[Paper Review] Non-monotonic Reasoning in Deductive Argumentation

Anthony Hunter|arXiv (Cornell University)|Sep 4, 2018

Multi-Agent Systems and Negotiation5 references3 citations

TL;DR

This paper investigates the interplay between non-monotonic reasoning and deductive argumentation, showing how monotonic base logics like classical logic can support non-monotonic behavior through defeasible rules and attack relations. It demonstrates that non-monotonicity emerges not from the base logic but from argument evaluation and counterargument dynamics, with default and conditional logics offering effective frameworks for modeling defeasible knowledge in argumentation systems.

ABSTRACT

Argumentation is a non-monotonic process. This reflects the fact that argumentation involves uncertain information, and so new information can cause a change in the conclusions drawn. However, the base logic does not need to be non-monotonic. Indeed, most proposals for structured argumentation use a monotonic base logic (e.g. some form of modus ponens with a rule-based language, or classical logic). Nonetheless, there are issues in capturing defeasible reasoning in argumentation including choice of base logic and modelling of defeasible knowledge. And there are insights and tools to be harnessed for research in non-monontonic logics. We consider some of these issues in this paper.

Motivation & Objective

• To clarify the relationship between non-monotonic reasoning and deductive argumentation, especially in the context of AI systems handling incomplete or inconsistent information.
• To investigate how non-monotonic behavior arises in deductive argumentation despite using monotonic base logics such as classical logic or simple logic.
• To examine how formalisms from non-monotonic logic—such as default logic and conditional logics—can be harnessed to model defeasible knowledge in structured argumentation frameworks.
• To address the challenge of formalizing defeasible rules (e.g., 'birds fly') in a way that reflects real-world uncertainty, exceptions, and varying interpretations of 'normality' or 'majority'.

Proposed method

• Uses deductive argumentation frameworks defined over a base logic (e.g., classical logic or simple logic) where arguments are pairs ⟨Φ, α⟩ such that Φ ⊢ᵢ α.
• Applies defeasible rules with abnormality predicates to model exceptions, allowing arguments to be attacked or withdrawn when abnormality is inferred.
• Introduces default logic as a mechanism to formalize default inferences, enabling non-monotonic reasoning through the use of default rules with consistency and justification conditions.
• Employs conditional logics to represent defeasible conditionals (e.g., 'if a bird, then it normally flies'), capturing non-monotonicity via specialized semantics that avoid contrapositive reasoning.
• Proposes modeling defeasible knowledge through multiple interpretations—such as 'most birds fly', 'normally', or 'prototypical'—to reflect different real-world reasoning contexts.
• Uses argumentation frameworks with attack relations (e.g., rebuttal, undercutting) to model how new information can retract previously accepted conclusions, even when the base logic is monotonic.

Experimental results

Research questions

• RQ1 How does non-monotonic reasoning emerge in deductive argumentation when the underlying base logic is monotonic?
• RQ2 What role do defeasible rules play in enabling non-monotonic behavior in argumentation systems, and how can they be formally modeled?
• RQ3 In what ways can default logic and conditional logics be integrated into deductive argumentation to support defeasible reasoning?
• RQ4 How do different interpretations of 'defeasible' (e.g., 'normally', 'most', 'prototypical') affect the formalization and reasoning in argumentation systems?
• RQ5 What is the distinction between monotonic argument construction and non-monotonic evaluation in argumentation frameworks?

Key findings

• Non-monotonicity in deductive argumentation arises not from the base logic but from the evaluation of argument extensions, where adding new arguments or counterarguments can invalidate previously accepted conclusions.
• Monotonic base logics such as classical logic can support non-monotonic reasoning when combined with defeasible rules and abnormality predicates, enabling the retraction of inferences upon new evidence.
• Default logic provides a formal mechanism for defeasible inference by allowing default inferences that can be blocked by conflicting information, thus modeling exceptions systematically.
• Conditional logics offer a flexible framework for representing defeasible conditionals (e.g., 'if a bird, then it normally flies') with semantics that avoid problematic inferences like contrapositive reasoning.
• Defeasible rules can be interpreted in multiple ways—such as 'most', 'normally', or 'prototypical'—and different interpretations require different formalizations, with description logic or probabilistic logic offering useful modeling support.
• The construction of arguments and counterarguments is monotonic (adding knowledge never removes existing arguments), but the assessment of which arguments are acceptable in a given extension is non-monotonic, reflecting real-world reasoning dynamics.