On the Semantics of Abstract Argumentation Frameworks: A Logic Programming Approach
This work addresses the need for a unified semantic characterization in computational argumentation, particularly for researchers in logic programming and AI, but it is incremental as it builds on known relationships between AFs and PSMs.
The paper tackles the problem of extending Dung's abstract argumentation frameworks (AFs) by exploring relationships between AF-based frameworks and partial stable models (PSMs) of logic programs, showing that every AF-based framework can be translated into a logic program so that extensions coincide with subsets of PSMs, enabling a uniform characterization of semantics for frameworks like AFs with recursive attacks and supports.
Recently there has been an increasing interest in frameworks extending Dung's abstract Argumentation Framework (AF). Popular extensions include bipolar AFs and AFs with recursive attacks and necessary supports. Although the relationships between AF semantics and Partial Stable Models (PSMs) of logic programs has been deeply investigated, this is not the case for more general frameworks extending AF. In this paper we explore the relationships between AF-based frameworks and PSMs. We show that every AF-based framework $Δ$ can be translated into a logic program $P_Δ$ so that the extensions prescribed by different semantics of $Δ$ coincide with subsets of the PSMs of $P_Δ$. We provide a logic programming approach that characterizes, in an elegant and uniform way, the semantics of several AF-based frameworks. This result allows also to define the semantics for new AF-based frameworks, such as AFs with recursive attacks and recursive deductive supports. Under consideration for publication in Theory and Practice of Logic Programming.