Bayesian Networks for Logical Reasoning
Jon Williamson · Kent Academic Repository (University of Kent) · 2001
By identifying and pursuing analogies between causal and logical influence I show how the Bayesian network formalism can be applied to reasoning about logical deductions. Despite the fact that logic itself is about certainty, logical reasoning takes place in a context of very little certainty. In fact the very search for a proof of a proposition is usually a search for certainty: we are unsure about the proposition and want to become sure by finding a proof or a refutation. Even the search for a better proof takes place under uncertainty: we are sure of the conclusion but not of the alternative premises or lemmas. Uncertainty is rife in mathematics, for instance. A good mathematician is one who can assess which conjectures are likely to be true, and from where a proof of a conjecture is likely to emerge - which hypotheses, intermediary steps and proof techniques are likely to be required and are most plausible in themselves. Mathematics is not a list of theorems but a web of beliefs...