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An Axiomatic Study of the Evaluation of Enthymeme Decoding in Weighted Structured Argumentation

Jonathan Ben-Naim, Victor David, Anthony Hunter

TL;DR

Seven criteria related to decoding are introduced, based on different research areas, and the notion of criterion measure, the objective of which is to evaluate a decoding with regard to a certain criterion, is introduced.

Abstract

An argument can be seen as a pair consisting of a set of premises and a claim supported by them. Arguments used by humans are often enthymemes, i.e., some premises are implicit. To better understand, evaluate, and compare enthymemes, it is essential to decode them, i.e., to find the missing premisses. Many enthymeme decodings are possible. We need to distinguish between reasonable decodings and unreasonable ones. However, there is currently no research in the literature on "How to evaluate decodings?". To pave the way and achieve this goal, we introduce seven criteria related to decoding, based on different research areas. Then, we introduce the notion of criterion measure, the objective of which is to evaluate a decoding with regard to a certain criterion. Since such measures need to be validated, we introduce several desirable properties for them, called axioms. Another main contribution of the paper is the construction of certain criterion measures that are validated by our axioms. Such measures can be used to identify the best enthymemes decodings.

An Axiomatic Study of the Evaluation of Enthymeme Decoding in Weighted Structured Argumentation

TL;DR

Seven criteria related to decoding are introduced, based on different research areas, and the notion of criterion measure, the objective of which is to evaluate a decoding with regard to a certain criterion, is introduced.

Abstract

An argument can be seen as a pair consisting of a set of premises and a claim supported by them. Arguments used by humans are often enthymemes, i.e., some premises are implicit. To better understand, evaluate, and compare enthymemes, it is essential to decode them, i.e., to find the missing premisses. Many enthymeme decodings are possible. We need to distinguish between reasonable decodings and unreasonable ones. However, there is currently no research in the literature on "How to evaluate decodings?". To pave the way and achieve this goal, we introduce seven criteria related to decoding, based on different research areas. Then, we introduce the notion of criterion measure, the objective of which is to evaluate a decoding with regard to a certain criterion. Since such measures need to be validated, we introduce several desirable properties for them, called axioms. Another main contribution of the paper is the construction of certain criterion measures that are validated by our axioms. Such measures can be used to identify the best enthymemes decodings.

Paper Structure

This paper contains 9 sections, 9 theorems, 24 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Weighted Logics
  3. Normalization Methods
  4. Weighted Structured Argumentation
  5. Criterion Measures and Axioms
  6. Construction of Criterion Measures
  7. Quality Measure
  8. Conclusion
  9. Appendix: Proofs

Key Result

Proposition 1

Let ${\mathbf{L}} = ({\mathcal{W}},{| \! \! \! \sim},t)$ be a weighted logic, ${\mathbf{M}},{\mathbf{M}}',{\mathbf{M}}"$ be 3 criterion measures on ${\mathbf{L}}$ satisfying ideal weighted inference, any ideal coherence, and ideal minimality, respectively. Let $E \in \mathtt{Enth}$ and $D \in {\sf a

Figures (1)

  • Figure 1: Criteria from argumentation ($\Box$), XAI ( $\diamond$), philosophy ( $\bigtriangleup$) which have inspired our decoding criteria ( $\bigcirc$).

Theorems & Definitions (64)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Definition 7
  • Definition 8
  • Example 1
  • Definition 9
  • ...and 54 more