[Paper Review] Well-Founded Argumentation Semantics for Extended Logic Programming

Ralf Schweimeier, Michael Schroeder|ArXiv.org|Jul 10, 2002

Multi-Agent Systems and Negotiation8 references3 citations

TL;DR

This paper introduces a well-founded argumentation semantics for extended logic programs with explicit negation, proving its equivalence to the well-founded semantics with explicit negation (WFSX). It establishes a general framework for classifying argumentation semantics based on attack types (undercut and rebut), defines a dialectical proof theory using dialogue trees, and shows that successful T-trees in WFSX correspond exactly to provably u/a-justified arguments.

ABSTRACT

This paper defines an argumentation semantics for extended logic programming and shows its equivalence to the well-founded semantics with explicit negation. We set up a general framework in which we extensively compare this semantics to other argumentation semantics, including those of Dung, and Prakken and Sartor. We present a general dialectical proof theory for these argumentation semantics.

Motivation & Objective

• To define a least fixpoint argumentation semantics for extended logic programs that is equivalent to the well-founded semantics with explicit negation (WFSX).
• To establish a general framework for classifying argumentation semantics based on different notions of attack (undercut and rebut).
• To compare the proposed semantics with existing frameworks, including Dung's and Prakken and Sartor's argumentation semantics.
• To develop a dialectical proof theory based on dialogue trees for the introduced argumentation semantics.
• To prove the soundness and completeness of the dialectical proof theory with respect to the fixpoint semantics.

Proposed method

• Defines arguments in extended logic programs as finite sequences of rules with conclusions derived from assumptions (default literals).
• Introduces two types of attacks: undercut (targeting assumptions) and rebut (targeting conclusions), forming the basis for argumentation frameworks.
• Proposes a hierarchy of argumentation semantics via a lattice of justified arguments, parameterized by attack types used by proponent and opponent.
• Defines $x/y$-dialogue trees where the proponent uses attack type $y$ to defend and the opponent uses $x$ to attack, with winning trees indicating justified arguments.
• Establishes a dialectical proof theory using transfinite induction to prove soundness and completeness of the $x/y$-dialogue trees with respect to the fixpoint semantics.
• Proves equivalence between the $u/a$-justified semantics and WFSX by showing that successful T-trees in WFSX correspond exactly to winning $u/a$-dialogue trees.

Experimental results

Research questions

• RQ1 Can a well-founded argumentation semantics be defined for extended logic programs that is equivalent to the well-founded semantics with explicit negation (WFSX)?
• RQ2 How do different combinations of attack types (undercut and rebut) affect the resulting argumentation semantics in extended logic programs?
• RQ3 Is there a dialectical proof theory that is sound and complete for the proposed argumentation semantics?
• RQ4 How does the proposed $u/a$-justified semantics relate to existing argumentation semantics such as Dung's and Prakken and Sartor's?
• RQ5 Can the T-tree proof procedure in WFSX be formally linked to a dialectical proof system for argumentation?

Key findings

• The proposed $u/a$-justified argumentation semantics is formally equivalent to the well-founded semantics with explicit negation (WFSX).
• The hierarchy of argumentation semantics satisfies $J_{Dung} \subseteq J_{PS} \subseteq J_{u/a} = \text{WFSX}$, showing increasing strength in justification power.
• The dialectical proof theory based on $x/y$-dialogue trees is sound and complete with respect to the corresponding fixpoint semantics.
• Successful T-trees in WFSX are formally equivalent to winning $u/a$-dialogue trees, establishing a direct link between proof-theoretic and model-theoretic approaches.
• The $u/a$-dialogue tree system correctly captures the well-founded semantics, providing a dialectical foundation for WFSX.
• The framework allows for systematic comparison of argumentation semantics based on attack types, enabling classification and analysis of different reasoning behaviors.