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Understanding Enthymemes in Argument Maps: Bridging Argument Mining and Logic-based Argumentation

Jonathan Ben-Naim, Victor David, Anthony Hunter

TL;DR

Understanding Enthymemes in Argument Maps proposes a formal bridge between argument mining outputs and logic-based argumentation by translating explicit premises and claims into classical logic and modeling implicit content with default logic. It introduces default arguments as structured units that separate explicit and implicit premises and claims, and defines rich attack and support relations to reason over instantiated argument maps. The framework includes a bridging mechanism that translates text to logic and instantiates maps with logical arguments, enabling analysis, comparison, and robustness assessment of different instantiations. The work situates the approach within bipolar and structured argumentation and discusses practical directions for translation, uncertainty handling, and scalable knowledge acquisition, highlighting a path toward systematic enthymeme decoding in real-world discourse.

Abstract

Argument mining is natural language processing technology aimed at identifying arguments in text. Furthermore, the approach is being developed to identify the premises and claims of those arguments, and to identify the relationships between arguments including support and attack relationships. In this paper, we assume that an argument map contains the premises and claims of arguments, and support and attack relationships between them, that have been identified by argument mining. So from a piece of text, we assume an argument map is obtained automatically by natural language processing. However, to understand and to automatically analyse that argument map, it would be desirable to instantiate that argument map with logical arguments. Once we have the logical representation of the arguments in an argument map, we can use automated reasoning to analyze the argumentation (e.g. check consistency of premises, check validity of claims, and check the labelling on each arc corresponds with thw logical arguments). We address this need by using classical logic for representing the explicit information in the text, and using default logic for representing the implicit information in the text. In order to investigate our proposal, we consider some specific options for instantiation.

Understanding Enthymemes in Argument Maps: Bridging Argument Mining and Logic-based Argumentation

TL;DR

Understanding Enthymemes in Argument Maps proposes a formal bridge between argument mining outputs and logic-based argumentation by translating explicit premises and claims into classical logic and modeling implicit content with default logic. It introduces default arguments as structured units that separate explicit and implicit premises and claims, and defines rich attack and support relations to reason over instantiated argument maps. The framework includes a bridging mechanism that translates text to logic and instantiates maps with logical arguments, enabling analysis, comparison, and robustness assessment of different instantiations. The work situates the approach within bipolar and structured argumentation and discusses practical directions for translation, uncertainty handling, and scalable knowledge acquisition, highlighting a path toward systematic enthymeme decoding in real-world discourse.

Abstract

Argument mining is natural language processing technology aimed at identifying arguments in text. Furthermore, the approach is being developed to identify the premises and claims of those arguments, and to identify the relationships between arguments including support and attack relationships. In this paper, we assume that an argument map contains the premises and claims of arguments, and support and attack relationships between them, that have been identified by argument mining. So from a piece of text, we assume an argument map is obtained automatically by natural language processing. However, to understand and to automatically analyse that argument map, it would be desirable to instantiate that argument map with logical arguments. Once we have the logical representation of the arguments in an argument map, we can use automated reasoning to analyze the argumentation (e.g. check consistency of premises, check validity of claims, and check the labelling on each arc corresponds with thw logical arguments). We address this need by using classical logic for representing the explicit information in the text, and using default logic for representing the implicit information in the text. In order to investigate our proposal, we consider some specific options for instantiation.
Paper Structure (16 sections, 10 theorems, 22 equations, 15 figures, 1 table)

This paper contains 16 sections, 10 theorems, 22 equations, 15 figures, 1 table.

Table of Contents

  1. Introduction
  2. Translation of explicit premise and claim into logic
  3. Argument maps
  4. Logical translation
  5. Review of default logic
  6. Types of default theory
  7. Singular default theories
  8. Default arguments
  9. Relationships between arguments
  10. Bridging framework
  11. Literature review
  12. Bipolar argumentation
  13. Structured argumentation
  14. Handling enthymemes
  15. Translating text into logic
  16. ...and 1 more sections

Key Result

Proposition 1

(Proposition 6.2.23 in Besnard1989) For a default theory $(D,W)$, $(D,W)$ is singular if $W$ is consistent with $\{\beta\wedge\gamma \mid \alpha : \beta / \gamma \in D \}$.

Figures (15)

  • Figure 1: Example of an argument graph where each node in $\{n0,n1,n2,n3,n4\}$ represents an argument, and the text exposition is given after the colon. The $+$ (resp. $-$) label on an arc denotes a support (resp. attack) relationship. According to the text, $n0$ appears to be a claim without premises, though $n1$ appears to provide support for what might be implicit premises of $n0$. Also $n1$ appears to have premises for its own claim. So what are the implicit premises of $n0$ and how do they entail the claim of $n0$? And what does the claim of $n1$ entail for supporting the implicit premise of $n0$? We can also ask about how the claim of $n2$ attacks $n0$. Is $n2$ attacking the claim of $a0$ or is it attacking the implicit premises of $n0$? We can ask the same kind of questions for the remaining arguments and arcs here.
  • Figure 2: Continuing Figure \ref{['fig:intrograph']}, an argument map where each node in $\{n0,n1,n2,n3,n4\}$ is an argument. After the colon, the text for the premise follows (P) and text for the claim follows (C). The $+$ (resp. $-$) on an arc denotes a support (resp. attack) relationship.
  • Figure 3: Structure of a default argument
  • Figure 4: Overview of our pipeline for understanding enthymemes. The input is the white box at the top, and the outputs are the the white boxes at the bottom. The focus of this paper is on the knowledge representation and reasoning aspects of the yellow boxes (i.e. how do we represent the explicit and implicit aspects of a logical argument, how do we represent the instantiation of an argument map with logical arguments, and what kinds of logical analyse can we undertake with the instantiation of an argument map). We leave the underlying mechanisms for these yellow boxes to future work (i.e. algorithms for identifying implicit formulae for each premise and claim, algorithms for instantiating each node in argument map with a logical argument, and algorithms for automated analysis of instantiated argument maps). We also leave the orange boxes to future work (i.e. the automated natural language understanding of premises and claims of natural language arguments, the acquisition of commonsense knowledge, and knowledge representation and reasoning with commonsense knowledge).
  • Figure 5: An argument map $(N,P,C,L)$ where the graph $(N,A)$ and the labelling function $L$ is given in Figure \ref{['fig:intrograph2']}, and the $P$ and $C$ functions for the arguments are in the table.
  • ...and 10 more figures

Theorems & Definitions (67)

  • Definition 1
  • Definition 2
  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • Definition 3
  • Example 5
  • Example 6
  • Definition 4
  • ...and 57 more