Abstract not found

We describe a new approach to default reasoning, based on a principle of indifference among possible worlds. We interpret default rules as extreme statistical statements, thus obtaining a knowledge base KB comprised of statistical and first-order statements. We then assign equal probability to all worlds consistent with KB in order to assign a degree of belief to a statement '. The degree of belief can be used to decide whether to defeasibly conclude '. Various natural patterns of reasoning, such as a preference for more specific defaults, indifference to irrelevant information, and the ability to combine independent pieces of evidence, turn out to follow naturally from this technique. Furthermore, our approach is not restricted to default reasoning; it supports a spectrum of reasoning, from quantitative to qualitative. It is also related to other systems for default reasoning. In particular, we show that the work of [ Goldszmidt et al., 1990 ] , which applies maximum entropy ideas t...

An intelligent agent uses known facts, including statistical knowledge, to assign degrees of belief to assertions it is uncertain about. We investigate three principled techniques for doing this. All three are applications of the principle of indifference, because they assign equal degree of belief to all basic "situations " consistent with the knowledge base. They differ because there are competing intuitions about what the basic situations are. Various natural patterns of reasoning, such as the preference for the most specific statistical data available, turn out to follow from some or all of the techniques. This is an improvement over earlier theories, such as work on direct inference and reference classes, which arbitrarily postulate these patterns without offering any deeper explanations or guarantees of consistency. The three methods we investigate have surprising characterizations: there are connections to the principle of maximum entropy, a principle of maximal independence, an...

We present an approach to reasoning from statistical and subjective knowledge, which is based on a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. More precisely, we introduce the notions of -, lexicographic, and conditional entailment for conditional constraints, which are probabilistic generalizations of Pearl's entailment in system , Lehmann's lexicographic entailment, and Geffner's conditional entailment, respectively. We show that the new formalisms have nice properties. In particular, they show a similar behavior as referenceclass reasoning in a number of uncontroversial examples. The new formalisms, however, also avoid many drawbacks of reference-class reasoning. More precisely, they can handle complex scenarios and even purely probabilistic subjective knowledge as input. Moreover, conclusions are drawn in a global way from all the available knowledge as a whole. We then show that the new formalisms also have nice general nonmonotonic properties. In detail, the new notions of -, lexicographic, and conditional entailment have similar properties as their classical counterparts. In particular, they all satisfy the rationality postulates proposed by Kraus, Lehmann, and Magidor, and they have some general irrelevance and direct inference properties. Moreover, the new notions of - and lexicographic entailment satisfy the property of rational monotonicity. Furthermore, the new notions of -, lexicographic, and conditional entailment are proper generalizations of both their classical counterparts and the classical notion of logical entailment for conditional constraints. Finally, we provide algorithms for reasoning under the new formalisms, and we analyze its computational com...

. In this paper, we focus on the combination of probabilistic logic programming with the principle of maximum entropy. We start by defining probabilistic queries to probabilistic logic programs and their answer substitutions under maximum entropy. We then present an efficient linear programming characterization for the problem of deciding whether a probabilistic logic program is satisfiable. Finally, and as a central contribution of this paper, we introduce an efficient technique for approximative probabilistic logic programming under maximum entropy. This technique reduces the original entropy maximization task to solving a modified and relatively small optimization problem. 1 Introduction Probabilistic propositional logics and their various dialects are thoroughly studied in the literature (see especially [19] and [5]; see also [15] and [16]). Their extensions to probabilistic first-order logics can be classified into first-order logics in which probabilities are defined over the do...

0 =h 0 in the diagram. The sawtooth line reflects the fact that even when the principle of indifference can be applied, there may be arguments whose strength can be bounded no more precisely than by an adjacent pair of indifference arguments. Note that a=h in the diagram is bounded numerically only by 0.0 and the strength of a 00 =h 00 . Keynes' ideas were taken up by B. O. Koopman [14, 15, 16], who provided an axiomatization for Keynes' probability values. The axioms are qualitative, and reflect what Keynes said about probability judgment. (It should be remembered that for Keynes probability judgment was intended to be objective in the sense that logic is objective. Although different people may accept different premises, whether or not a conclusion follows logically from a given set of premises is objective. Though Ramsey [26] attacked this aspect of Keynes' theory, it can be argued

A model of providing service in a P2P network is analyzed. It is shown that by adding a scrip system, a mechanism that admits a reasonable Nash equilibrium that reduces free riding can be obtained. The effect of varying the total amount of money (scrip) in the system on efficiency (i.e., social welfare) is analyzed, and it is shown that by maintaining the appropriate ratio between the total amount of money and the number of agents, efficiency is maximized. The work has implications for many online systems, not only P2P networks but also a wide variety of online forums for which scrip systems are popular, but formal analyses have been lacking.

Data mining algorithms produce huge sets of rules, practically impossible to analyze manually. It is thus important to develop methods for removing redundant rules from those sets. We present a solution to the problem using the Maximum Entropy approach. The problem of eciency of Maximum Entropy computations is addressed by using closed form solutions for the most frequent cases. Analytical and experimental evaluation of the proposed technique indicates that it eciently produces small sets of interesting association rules.

Motivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for first-order formulas. That is, given first-order formulas ' and `, we consider the number of structures with domain f1; : : : ; Ng that satisfy `, and compute the fraction of them in which ' is true. We then consider what happens to this probability as N gets large. This is closely connected to the work on 0-1 laws that considers the limiting probability of first-order formulas, except that now we are considering asymptotic conditional probabilities. Although work has been done on special cases of asymptotic conditional probabilities, no general theory has been developed. This is probably due in part to the fact that it has been known that, if there is a binary predicate symbol in the vocabulary, asymptotic conditional probabilities do not always exist. We show that in this general case, almost all the questions one might want to ask (such as d...

In previous work [BGHK92, BGHK93], we have studied the random-worlds approach---a particular (and quite powerful) method for generating degrees of belief (i.e., subjective probabilities) from a knowledge base consisting of objective (first-order, statistical, and default) information. But allowing a knowledge base to contain only objective information is sometimes limiting. We occasionally wish to include information about degrees of belief in the knowledge base as well, because there are contexts in which old beliefs represent important information that should influence new beliefs. In this paper, we describe three quite general techniques for extending a method that generates degrees of belief from objective information to one that can make use of degrees of belief as well. All of our techniques are based on well-known approaches, such as cross-entropy. We discuss general connections between the techniques and in particular show that, although conceptually and techn...