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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 KnowledgeBased Methodology for Tuning Analytical Models
 IEEE Transactions on Systems, Man, and Cybernetics
, 1991
"... Many computerbased analytical models for decisionmaking and forecasting have been developed in recent years, particularly in the areas of economics and finance. Analytic models have an important limitation which has restricted their use: a model cannot anticipate every factor that may be important ..."
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Cited by 1 (1 self)
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Many computerbased analytical models for decisionmaking and forecasting have been developed in recent years, particularly in the areas of economics and finance. Analytic models have an important limitation which has restricted their use: a model cannot anticipate every factor that may be important in making a decision. Some analysts attempt to compensate for this limitation by making heuristic adjustments to the model in order to "tune" the results. Tuning produces a model forecast that is consistent with intuitive expectations, and maintains the detail and structure of the analytic model. This is a very difficult task unless the user has expert knowledge of the model and the task domain. This paper describes a new methodology, called knowledgebased tuning, that allows a human analyst and a knowledgebased system to collaborate in adjusting an analytic model. Such a methodology makes the model more acceptable to a decisionmaker, and offers the potential of improving the decisions t...
Maximum Entropy in Nilsson's Probabilistic Logic
 in: Proceedings of IJCAI 1989
, 1989
"... Nilsson's Probabilistic Logic is a set theoretic mechanism for reasoning with uncertainty. We propose a new way of looking at the probability constraints enforced by the framework, which allows the expert to include conditional probabilities in the semantic tree, thus making Probabilistic Logic more ..."
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Cited by 1 (0 self)
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Nilsson's Probabilistic Logic is a set theoretic mechanism for reasoning with uncertainty. We propose a new way of looking at the probability constraints enforced by the framework, which allows the expert to include conditional probabilities in the semantic tree, thus making Probabilistic Logic more expressive. An algorithm is presented which will find the maximum entropy point probability for a rule of entailment without resorting to solution by iterative approximation. The algorithm works for both the propositional and the predicate logic. Also presented are a number of methods for employing the conditional
Market Analysis for Risk Management and Regulation: An Artificial Intelligence Approach
, 1995
"... The key points in this chapter are: 1. Purely statistical market analysis techniques for determining risk are incomplete because, in the real world, risk is effected by nonstatistical phenomena such as news. Quantitative models can ignore such "shocks," but analysts still need to explain their mode ..."
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The key points in this chapter are: 1. Purely statistical market analysis techniques for determining risk are incomplete because, in the real world, risk is effected by nonstatistical phenomena such as news. Quantitative models can ignore such "shocks," but analysts still need to explain their models in the face of such shocks. 2. Risk must include the effects of all relationships. This is only partially accounted by models using correlation statistics. 3. Market analysis techniques used for risk management have much in common with the techniques used in market surveillance for regulation. In this paper, we provide a framework that can be applied either to risk management for trading or to the regulation of markets. Our framework lets analysts define patterns of market behavior and detect new or hidden relationships between subjects in order to evaluate risk and discover information flows. Introduction From the information technology perspective, Wall Street represents a complex and ...