Reasoning about change requires predicting how long a proposition, having become true, will continue to be so. Lacking perfect knowledge, an agent may be constrained to believe that a proposition persists indefinitely simply because there is no way for the agent to infer a contravening proposition with certainty. In this paper, we describe a model of causal reasoning that accounts for knowledge concerning cause-and-effect relationships and knowledge concerning the tendency for propositions to persist or not as a function of time passing. Our model has a natural encoding in the form of a network representation for probabilistic models. We consider the computational properties of our model by reviewing recent advances in computing the consequences of models encoded in this network representation. Finally, we discuss how our probabilistic model addresses certain classical problems in temporal reasoning (e.g., the frame and qualification problems).Le raisonnement a propos des modifications nkcessite de prkdire combien de temps une proposition demeurera vraie une fois qu'elle I'est devenue. En I'absence de connaissances parfaites, un agent peut itre force de croire qu'une proposition persiste indefiniment simplement parce qu'il lui est impossible d'inferer avec certitude une proposition contraire. Dans cet article, nous decrivons un modele de raisonnement causal qui tient compte des connaissances concernant la relation entre la cause et I'effet et la tendance des propositions a persister ou non en fonction du temps. Le modele comporte un encodage nature1 sous forme de representation en reseau pour les modeles probabilistiques. Les proprietes informatiques du modele sont prises en consideration a la lumiere des recents developpements dans le domaine de I'estimation des consequences des modeles encodes dans cette representation en rkseau. Enfin, on y discute comment Ie modele probabilistique traite certains problemes classiques de raisonnement temporel (par exemple, les problhes de cadre et de qualification). que, reseau de croyances.Mots clPs : raisonnement tenmorel. raisonnement causal, incertitude, modeles probabilistiques, inference probabilisti-[Traduit par la revue] Comput. Intell. 5. 142-150 (1989)

Predicting the future is an essential compo nent of decision making. In most situations, however, there is not enough information to make accurate predictions. In this paper, we develop a theory of causal reasoning for pre dictive inference under uncertainty. We em phasize a common type of prediction that in volves reasoning about persistence: whether or not a proposition once made true remains true at some later time. We provide a decision procedure with a polynomial-time algorithm for determining the probability of the possible consequences of a set events and initial con ditions. The integration of simple probabil ity theory with temporal projection enables us to circumvent problems in dealing with per sistence by nonmonotonic temporal reasoning .schemes. The ideas in this paper have been �m plemented in a prototype system that refines a database ofcausal rules in the course of ap plying those rules to construct and carry out plans in a manufacturing domain.

Abstract. Probabilistic networks (also known as Bayesian belief networks) allow a compact description of complex stochastic relationships among several random variables. They are used widely for uncertain reasoning in artificial intelligence. In this paper, we investigate the problem of learning probabilistic networks with known structure and hidden variables. This is an important problem, because structure is much easier to elicit from experts than numbers, and the world is rarely fully observable. We present a gradient-based algorithm and show that the gradient can be computed locally, using information that is available as a byproduct of standard inference algorithms for probabilistic networks. Our experimental results demonstrate that using prior knowledge about the structure, even with hidden variables, can significantly improve the learning rate of probabilistic networks. We extend the method to networks in which the conditional probability tables are described using a small number of parameters. Examples include noisy-OR nodes and dynamic probabilistic networks. We show how this additional structure can be exploited by our algorithm to speed up the learning even further. We also outline an extension to hybrid networks, in which some of the nodes take on values in a continuous domain.