## Bayesian networks for logical reasoning (2001)

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Venue: | in Proceedings of the AAAI Fall Symposium on Using Uncertainty in Computation |

Citations: | 2 - 0 self |

### BibTeX

@INPROCEEDINGS{Williamson01bayesiannetworks,

author = {Jon Williamson},

title = {Bayesian networks for logical reasoning},

booktitle = {in Proceedings of the AAAI Fall Symposium on Using Uncertainty in Computation},

year = {2001},

pages = {136--164}

}

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### Abstract

By identifying and pursuing analogies between causal and logical influence I show how the Bayesian network formalism can be applied

### Citations

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Citation Context ...kground knowledge. But this interpretation only works if the Bayesian network independence assumption holds for rational belief. Furthermore, the question of whether the independence assumption 5See (=-=Pearl 1988-=-) or (Neapolitan 1990) for more on the formal properties of Bayesianetworks. 6(Pearl 1988), (Neapolitan 1990). 7(Neapolitan 1990). sI leave it open as to whether the specified probabilities are object... |

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Citation Context ...because Copyright @ 2001, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. 1This point is made very compellingly by (Corfield 2001). 2(Bundy 1999), (Bundy 2001), (=-=Melis 1998-=-), (Richardson Bundy 1999). they permit the application of Bayesian networks: the fact that causality, for example, is an influence relation explains why Bayesian networks can be applied to causal rea... |

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24 | 2001: ’A critique of proof planning
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Citation Context ...are important because Copyright @ 2001, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. 1This point is made very compellingly by (Corfield 2001). 2(Bundy 1999), (=-=Bundy 2001-=-), (Melis 1998), (Richardson Bundy 1999). they permit the application of Bayesian networks: the fact that causality, for example, is an influence relation explains why Bayesian networks can be applied... |

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Citation Context ...nce relations are important because Copyright @ 2001, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. 1This point is made very compellingly by (Corfield 2001). 2(=-=Bundy 1999-=-), (Bundy 2001), (Melis 1998), (Richardson Bundy 1999). they permit the application of Bayesian networks: the fact that causality, for example, is an influence relation explains why Bayesian networks ... |

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Citation Context ...cerning these variables. Then she leams that smoking S causes each of lung 9In some circumstances there may be more than one most rational function, in which case X may adopt any one of them. 10 See (=-=Jaynes 1998-=-). 137Figure 3: A logical dag. Figure 1: Smoking, lung cancer and bronchitis. Figure 2: Smoking, lung cancer, bronchitis and chest pains. cancer and bronchitis, yielding causal graph Figure 1. One ca... |

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(Show Context)
Citation Context ... causal reasoning just because, it is thought, causal graphs are normally sparse. But logical graphs are sparse too. The maximum number of parents is dictated by the maximum number of premises 13See (=-=Williamson 1999-=-) for a justification of the dependence principle. 14This assumes that only the logical truths have probability 1. This is a common assumption for objective Bayesians to make: once a sentence is award... |

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