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

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

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