferences. Synthese, 30:429--460, 1975.

....on the probability of other sentences can be computed. This problem seems to have been first considered by De Finetti (1937) as follows : given a set of events E 1 , E n with known probabilities what can be said of the probability of another event E This problem has been further studied by Adams and Levine (1975) and Nilsson (1986) Clearly this view of probabilistic logic is in accordance with upper and lower probability systems, because it is clearly an example of incomplete knowledge about probabilities. This view of probabilistic logic enables conditional statements involving exceptions to be ....

....less obvious, path is to find inference rules for this type of logic. For instance the quantified syllogism pattern in which P(r p) is computed in terms of P(p q) P(q p) and P(r q) is an example of such an inference rule (see Dubois and Prade, 1988c) An extreme case of this approach is Adams (1975) conditional logics, recently revived by Pearl (1988) In this logic, conditional statements are of the form P(q p) 1 e where e is infinitesinally small. A theory is then a pair (F,D) where F is a set of propositional sentences and D is a set of conditional statements of the form p q ....

Adams E.W., Levine H.P. (1975) On the uncertainties transmitted from premises to conclusions in deductive inferences. Synthese, 30, 429-460.

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