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Dialogue-based Explanations for Logical Reasoning using Structured Argumentation

Loan Ho, Stefan Schlobach

TL;DR

This work introduces a generic argumentation-based framework (P-SAF) for explaining reasoning in inconsistent knowledge bases by translating logics based on maximal consistent subsets into dialectical proof procedures. It defines arguments as tree-derivations, supports collective attacks to handle n-ary conflicts, and shows how classical logics, defeasible logic, and Datalog± can be instantiated within P-SAFs. A novel explanatory dialogue model is proposed, with dialogue trees that render procedural explanations and provide soundness and completeness results for credulous, grounded, and sceptical acceptances. The framework ties MSC-based semantics to argumentation extensions, enabling interpretable, graphically representable explanations and focusing on human-friendly communication of intermediate reasoning steps. The approach offers a flexible bridge between inconsistency-tolerant reasoning and interpretable explanations, with potential for human-in-the-loop evaluation and scalability studies in real-world domains.

Abstract

The problem of explaining inconsistency-tolerant reasoning in knowledge bases (KBs) is a prominent topic in Artificial Intelligence (AI). While there is some work on this problem, the explanations provided by existing approaches often lack critical information or fail to be expressive enough for non-binary conflicts. In this paper, we identify structural weaknesses of the state-of-the-art and propose a generic argumentation-based approach to address these problems. This approach is defined for logics involving reasoning with maximal consistent subsets and shows how any such logic can be translated to argumentation. Our work provides dialogue models as dialectic-proof procedures to compute and explain a query answer wrt inconsistency-tolerant semantics. This allows us to construct dialectical proof trees as explanations, which are more expressive and arguably more intuitive than existing explanation formalisms.

Dialogue-based Explanations for Logical Reasoning using Structured Argumentation

TL;DR

This work introduces a generic argumentation-based framework (P-SAF) for explaining reasoning in inconsistent knowledge bases by translating logics based on maximal consistent subsets into dialectical proof procedures. It defines arguments as tree-derivations, supports collective attacks to handle n-ary conflicts, and shows how classical logics, defeasible logic, and Datalog± can be instantiated within P-SAFs. A novel explanatory dialogue model is proposed, with dialogue trees that render procedural explanations and provide soundness and completeness results for credulous, grounded, and sceptical acceptances. The framework ties MSC-based semantics to argumentation extensions, enabling interpretable, graphically representable explanations and focusing on human-friendly communication of intermediate reasoning steps. The approach offers a flexible bridge between inconsistency-tolerant reasoning and interpretable explanations, with potential for human-in-the-loop evaluation and scalability studies in real-world domains.

Abstract

The problem of explaining inconsistency-tolerant reasoning in knowledge bases (KBs) is a prominent topic in Artificial Intelligence (AI). While there is some work on this problem, the explanations provided by existing approaches often lack critical information or fail to be expressive enough for non-binary conflicts. In this paper, we identify structural weaknesses of the state-of-the-art and propose a generic argumentation-based approach to address these problems. This approach is defined for logics involving reasoning with maximal consistent subsets and shows how any such logic can be translated to argumentation. Our work provides dialogue models as dialectic-proof procedures to compute and explain a query answer wrt inconsistency-tolerant semantics. This allows us to construct dialectical proof trees as explanations, which are more expressive and arguably more intuitive than existing explanation formalisms.

Paper Structure

This paper contains 36 sections, 30 theorems, 12 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Classical Logic
  4. Defeasible Logic
  5. $\text{Datalog}^\pm$
  6. Proof-oriented (Logical) Argumentations
  7. Arguments, Collective Attacks and Proof-oriented Argumentations
  8. Translating the Existing Argumentation Frameworks to P-SAFs
  9. Acceptability of P-SAFs and Relations to Reasoning with MSCs
  10. Explanatory Dialogue Models
  11. Basic Notions
  12. Dialogue Trees, Dialogues and Focused Sub-dialogues
  13. Focused Dialogue Trees
  14. Results of the Paper
  15. Notions for Soundness and Completeness Results
  16. ...and 21 more sections

Key Result

Lemma 2.6

$(\mathcal{L}_{p} , \texttt{CN}_{p})$ is an abstract logic.

Figures (8)

  • Figure 1: Tree-representation for arguments wrt logics.
  • Figure 2: Given $\mathcal{L}_t$ is $\mathcal{K}_1$, a dialogue $D(\texttt{Re}(\texttt{v}))$$= u_1, \ldots, u_9$ for $q_1 = \texttt{Re}(\texttt{v})$
  • Figure 3: Construction of the dialogue tree $\mathcal{T}(\delta) = \mathcal{T}_{7}(\delta)$ drawn from $D(\texttt{Re}(\texttt{v}))$.
  • Figure 4: A final version of the dialogue tree $\mathcal{T}(\delta)$ is displayed for users
  • Figure 5: Left: A non-focused dialogue tree. Right: A focused dialogue tree $\mathcal{T}(\delta_1)$.
  • ...and 3 more figures

Theorems & Definitions (98)

  • Example 1.1
  • Definition 2.1
  • Example 2.2
  • Definition 2.3
  • Definition 2.4
  • Example 2.5
  • Lemma 2.6
  • Example 2.7: Continue Example \ref{['ex:pro-logic']}
  • Definition 2.8
  • Remark 2.9
  • ...and 88 more