[Paper Review] Range-based argumentation semantics as 2-valued models

Mauricio Osorio, Juan Carlos Nieves|arXiv (Cornell University)|Feb 29, 2016

Multi-Agent Systems and Negotiation23 references3 citations

TL;DR

This paper introduces a logic programming framework, $SC_{1}$, that captures argumentation semantics based on the concept of 'range'—a key component in semi-stable and stage semantics. By applying the Gelfond-Lifschitz reduction to logic program mappings of argumentation frameworks, the authors define GL-supported and GL-stage models, which formally characterize semi-stable and stage extensions as 2-valued models, thereby establishing a unified logic programming foundation for range-based semantics.

ABSTRACT

Characterizations of semi-stable and stage extensions in terms of 2-valued logical models are presented. To this end, the so-called GL-supported and GL-stage models are defined. These two classes of logical models are logic programming counterparts of the notion of range which is an established concept in argumentation semantics.

Motivation & Objective

• To formalize the concept of 'range'—central to semi-stable and stage semantics—within logic programming.
• To develop a general schema, $SC_{1}$, that captures range-based semantics using logic programming reductions.
• To demonstrate that semi-stable and stage semantics can be characterized as 2-valued models via GL-supported and GL-stage models.
• To show that existing logic program mappings ($\Pi_{AF}$ and $\Pi_{AF}^{-}$) can support these characterizations.
• To establish a unified logic programming foundation for range-based argumentation semantics.

Proposed method

• Introduce a general schema $SC_{1}$ that takes a logic program $P$ and a set of atoms $M$, and returns a subset of atoms using a reduction function $R$.
• Instantiate $R$ with the Gelfond-Lifschitz reduction to define GL-supported and GL-stage models.
• Use the $\Pi_{AF}$ and $\Pi_{AF}^{-}$ mappings to translate argumentation frameworks into logic programs.
• Apply the Gelfond-Lifschitz reduction to the resulting logic programs to derive models corresponding to semi-stable and stage extensions.
• Show that GL-supported models correspond to semi-stable extensions and GL-stage models to stage extensions.
• Demonstrate that the $RED$ reduction (core of p-stable semantics) yields equivalent results, confirming robustness of the approach.

Experimental results

Research questions

• RQ1 How can the concept of 'range' in argumentation semantics be captured from a logic programming perspective?
• RQ2 Can existing logic program mappings ($\Pi_{AF}$ and $\Pi_{AF}^{-}$) be used to characterize range-based semantics via $SC_{1}$?
• RQ3 Can semi-stable and stage semantics be formally characterized as 2-valued models in logic programming?
• RQ4 What role do reductions like Gelfond-Lifschitz and $RED$ play in constructing these models?
• RQ5 Is there a generic framework for defining new range-based argumentation semantics using logic programming?

Key findings

• GL-supported models are formally equivalent to semi-stable extensions, providing a logic programming characterization of semi-stable semantics.
• GL-stage models are formally equivalent to stage extensions, establishing a logic programming foundation for stage semantics.
• The $SC_{1}$ schema successfully captures the concept of range using logic programming reductions, particularly the Gelfond-Lifschitz reduction.
• The $\Pi_{AF}$ and $\Pi_{AF}^{-}$ mappings can be used to characterize both semi-stable and stage semantics via $SC_{1}$, confirming their versatility.
• The $RED$ reduction yields equivalent results to the Gelfond-Lifschitz reduction in constructing GL-supported and GL-stage models, indicating robustness of the framework.
• The study provides a generic approach for defining and analyzing new range-based argumentation semantics through logic programming models.