Bayesian networks for logical reasoning

Williamson, J. (2001) Bayesian networks for logical reasoning. In: Proceedings of the AAAI Fall Symposium on using Uncertainty within Computation. AAAI Press, pp. 136-143. (The full text of this publication is not available from this repository)

The full text of this publication is not available from this repository. (Contact us about this Publication)
Official URL
http://www.aaai.org/Papers/Symposia/Fall/2001/FS-0...

Abstract

By identifying and pursuing analogies between causal and logical in uence 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 nding 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, and mathematical propositions are constantly being evaluated on the basis of the mathematical and physical evidence available at the time. 1 Of course logical reasoning has many other applications, notably throughout the eld of articial intelligence. Planning a decision, parsing a sentence, checking a computer program, maintaining consistency of a knowledge base and deriving predictions from a model are only few of the tasks that can be considered theorem-proving problems. Finding a proof is rarely an easy matter, thus automated theorem proving and automated proof planning are important areas of active research. 2 However, current systems do not tackle uncertainty in any fundamental way. I will argue in this paper that Bayesian networks are particularly suited as a formalism for logical reasoning under uncertainty, just as they are for causal reasoning

Item Type: Book section
Subjects: Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities
B Philosophy. Psychology. Religion > BC Logic
Q Science > QA Mathematics (inc Computing science) > QA 75 Electronic computers. Computer science
Divisions: Faculties > Humanities > School of European Culture and Languages
Depositing User: Jon Williamson
Date Deposited: 19 Mar 2009 17:58
Last Modified: 20 Jan 2012 15:01
Resource URI: http://kar.kent.ac.uk/id/eprint/7396 (The current URI for this page, for reference purposes)
  • Depositors only (login required):