In the previous essay in this series, we introduced the basic ideas and terminology of Bayesian argumentation, including the concept of relevance. In this essay I explore a precise mathematical definition of relevance and the related concept of acceptance.
In the previous essay in this series, we introduced the idea of relevance, and said that a premise is relevant to the conclusion iff $P(A \vert B) > P(A \vert \bar{B})$.
Consider the argument (𝐴) this is a good candidate for the job because (𝐵) he has a pulse. Having a pulse may not be a very persuasive reason to hire somebody, but it is probably quite relevant, because if the candidate did not have a pulse, the subject would probably be much less likely to want to hire him. That is $P(A \vert B) > P(A \vert \bar{B})$.
In the previous essay in this series, we defined the ideas of necessity and sufficiency from the perspective of a Bayesian rational agent. If an argument is necessary, then if the subject were to reject the premise, they would decrease their acceptance of the conclusion. And if an argument is sufficient, then if the subject were to accept the premise, they would increase their acceptance of the conclusion.
This is the final article in my series on Bayesian Argumentation. To understand this essay, read the introductory article and the article on [Relevance and Acceptance] (/relevance-and-acceptance).
Relevance exists in the context of the subject’s other prior beliefs. For example, if the subject believes that ($\bar{𝐶}$) the car is out of gas, and also ($\bar{B}$) the battery is dead, then both of these are good reasons to believe ($\bar{A}$) the car won’t start.
Below is a summary of all the terms and equations defined in the essays in this series, followed by a detailed example.
Claim: A statement that one can agree or disagree with
Premise: A claim intended to support or oppose some conclusion
Conclusion: The claim supported or opposed by the premise
Argument: A premise asserted in support of or opposition to some conclusion
For an argument with premise 𝐵 and conclusion 𝐴, and a subject whose beliefs are represented by probability measure P…