## Forming Beliefs About a Changing World (1994)

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Citations: | 9 - 3 self |

### BibTeX

@MISC{Bacchus94formingbeliefs,

author = {Fahiem Bacchus and Adam J. Grove and Joseph Y. Halpern and Daphne Koller},

title = {Forming Beliefs About a Changing World},

year = {1994}

}

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### Abstract

The situation calculus is a popular technique for reasoning about action and change. However, its restriction to a firstorder syntax and pure deductive reasoning makes it unsuitable in many contexts. In particular, we often face uncertainty, due either to lack of knowledge or to some probabilistic aspects of the world. While attempts have been made to address aspects of this problem, most notably using nonmonotonic reasoning formalisms, the general problem of uncertainty in reasoning about action has not been fully dealt with in a logical framework. In this paper we present a theory of action that extends the situation calculus to deal with uncertainty. Our framework is based on applying the random-worlds approach of [BGHK94] to a situation calculus ontology, enriched to allow the expression of probabilistic action effects. Our approach is able to solve many of the problems imposed by incomplete and probabilistic knowledge within a unified framework. In particular, we obtain a default ...

### Citations

7043 |
Probabilistic reasoning in intelligent systems: networks of plausible inference
- Pearl
- 1988
(Show Context)
Citation Context ...approach [Bak91] to the frame problem is, in fact, also based on the use of counterfactuals. We have already mentioned that random-worlds subsumes the principle of maximum entropy. It has been argued =-=[Pea88]-=- that maximum entropy (and hence random-worlds) cannot deal appropriate with causal information. In fact, our example above is closely related, in a technical sense, to the problematic examples descri... |

1483 | Some philosophical problems from the standpoint of artificial intelligence
- McCarthy, Hayes
- 1969
(Show Context)
Citation Context ... F49620-91-C-0080, and by a University of California President's Postdoctoral Fellowship. 1 Introduction The situation calculus is a well-known logical technique for reasoning about action and change =-=[MH69]-=-. Calculi of this sort provide a useful mechanism for dealing with simple temporal phenomena, and serve as a foundation for work in planning. Nevertheless, the many restrictions inherent in the situat... |

553 | The frame problem in the situation calculus: A simple solution (sometimes) and a completeness result for goal regression - Reiter - 1991 |

468 |
Estimating causal effects of treatments in randomized and non randomized studies
- Rubin
- 1974
(Show Context)
Citation Context ...f counterfactuals seems to arise over and over again in attempts to understand temporal and causal information. They have been used in both philosophy and statistics to give semantics to causal rules =-=[Rub74]-=-. In game theory [Sta94] the importance of counterfactuals (or strategies) has long been recognized. Baker's approach [Bak91] to the frame problem is, in fact, also based on the use of counterfactuals... |

289 | ADL: exploring the middle ground between STRIPS and the situation calculus - Pednault - 1989 |

250 |
Representing and reasoning with probabilistic knowledge
- Bacchus
- 1990
(Show Context)
Citation Context ...guage for expressing statistical information, and a mechanism for probabilistic reasoning from such information. The language we use extends full first-order logic with statistical information, as in =-=[Bac90]-=-), by allowing proportion expressions of the form jj'(x)j/(x)jj x . This is interpreted as denoting the proportion of domain elements satisfying ', among those satisfying /. 2 (Actually, an arbitrary ... |

249 |
Nonmonotonic Logic and Temporal Projection
- HANKS, MCDERMOTT
- 1987
(Show Context)
Citation Context ...ests that if we could formalize this general principle (that change is unusual), it could serve as a substitute for the many explicit frame axioms that would otherwise be needed. However, as shown in =-=[HM87]-=-, the most obvious formulations of this idea in standard nonmonotonic logics often fail. Suppose we use a formalism that, in some way, tries to minimize the number of changes in the world. In the YSP,... |

142 |
Where do we stand on maximum entropy
- Jaynes
- 1978
(Show Context)
Citation Context ...nd the ability to ignore irrelevant information. In a precise sense, it generalizes both the powerful theory of default reasoning of [GMP90] and (as shown in [GHK94]) the principle of maximum entropy =-=[Jay78]-=-; it can also be used to do reference class reasoning from statistics in the spirit of [Kyb74]. The two basic ideas underlying the random-worlds method are the provision of a general language for expr... |

132 | Nonmonotonic reasoning in the framework of the situation calculus
- Baker
- 1991
(Show Context)
Citation Context ...vior. We state a theorem, based on the criterion of Kartha [Kar93], showing the general correctness of our approach's solution to the frame problem. We also compare our solution to one given by Baker =-=[Bak91]-=-. 2 Preliminaries 2.1 The situation calculus We assume some familiarity with the situation calculus and associated issues. In brief, by situation calculus we refer to a method of reasoning about tempo... |

112 | From statistical knowledge bases to degrees of belief
- Bacchus, Grove, et al.
- 1996
(Show Context)
Citation Context ...with in a logical framework. In this paper we present a theory of action that extends the situation calculus to deal with uncertainty. Our framework is based on applying the random-worlds approach of =-=[BGHK94]-=- to a situation calculus ontology, enriched to allow the expression of probabilistic action effects. Our approach is able to solve many of the problems imposed by incomplete and probabilistic knowledg... |

91 |
Probabilistic semantics for nonmonotonic reasoning: A survey,” to appear
- Pearl
- 1989
(Show Context)
Citation Context ...description of the formal semantics, noting that the main subtlety concerns the interpretation of approximate comparisons, and that the special case of �� 1 is related to the well-known ffl-semant=-=ics [Pea89]-=-. The second aspect of the method is, of course, the specific way in which degrees of belief are computed. Before reviewing these, we remark that for the purposes of most of this paper, the random-wor... |

90 | The Logic of Persistence
- Kautz
- 1986
(Show Context)
Citation Context ...cially to deal with the problem of minimizing frame violations. Our solution to the frame problem and the YSP arises naturally and almost directly from our general approach. problems, such as Kautz's =-=[Kau86]-=- stolen car example. Our approach deals well with explanation problems. In Kautz's example, we park our car in the morning only to find when we return in the evening that it has been stolen. Theories ... |

85 |
Representing actions in extended logic programs
- Gelfond, Lifschitz
- 1992
(Show Context)
Citation Context ... that in which we consider actions one at a time, assuming minimal change at each step) has recently been formalized by Kartha [Kar93]. Roughly speaking, he showed that a simple procedural language A =-=[GL92] can be em-=-bedded into three approaches for dealing with the frame problem [Bak91, Ped89, Rei91], so that the answers prescribed by A's semantics (which are the intuitively "right" answers) are also ob... |

81 |
A maximum entropy approach to nonmonotonic reasoning
- Goldszmidt, Morris, et al.
- 1993
(Show Context)
Citation Context ...es [BGHK94], including a preference for more specific information and the ability to ignore irrelevant information. In a precise sense, it generalizes both the powerful theory of default reasoning of =-=[GMP90]-=- and (as shown in [GHK94]) the principle of maximum entropy [Jay78]; it can also be used to do reference class reasoning from statistics in the spirit of [Kyb74]. The two basic ideas underlying the ra... |

77 |
r.: The Logical Foundations of Statistical Inference
- Kyburg
- 1974
(Show Context)
Citation Context ...t handle explanation problems (since they do not place a prior probability distribution over the space of actions). [Ten91] achieves a first-order ontology by applying the reference-class approach of =-=[Kyb74] to this p-=-roblem. His approach, however, has a somewhat "procedural" rather than a purely logical (semantic) character. Hence, although it specifies how to do forward projection---assessing probabilit... |

59 |
Soundness and completeness theorems for three formalizations of action
- Kartha
- 1993
(Show Context)
Citation Context ...ring from the latter, almost automatically. Writing down a very natural expression of a frame axiom almost immediately gives the desired behavior. We state a theorem, based on the criterion of Kartha =-=[Kar93]-=-, showing the general correctness of our approach's solution to the frame problem. We also compare our solution to one given by Baker [Bak91]. 2 Preliminaries 2.1 The situation calculus We assume some... |

51 | A simple solution to the Yale Shooting problem
- Baker
- 1989
(Show Context)
Citation Context ...on a similar notion of counterfactual situations. But while the solutions are related, they are not identical: for instance, we do not suffer from the problem concerning extraneous fluents that Baker =-=[Bak89]-=- mentions. 7 Some solutions to the YSP work by augmenting a principle of minimal change with a requirement that we should prefer models in which change occurs as late as possible (e.g., [Kau86, Sho88]... |

49 | Random worlds and maximum entropy
- Grove, Halpern, et al.
- 1994
(Show Context)
Citation Context ...preference for more specific information and the ability to ignore irrelevant information. In a precise sense, it generalizes both the powerful theory of default reasoning of [GMP90] and (as shown in =-=[GHK94]-=-) the principle of maximum entropy [Jay78]; it can also be used to do reference class reasoning from statistics in the spirit of [Kyb74]. The two basic ideas underlying the random-worlds method are th... |

48 | Chronological ignorance: experiments in nonmonotonic temporal reasoning - Shoham - 1988 |

48 |
Belief and Counterfactual Reasoning
- Stalnaker, “Knowledge
- 1996
(Show Context)
Citation Context ...to arise over and over again in attempts to understand temporal and causal information. They have been used in both philosophy and statistics to give semantics to causal rules [Rub74]. In game theory =-=[Sta94]-=- the importance of counterfactuals (or strategies) has long been recognized. Baker's approach [Bak91] to the frame problem is, in fact, also based on the use of counterfactuals. We have already mentio... |

43 | From statistics to beliefs - Bacchus, Grove, et al. - 1992 |

36 | Projecting plans for uncertain worlds - Hanks - 1990 |

30 | Formal theories of action (preliminary report - Lifschitz - 1987 |

24 | Temporal projection and explanation
- Baker, Ginsberg
- 1989
(Show Context)
Citation Context ...rns out to be crucial in avoiding the YSP. Even if the gun does in fact become unloaded somehow, we do not escape the fact that shooting with a loaded gun would have killed Fred. Baker and Ginsberg's =-=[BG89]-=- solution to the frame problem (based on circumscription) relies on a similar notion of counterfactual situations. But while the solutions are related, they are not identical: for instance, we do not ... |

17 |
Causality and maximum entropy updating
- Hunter
- 1989
(Show Context)
Citation Context ... above is closely related, in a technical sense, to the problematic examples described by Pearl. But once again, an appropriate representation of causal rules using counterfactuals solves the problem =-=[Hun89]-=-. In fact, counterfactuals have been used recently to provide a formulation of Bayesian networks based on deterministic functions [Pea93]. All these applications of counterfactuals turn out to be clos... |

13 | Aspects of graphical models connected with causality
- Pearl
- 1993
(Show Context)
Citation Context ...ation of causal rules using counterfactuals solves the problem [Hun89]. In fact, counterfactuals have been used recently to provide a formulation of Bayesian networks based on deterministic functions =-=[Pea93]-=-. All these applications of counterfactuals turn out to be closely linked to our own, even though none consider the random-worlds method. The ontology of this paper is, in some sense, the convergence ... |

11 | Persistence and probabilistic projection - Dean, Kanazawa - 1989 |

5 |
Reasoning with noisy sensors in the situation calculus
- Bacchus, Grove, et al.
- 1933
(Show Context)
Citation Context ...itations. 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 =-=[BGHK95]-=-, 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... |

4 |
Abandoning the completeness assumptions: A statistical approach to the frame problem
- Tenenberg
- 1991
(Show Context)
Citation Context ...Furthermore, even those that are able to deal with abductive queries typically cannot handle explanation problems (since they do not place a prior probability distribution over the space of actions). =-=[Ten91] achieves -=-a first-order ontology by applying the reference-class approach of [Kyb74] to this problem. His approach, however, has a somewhat "procedural" rather than a purely logical (semantic) charact... |

2 | Generating degrees of belief from statistical information - Bacchus, Grove, et al. - 1994 |

2 | Chronological ingorance: experiments in nonmonotonic temporal reasoning - Shoham - 1988 |