F. Bacchus, A. J. Grove, J. Y. Halpern, and D. Koller, From statistics to belief, in Proc. National Conference on Artificial Intelligence (AAAI '92), 1992, pp. 602--608.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....for example, Chan Chua, 1994) One way in which default reasoning has been formalized is to apply a Bayesian perspective to reasoning with subjective probabilities. It is a complex matter to move from statistics to degrees of belief and this topic has engendered much debate in the formal arena (Bacchus, Grove, Halpern, Koller, 1992; Kyburg, 1994) It is relatively straightforward to model aspects of the belief revision results reported here within a Bayesian framework 8 . For as soon as we assign the conditional probability pr(q p) 1.0, we are indicating that p is not sufficient reason to conclude q. We may specify a ....

....some evaluation function that must still assign a metric to each candidate epistemic state, by which one emerges as the most plausible. One approach is to assign a degree of belief to each possible contender, and the formal semantics for deriving degrees of belief from probabilities developed by Bacchus et al. 1992) are relevant here. They consider the problem of what prior probability distribution might characterize this set of imagined situations, and they note that as long as there is some probability distribution, degrees of belief can be generated from statistical information using Bayesian ....

Bacchus, F., Grove, A., Halpern, J.Y., & Koller, D. (1992). From statistics to belief. In Proceedings of the Tenth National Conference on Artificial Intelligence, (pp. 602-608).

.... for extending models of human propositional inference to encompass subjective or probabilistic elements (e.g. George 1995; Johnson Laird 1994; Stevenson and Over 1995) address issues similar to those found in probabilistic treatments of plausible inference offered in the AI literature (e.g. Bacchus, Grove, Halpern, and Koller 1992; Kyburg 1994) The matter of belief revisionupdating ones confidence in or acceptance of previously accepted beliefs in light of new informationhas been studied extensively in management science and psychology literature (e.g. Einhorn and Hogarth 1981; Ashton and Ashton 1990; Baron 1994) in ....

Bacchus, F., A. Grove, J.Y. Halpern, and D. Koller (1992). From statistics to belief. In Proceedings of the Tenth National Conference on Artificial Intelligence, pp. 602-608.

....of type l and half are of type h. Of course, in such situations, if BankA does not have any additional information, it will believe with probability 1 2 that its opponent is of type l. During the negotiation encounters it may update its belief. Techniques that were presented by Bacchus et al. [3], for assigning degrees of beliefs by an intelligent agent based on known facts, including statistical knowledge, can be used in our situation. If there is no prior information about the opponent s type, then the agent can always assume that there is equal distribution of the types of agents and ....

F. Bacchus, A. Grove, J. Halpern, and D. Koller. From statistics to beliefs. In Proc. of AAAI-92, pages 602--608, California, 1992.

....may within the limits of consistency be any he likes. 27, p. 189] INTERVAL VALUED PROBABILITIES 9 Carnap and other writers thought that some more constraints could be imposed. These are constraints expressed in terms of symmetries [2, 3] or entropy [12] Similar constraints are suggested by [1, 8, 9]. According to the objective view developed in [17] 18] and [22] constraints on the functions representing uncertainty are imposed by the statistical knowledge of the agent. These constraints may take either of two forms. First, we may stipulate that the credibilities of the agent ought to form ....

F. Bacchus, A. J. Grove, J. Y. Halpern, and D. Koller. From statistics to beliefs. In Proceedings of AAAI-92 (Proceedings of the Tenth National Conference on Artificial Intelligence), pages 602--608. 1992.

.... cross entropy minimization that, generalizing the rule of direct inference, seems to go a long way towards an adequate modelling of that part of default reasoning about probabilities that links statistical with uncertain information. Thus, our basic motivation is very similar to the one in [BGHK92], BGHK93] The formalism to be developed, however, will be quite different from the one proposed by Bacchus et al. this one being unsatisfactory for our purpose, because it does not make any provisions for using existing degrees of belief in the derivation of new ones. Other related work ....

F. Bacchus, A. Grove, J.Y. Halpern, and D. Koller. From statistics to beliefs. In Proc. of National Conference on Artificial Intelligence (AAAI92) , 1992.

....only one kind of probabilistic information is represented in the knowledge base, this type of inference is the one most frequently encountered. Entropy maximization is the most common rule of this type. A second type of probabilistic inference is given by the random worlds formalism of Bacchus et al. 1992 ] Here constraints on statistical probabilities are used to derive degrees of belief. In [ Bacchus et al. 1994 ] it is also shown how this method can be extended to make the resulting subjective probabilities also depend on given prior degrees of belief. It is this third kind of probabilistic ....

F. Bacchus, A. Grove, J.Y. Halpern, and D. Koller. From statistics to beliefs. In Proc. of National Conference on Artificial Intelligence (AAAI-92), 1992.

....relational data is an important research subject in nonmonotonic and uncertain reasoning. Our emphasis on transactions in our definition of robustness is analogous in spirit to the notion of accessibility in the possible worlds semantics of modal logic (Ramsay , 1988) The formalism proposed by (Bacchus et al. 1992, DATABASES THAT CHANGE 25 Bacchus et al. 1994) for uncertain reasoning, in spite of the different motivation, is quite similar to robustness. Bacchus et al. 1992) defines the degree of belief in a given logic sentence as the probability of the set of worlds where is true. They further ....

....spirit to the notion of accessibility in the possible worlds semantics of modal logic (Ramsay , 1988) The formalism proposed by (Bacchus et al. 1992, DATABASES THAT CHANGE 25 Bacchus et al. 1994) for uncertain reasoning, in spite of the different motivation, is quite similar to robustness. (Bacchus et al. 1992) defines the degree of belief in a given logic sentence as the probability of the set of worlds where is true. They further define this probability as the ratio between the number of all possible worlds and worlds where is true. This is the same as Definition 1, if we consider a database ....

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Bacchus, F., Grove, A., Halpern, J. Y., and Koller, D. 1992. From statistics to beliefs. In Proceedings of the Tenth National Conference on Artificial Intelligence (AAAI-92), 602--608.

.... reasoning [Ginsberg, 1987, Shafer and Pearl, 1990] Our emphasis on transactions in our definition of robustness is analogous in spirit to the notion of accessibility in the possible worlds semantics of modal logic [Ramsay, 1988] The formalism proposed by [Bacchus, 1988] Halpern, 1990] and [Bacchus et al. 1992, Bacchus et al. 1993, Bacchus et al. 1994] for uncertain reasoning, in spite of the different motivation, is quite similar to robustness. Bacchus et al. 1992] defines the degree of belief in a given logic sentence as the probability of the set of worlds where is true. They further ....

....in the possible worlds semantics of modal logic [Ramsay, 1988] The formalism proposed by [Bacchus, 1988] Halpern, 1990] and [Bacchus et al. 1992, Bacchus et al. 1993, Bacchus et al. 1994] for uncertain reasoning, in spite of the different motivation, is quite similar to robustness. [Bacchus et al. 1992] defines the degree of belief in a given logic sentence as the probability of the set of worlds where is true. They further define this probability as the ratio between the number of all possible worlds and worlds where is true. This is the same as Definition 2.1, if we consider a ....

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Fahiem Bacchus, Adam Grove, Joseph Y. Halpern, and Daphne Koller. From statistics to beliefs. In Proceedings of the Tenth National Conference on Artificial Intelligence(AAAI-92), pages 602--608, San Jose, CA, 1992.

....some evaluation function that must still assign a metric to each candidate epistemic state, by which one emerges as the most plausible. One approach is to assign a degreeof belief to each possible contender, and the formal semantics for deriving degrees of belief from probabilities developed by Bacchus et al. 1992) are relevant here. They consider the problem of what prior probability distribution might characterize this set of imagined situations, and they note that as long as there is some probability distribution, degrees of belief can be generated from statistical information using Bayesian ....

Bacchus, F., Grove, A., Halpern, J.Y., & Koller, D. (1992). From statistics to belief. Proceedings. of the Tenth National Conference on Artificial Intelligence, (pp. 602-608). Cambridge, MA: MIT Press.

....Several attempts have been made to give an objective definition of subjective probability. These attempts can be divided into two approaches. The first approach uses an a priori probability distribution on the set of interpretations of the language that we are using to describe information [1, 4, 2, 6]. The idea is to define such an a priori probability distribution using some general principles. The second approach does not start from a set of interpretations among which we try to find the one describing the world, but instead tries to build a partial model of the world [7, 8, 9] Uncertainty ....

....in a reference class. Furthermore, since Roos requires that all views have the same objects, it also leads to conceptual difficulties. Knowing that there are 4 or 5 house in a street, what denotes the fifth object in the view where we only know of 4 houses Bacchus, Grove, Halpern and Koller [1, 4, 2] propose to define a probability distributions over the set of interpretations. To assure that the interpretations are mutually exclusive, they introduce an important restriction on the set of interpretation. They assume that all interpretations possess the same set of objects. Furthermore, they ....

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F. Bacchus, A. J. Grove, J. Y. Halpern, D. Koller, From statistics to beliefs, AAAI-92 (1992) 602-608.

....Goldszmidt and Darwiche [ 1994a ] have developed a causal theory of action in the Kappa calculus, which they claim can handle observations correctly [ Goldszmidt and Darwiche, 1994b ] but we have yet to explore how their approach handles the problematic examples we (and others) have identified. Bacchus et al. [ 1994; 1992 ] do not provide sufficient details to work through examples such as the Jersey Drive By in detail [ Bacchus, 1995 ] but their comments (including the result embedding Kartha s language, A; in their framework) suggest that, if nothing else, some care will be required to ensure that ....

F. Bacchus, A. Grove, J. Halpern, and D. Koller. From statistics to belief. In Proceedings Tenth National Conference on Artificial Intelligence (AAAI-92), pages 602--608, 1992.

.... of specificity and accuracy have been considered in [ Cussens and Hunter, 1991; Cussens and Hunter, 1993 ] but there is a clear need to further clarify this relationship by building on more general results relating non monotonic reasoning and probabilistic inference [ Pearl, 1990; Bacchus, 1990; Bacchus et al. 1992 ] A preliminary empirical comparison In our preliminary comparison, we considered two domains. The first was for rules that predict whether a protein residue is part of an alpha helix. These rules were defined in terms of relative position in a protein and various biochemical parameters. We ....

Bacchus, Fahiem; Grove, Adam; Halpern, Joseph Y.; and Koller, Daphne 1992. From statistics to belief. In Tenth National Conference on Artificial Intelligence (AAAI-92). 602--608.

....side to it. The problem of choosing relevant dataset characteristics is that of finding the right reference class within which to situate the current dataset and for which we have statistical information. More work needs to be devoted to this problem, but much progress has already been made: see [Bacchus et al. 1992] for a particularly elegant approach. We noted above that cross validation made sense when we had no prior preference between the algorithms under consideration. It seems likely that in many cases, we will have prior preferences which should be used. These might come from the sort of empirical ....

Bacchus, F., Grove, A., Halpern, J. Y., and Koller, D. (1992). From statistics to belief. In Tenth National Conference on Artificial Intelligence (AAAI-92), pages 602--608.

....perspective here is that epistemic entrenchment is the by product of generating and assessing alternative accounts of an unexpected contradiction. The formalization of this process may ultimately involve elements of a probabilistic approach, which too has been applied to default reasoning (e.g. Bacchus et al. 1992) as well as to belief revision (Dubois Prade, 1991) When a conditional has many known disablers, one way to account for the contradicted inference is to appeal to the existence of those disablers and reject the idea that the rule is holding, at least in a particular case. Generally speaking, ....

Bacchus, F., Grove, A., Halpern, J.Y., & Koller, D. (1992). From statistics to belief. In Proceedings of the Tenth National Conference on Artificial Intelligence, (pp. 602-608).

....perspective here is that epistemic entrenchment is the by product of generating and assessing alternative accounts of an unexpected contradiction. The formalization of this process may ultimately involve elements of a probabilistic approach, which too has been applied to default reasoning (e.g. Bacchus et al. 1992) as well as to belief revision (Dubois Prade, 1991) When a conditional has many known disablers, one way to account for the contradicted inference is to appeal to the existence of those disablers and reject the idea that the rule is holding, at least in a particular case. Generally speaking, ....

Bacchus, F., Grove, A., Halpern, J.Y., & Koller, D. (1992). From statistics to belief. In Proceedings of the Tenth National Conference on Artificial Intelligence, (pp. 602-608).

.... Ginsberg, 1987, Shafer and Pearl, 1990 ] Our emphasis on transactions in our definition of robustness is analogous in spirit to the notion of accessibility in the possible worlds semantics of modal logic [ Ramsay, 1988 ] The formalism proposed by [ Bacchus, 1988 ] Halpern, 1990 ] and [ Bacchus et al. 1992, Bacchus et al. 1993, Bacchus et al. 1994 ] for uncertain reasoning, in spite of the different motivation, is quite similar to robustness. Bacchus et al. 1992 ] defines the degree of belief in a given logic sentence as the probability of the set of worlds where is true. They further ....

....possible worlds semantics of modal logic [ Ramsay, 1988 ] The formalism proposed by [ Bacchus, 1988 ] Halpern, 1990 ] and [ Bacchus et al. 1992, Bacchus et al. 1993, Bacchus et al. 1994 ] for uncertain reasoning, in spite of the different motivation, is quite similar to robustness. Bacchus et al. 1992 ] defines the degree of belief in a given logic sentence as the probability of the set of worlds where is true. They further define this probability as the ratio between the number of all possible worlds and worlds where is true. This is the same as Definition 1, if we consider a database ....

[Article contains additional citation context not shown here]

Fahiem Bacchus, Adam Grove, Joseph Y. Halpern, and Daphne Koller. From statistics to beliefs. In Proceedings of the Tenth National Conference on Artificial Intelligence(AAAI-92), pages 602--608, San Jose, CA, 1992.

....beyond intuition to adjudicate between candidate reference class descriptions. Furthermore, there is no empirical data to support the efficacy of this approach. It is often stated that the crux of this type of statistical reasoning is the problem of choosing the right reference class [Bac90, BGHK92]. However, this premise might actually be leading us away from the most effective learning approaches here. Fundamentally, our goal should be to preserve all available statistical information, rather than throwing away statistics from one class in favor of those from another. The best approach ....

F. Bacchus, A. Grove, J. Halpern, and D. Koller. From statistics to beliefs. In AAAI-92, 1992.

....of belief is that of assigning equal degree of belief to all basic situations consistent with the knowledge base, and computing the fraction of those which are consistent with the query. Much work has been done on how to apply this principle, and how to determine what are the basic situations [4, 1, 2]. We consider here the question of computing the degree of belief in a restricted case, in which the knowledge base consists of a propositional theory and contains no statistical information. The hardness results we get in this restricted case just highlight the computational difficulties in the ....

F. Bacchus, A. Grove, J. Y. Halpern, and D. Koller. From statistics to beliefs. In Proceedings of the National Conference on Artificial Intelligence, pages 602--608, 1992.

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F. Bacchus, A. J. Grove, J. Y. Halpern, and D. Koller, From statistics to belief, in Proc. National Conference on Artificial Intelligence (AAAI '92), 1992, pp. 602--608.

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F. Bacchus, A. J. Grove, J. Y. Halpern, and D. Koller. From statistics to belief. In Proc. National Conference on Artificial Intelligence (AAAI '92), pages 602--608, 1992.

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F. Bacchus, A. J. Grove, J. Y. Halpern, and D. Koller. From statistics to belief. In Proc. National Conference on Artificial Intelligence (AAAI '92), pages 602--608, 1992.

....problem. The reasons for this failure are subtle, and cannot be explained within the space limitations. However, as we discuss in the full paper, the problem is closely related to the fact that random worlds does not learn statistics from samples. This aspect of random worlds was discussed in [BGHK92], where we also presented an alternative method to computing degrees of belief, the random propensities approach, that does support learning. In future work, we hope to apply this alternative approach to the ontology described in this framework. We have reason to hope that this approach will ....

F. Bacchus, A. J. Grove, J. Y. Halpern, and D. Koller. From statistics to belief. In Proc. National Conference on Artificial Intelligence (AAAI '92), pages 602--608, 1992.

....the general knowledge base, and model construction is performed using ideas arising from the study of direct inference. Direct inference involves reasoning from general statistical knowledge to probabilities assigned to particular cases and has been worked on by a number of authors including [BGHK92, Bac90b, Kyb61, Kyb74, Lev80, Lou87, Pol90, Sal71]. Our mechanism brings to light the important role expressive first order probability logics can play in representing general probabilistic knowledge, and the important relationship between KBMC and direct inference. In the sequel, we first introduce a probability logic that can be used for the ....

....inference. Old approaches to direct inference revolved around trying to find appropriate reference classes from which statistics can be drawn [Kyb83b] More recent work has taken an approach based on the principle of indifference that dispenses with the notion of a reference class altogether [BGHK92]. In general, however, determining the probabilities to assign to a particular event given a collection of statistical information about classes of similar events is a very difficult problem. For a practical enterprise like KBMC, however, we can use the work on direct inference to derive general ....

F. Bacchus, A. J. Grove, J. Y. Halpern, and D. Koller. From statistics to belief. In Proceedings of the AAAI National Conference, pages 602--608, 1992.

....of conditional probabilities. In this paper, motivated by our use our own terminology for these methods, partly because we feel it is more descriptive, and partly because there are other variants of the approach that do not fit into the standard labeled unlabeled structures dichotomy (see [BGHK92]) desire to apply these methods to computing degrees of belief, we consider the general question of when asymptotic probabilities exist for first order logic, and how to compute them if they do. We begin by showing that once we have a binary predicate symbol in the vocabulary, things are ....

F. Bacchus, A. J. Grove, J. Y. Halpern, and D. Koller. From statistics to belief. In Proc. National Conference on Artificial Intelligence (AAAI '92), pages 602--608, 1992.

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Bacchus, F., A. Grove, J. Y. Halpern, and D. Koller. 1992. From statistics to beliefs. In Proceedings of the National Conference on Artificial Intelligence, pages

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