Logical Argumentation, Abduction and Bayesian Decision Theory: A Bayesian Approach to Logical Arguments and its Application to Legal Evidential Reasoning

David Poole

Invited talk, Cardozo Conference on AI and Judicial Proof, New York, April 2000.


There are good normative arguments for using Bayesian decision theory for deciding what to do. However, there are also good arguments for using logic, where we want have a formal semantics for a language and use the structure of logical argumentation with logical variables to represent multiple individuals (things). This paper shows how decision theory and logical argumentation can be combined into a coherent framework. The Independent Choice Logic can be viewed as first-order representation of belief networks with conditional probability tables represented as first-order rules, or as a abductive/argument-based logic with probabilities over assumables. Intuitively we can use logic to model causally (in terms of logic programs with assumables). Given evidence, we abduce to the explanations, and then can predict what follows from these explanations. As well as abduction to the best explanation(s), from which we can bound probabilities, we can also do marginalization to reduce the detail of arguments. An example of Tillers is given is used to show the how the framework could be used for legal reasoning. The code to run this example is available from the authors web site.

You can get the paper or the slides from my talk.

I also have Independent Choice Logic Code that runs using Independent Choice Logic Interpreter (written in Prolog). You can also get a trace of the interpreter.

Last updated 2 June 2000 - David Poole