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A Logic for Reasoning about Probabilities
 Information and Computation
, 1990
"... We consider a language for reasoning about probability which allows us to make statements such as “the probability of E, is less than f ” and “the probability of E, is at least twice the probability of E,, ” where E, and EZ are arbitrary events. We consider the case where all events are measurable ( ..."
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Cited by 214 (19 self)
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We consider a language for reasoning about probability which allows us to make statements such as “the probability of E, is less than f ” and “the probability of E, is at least twice the probability of E,, ” where E, and EZ are arbitrary events. We consider the case where all events are measurable (i.e., represent measurable sets) and the more general case, which is also of interest in practice, where they may not be measurable. The measurable case is essentially a formalization of (the propositional fragment of) Nilsson’s probabilistic logic. As we show elsewhere, the general (nonmeasurable) case corresponds precisely to replacing probability measures by DempsterShafer belief functions. In both cases, we provide a complete axiomatization and show that the problem of deciding satistiability is NPcomplete, no worse than that of propositional logic. As a tool for proving our complete axiomatizations, we give a complete axiomatization for reasoning about Boolean combinations of linear inequalities, which is of independent interest. This proof and others make crucial use of results from the theory of linear programming. We then extend the language to allow reasoning about conditional probability and show that the resulting logic is decidable and completely axiomatizable, by making use of the theory of real closed fields. ( 1990 Academic Press. Inc 1.
A Method for Measuring Wide Range Performance of Boolean Queries in FullText Databases
, 2000
"... A new laboratorybased method for the evaluation of Boolean queries in freetext searching of fulltext databases is proposed. The method is based on a controlled formulation of inclusive query plans, on an automatic conversion of query plans into a set of elementary queries, and on composing optima ..."
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Cited by 23 (7 self)
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A new laboratorybased method for the evaluation of Boolean queries in freetext searching of fulltext databases is proposed. The method is based on a controlled formulation of inclusive query plans, on an automatic conversion of query plans into a set of elementary queries, and on composing optimal queries at varying operational levels by combining appropriate subsets of elementary queries. The method is based on the idea of reverse engineering, and exploits full relevance data of documents to find the query performing optimally within given operational constraints. The proposed
A Parallel Abductive Query Answering in Probabilistic Logic Programs
"... Actionprobabilistic logic programs (apprograms) are a class of probabilistic logic programs that have been extensively used during the last few years for modeling behaviors of entities. Rules in apprograms have the form “If the environment in which entity E operates satisfies certain conditions, ..."
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Cited by 1 (1 self)
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Actionprobabilistic logic programs (apprograms) are a class of probabilistic logic programs that have been extensively used during the last few years for modeling behaviors of entities. Rules in apprograms have the form “If the environment in which entity E operates satisfies certain conditions, then the probability that E will take some action A is between L and U”. Given an approgram, we are interested in trying to change the environment, subject to some constraints, so that the probability that entity E takes some action (or combination of actions) is maximized. This is called the Basic Abductive Query Answering Problem (BAQA). We first formally define and study the complexity of BAQA, and then go on to provide an exact (exponential time) algorithm to solve it, followed by more efficient algorithms for specific subclasses of the problem. We also develop appropriate heuristics to solve BAQA efficiently. The second problem, called the Costbased Query Answering (CBQA) problem checks to see if there is some way of achieving a desired action (or set of actions) with a probability exceeding a threshold, given certain costs. We first formally define and study an exact (intractable) approach to CBQA, and then go on to propose a more efficient algorithm for a specific subclass of apprograms that builds on the results for the basic version of this problem. We also develop the first algorithms for parallel evaluation of CBQA. We conclude with an extensive report on experimental evaluations performed over prototype implementations of the algorithms developed for both BAQA and CBQA, showing that our parallel algorithms work well in practice.