M. Ramoni, A. Riva, Belief maintenance with probabilistic logic, in: Proceedings AAAI Fall Symposium on Automated Deduction in Nonstandard Logics, Raleigh, NC, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....is ill suited for our purposes. One can think of the progression of the TNT inference algorithm as the evolution of a particular context, as more information becomes known or believed, but there is no reason to compare one context to another during the inference of function. Ramoni and Riva [39] have augmented the LTMS to propagate probabilistic intervals, and they use this logic based belief maintenance system (LBMS) as a substrate for a class of Bayesian belief networks they call ignorant belief networks, or IBNs [40,41] Their LBMS uses a variant of Nilsson s probabilistic logic [35] ....

M. Ramoni, A. Riva, Belief maintenance with probabilistic logic, in: Proceedings AAAI Fall Symposium on Automated Deduction in Nonstandard Logics, Raleigh, NC, 1993.

....during a particular time slice lies in a particular range. We associate to each sentence an interval truth value that represents the set of its admissible probability values. Reasoning over interval truth values is performed by a novel tool, called Logic Based Belief Maintenance System (lbms) (Ramoni and Riva, 1993), that is able to deal with incomplete probabilistic models. Initially all the propositions have the truth value [0 1] meaning that, since we have no information at all, we are not able to put bounds on their probability value. In the course of the monitoring process, the data coming from the ....

Ramoni, M. and A. Riva (1993); Belief maintenance with probabilistic logic, Proceedings of the AAAI Fall Symposium on Automated Deduction in Non-Standard Logics, Raleigh, NC.

.... tmss able to propagate probabilistic rather than binaries truth values are called Belief Maintenance Systems (bmss) Falkenhainer, 1986; Laskey and Lehner, 1989 ] ibns are belief maintained bbns: they exploit a bms based on probabilistic logic, and therefore called Logic based bms (lbms) Ramoni and Riva, 1993 ] 2.1 Belief Maintenance A lbms uses a standard propositional language L defined by a set of atomic propositions S = fa 1 ; a 2 ; ang and by the standard Boolean operators : oe, and j. A literal l is an atomic proposition a i or its negation :a i . An atomic proposition a i is a ....

.... P (a i ) P (a i ja j ; as) s Y k=j P (ak ) It is worth noting that the resulting posterior probability set is still convex, since it is the result of a linear mapping of the extreme values of a probability interval, and ecp was proved to preserve convexity during propagations [ Ramoni and Riva, 1993 ] Furthermore, in ibns, the inversion formula shares with the chain rule the appealing property of propagating only the available information, thus preserving the incremental refinement policy of ecp. 2.4 Properties From the theory of tmss, the lbms inherits the concept of consumer [ de ....

M. Ramoni and A. Riva. Belief maintenance with probabilistic logic. In Proceedings of the AAAI Fall Symposium on Automated Deduction in Non Standard Logics, Raleigh, NC, 1993. AAAI.

....to include probabilities in tmss. tmss that are able to reason on the basis of probabilistic rather than binary truth values are called Belief Maintenance Systems (bmss) 13,10,20] ibns are bbns developed on top of a new kind of bms based on probabilistic logic, called Logic based bms (lbms) [31]. 3.1 The Belief Maintenance System The lbms assumes a propositional language defined by a set of atomic propositions S = fa 1 ; a n g and by the standard Boolean operators : oe, and j. A literal l is an atomic proposition a i or its negation :a i . An atomic proposition a i is a ....

....i ) Gamma 1g In order to compute the overlap factor of a clause C, we need to know the probability of those clauses that contain exactly the same set of atomic propositions. Extending definition 2 to interval, we derived a set of constraints on the minimum and maximum probability of literals [31], by dropping the assumption that all literals in a clause are pairwise disjoint. The first constraint enforces the left hand side of inequality 2. Constraint 1 The probability of a literal l i in clause C is bounded by: P (l i ) P (C) FC Gamma X j 6=i P (l j ) where FC is the overlap ....

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M. Ramoni, and A. Riva, Belief maintenance with probabilistic logic, in: Proceedings of the AAAI Fall Symposium on Automated Deduction in Non Standard Logics (Raleigh, NC, 1993), AAAI.

....attempts have been made to include probabilities in 6 Marco Ramoni Alberto Riva tmss. tmss that are able to reason on the basis of probabilistic rather than binary truth values are called Belief Maintenance Systems (bmss) We have introduced a new class of bmss, called Logic based bms (lbms) [9] in which Boolean connectives of standard logic act as constraints on the (probabilistic) truth values of propositions. The lbms manipulates two basic kinds of structures: propositions, a 1 ; an , representing atomic propositions of a propositional language, and clauses, of the form (a 1 a ....

M. Ramoni and A. Riva. Belief maintenance with probabilistic logic. In Proceedings of the AAAI Fall Symposium on Automated Deduction in Non Standard Logics, Raleigh, NC, 1993. AAAI.

....have been made to include probabilities in tmss. tmss that are able to reason on the basis of probabilistic rather than binary truth values are called Belief Maintenance Systems (bmss) 3] We have introduced a kind of bms based on probabilistic logic, and therefore called Logic based bms (lbms) [14]. Using the lbms, we developed a new class of bbns, called ibns, able to reason with partially specified conditional dependencies (i.e. lacking some conditional probabilities) and interval probability values. 2.1 Belief Maintenance tmss are independent reasoning modules which incrementally ....

M. Ramoni and A. Riva. Belief maintenance with probabilistic logic. In Proceedings of the AAAI Fall Symposium on Automated Deduction in Non Standard Logics, Raleigh, NC, 1993. AAAI.

....of a bms based on probabilistic logic able to reason on the basis of incomplete probabilistic information. From a logical point of view, it can be regarded as an extensional system based on a set theoretic interpretation of probability. Logic based Belief Maintenance A logic based bms (lbms) (Ramoni and Riva, 1993) is a bms in which Boolean connectives of standard logic act as constraints on the probabilistic truth values of propositions. The lbms can be regarded as a generalization to interval truth values of the Boolean Constraint Propagation method (McAllester, 1990) The lbms manipulates two basic ....

....in the set theoretic interpretation of a clause, the intersection of all propositions is always empty. It is apparent that this assumption is too strong. Generalizing definition (2) to interval truth values, we derived a set of constraints on the minimum and maximum probability of propositions (Ramoni and Riva, 1993) . If we define P ( a i ) and P ( a i ) as denoting the minimum and the maximum probability of the proposition a i , then for each clause C in which it appears: 1: P (a i ) P (C) FC Gamma P j 6=i P (a j ) 2: P (a i ) 1 Gamma P j (1 Gamma P ( a i j ) 3) Inequality ....

Ramoni, M. and Riva, A. (1993). Belief maintenance with probabilistic logic. In Proceedings of the AAAI Fall Symposium on Automated Deduction in Non Standard Logics, Raleigh, NC. AAAI.

....proposition, and they provide a correct algorithm for computing the beliefs of these labels. D Ambrosio (D Ambrosio, 1987) exploited the atms architecture to compute a special case of belief functions. We have extended the third class of tmss to probability, thus producing a Logic based bms(lbms) (Ramoni and Riva, 1993) . This paper will describe how this method for belief maintenance can be applied to bbns, thus introducing a new class of bbns able to incrementally deal with partially specified conditional dependencies and prior probabilities, to provide wellfounded explanations for their conclusions, and to ....

....need to know the probability of those clauses that contain exactly the same set of atomic propositions, and hence to abandon the strict locality of clauses. Generalizing definition (2) to interval truth values, we derived a set of constraints on the minimum and maximum probability of propositions (Ramoni and Riva, 1993) , by dropping the assumption that all literals in a clause are pairwise disjoint. The first constraint enforces the left hand side of (2) Constraint 1 The probability of a proposition a i in clause C is bounded by: P (a i ) P (C) FC Gamma X j 6=i P (a j ) where FC is the overlapping ....

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Ramoni, M. and Riva, A. (1993). Belief maintenance with probabilistic logic. In Proceedings of the AAAI Fall Symposium on Automated Deduction in Non Standard Logics, Raleigh, NC. AAAI.

....of the solutions. This paper investigates the anytime character of a method for evaluating ids and provides a measure of the object related value of the solutions. This methods is based on a general anytime algorithm for probabilistic inference called Epistemic Constraint Propagation (ecp) Ramoni and Riva, 1993 ] The incremental character of ecp allows the decision maker to trade execution time with precisions of solutions and, given a measure of the object related value [ Boddy and Dean, 1994 ] of each solution that is, a measure of how good is the answer of the decision maker to plan the ....

....in it are labeled as false, thus producing a contradiction. When all literals but one in a clause are labeled as false bcp forces the unlabeled literal to be true. In order to extend the bcp from Boolean to probabilistic truth values, we derived, from the theory of probabilistic entailment [ Ramoni and Riva, 1993 ] a probabilistic interpretation of disjunction able to define which constraints are imposed by a clause over the (probabilistic) truth values of the literals occurring in it. However, since probabilistic entailment is unable to constrain the probability of formulas to point values, the standard ....

[Article contains additional citation context not shown here]

M. Ramoni and A. Riva. Belief maintenance with probabilistic logic. In Proceedings of the AAAI Fall Symposium on Automated Deduction in Non Standard Logics, Raleigh, NC, 1993. AAAI.

....been made to include probabilities in tmss. tmss that are able to reason on the basis of probabilistic rather than binary truth values are called Belief Maintenance Systems (bmss) 2. 1 Logic based Belief Maintenance Systems We have introduced a new kind of bms, called Logicbased bms (lbms) Ramoni and Riva, 1993 ] in which Boolean connectives of standard logic act as constraints on the (probabilistic) truth values of propositions. The lbms can be regarded as a generalization to interval truth values of the Boolean Constraint Propagation method [ McAllester, 1990 ] The lbms manipulates two basic kinds ....

....the Venn Diagrams representation of a clause, the intersection of all propositions is always empty. It is easy to see that this assumption is too strong. Generalizing definition (1) to interval truth values, we derived a set of constraints on the minimum and maximum probability of propositions [ Ramoni and Riva, 1993 ] If we define P (a i ) and P (a i ) as denoting the minimum and the maximum probability of the proposition a i , then for each clause C which it appears in: 1: P (a i ) P (C) 2: P (a i ) P (C) FC Gamma P j 6=i P (a j ) 3: P (a i ) 1 Gamma P j (1 Gamma P ( a i j ....

M. Ramoni and A. Riva. Belief maintenance with probabilistic logic. In Proceedings of the AAAI Fall Symposium on Automated Deduction in Non Standard Logics, Raleigh, NC, 1993. AAAI.

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