Logical Argumentation, Abduction and Bayesian Decision Theory: A Bayesian Approach to Logical Arguments and Its Application to Legal Evidential Reasoning
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 formal semantics for a language, and where we want to use the structure of logical argumentation with logical variables to represent multiple individuals (things). This Article shows how decision theory and logical argumentation can be combined into a coherent framework. The Independent Choice Logic (“ICL”) can be viewed as a 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). By abducing evidence to the explanations, we 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. Tillers’ example of judicial proof in the quandary of Able Attorney is used to show how the framework could be used for legal reasoning. The code to run this example is available from the author’s website.
KeywordsBayesian Network Logic Program Supra Note Stable Model Logical Argumentation
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