In this article we introduce an argument model: a set of terms for analyzing arguments by naming their parts. There are various argument models in the academic literature on argumentation theory and related fields but none provide us with precise definitions for all the concepts behind our algorithms for improving for online conversations. So we will define those concepts here. Our model incorporates the basic ideas from the influential Toulmin model of argumentation first introduced in 1948.

# Argumentation Theory

## A Bayesian Account of Argumentation

### Part of the Bayesian Argumentation series

In this essay, I present an account of argumentation as the exchange of information between Bayesian rational agents. The basic idea of the Bayesian view of probability is that probabilities represent subjective degrees of belief. So if we know the beliefs of some rational “subject”, we can precisely define and measure various concepts relating to the quality of an argument in the mind of the subject. In other words we can objectively measure the subjective quality of an argument.

## Relevance and Corelevance

### Part of the Bayesian Argumentation series

## Definition of Relevance

In the previous essay in this series, we introduced the basic ideas and terminology of Bayesian argumentation, including the concept of **relevance**.

## Necessity and Sufficiency

### Part of the Bayesian Argumentation series

Argument and Information 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.

## Informativeness and Persuasiveness

### Part of the Bayesian Argumentation series

Why Accept the Premise? 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.

## Bayesian Argumentation Definitions

### Part of the Bayesian Argumentation series

Bayesian Argumentation: Summary of Definitions Below is a summary of all the terms and equations defined in the essays in this series, followed by a detailed example.
For an argument with premise 𝐵 and conclusion 𝐴, and a subject whose beliefs are represented by probability measure P…
Relevant: The premise is relevant to the conclusion (or, the argument is relevant) iff $P(A \vert B) ≠ P(A \vert \bar{B})$
Otherwise, the premise is irrelevant to the conclusion (or, the argument is irrelevant) Irrelevance implies statistical independence of A and B.