Abstract Argumentation Framework with Conditional Preferences
Gianvincenzo Alfano, Sergio Greco, Francesco Parisi, Irina Trubitsyna
Abstract
Dung's abstract Argumentation Framework (AF) has emerged as a central formalism in the area of knowledge representation and reasoning. Preferences in AF allow to represent the comparative strength of arguments in a simple yet expressive way. Preference-based AF (PAF) has been proposed to extend AF with preferences of the form a > b, whose intuitive meaning is that argument a is better than b. In this paper we generalize PAF by introducing conditional preferences of the form a > b \leftarrow body that informally state that a is better than b whenever the condition expressed by body is true. The resulting framework, namely Conditional Preference-based AF (CPAF), extends the PAF semantics under three well-known preference criteria, i.e. democratic, elitist, and KTV. After introducing CPAF, we study the complexity of the verification problem (deciding whether a set of arguments is a ``best'' extension) as well as of the credulous and skeptical acceptance problems (deciding whether a given argument belongs to any or all ``best'' extensions, respectively) under multiple-status semantics (that is, complete, preferred, stable, and semi-stable semantics) for the above-mentioned preference criteria.
BibTeX
@article{Alfano_Greco_Parisi_Trubitsyna_2023, title={Abstract Argumentation Framework with Conditional Preferences}, volume={37}, url={https://ojs.aaai.org/index.php/AAAI/article/view/25766}, DOI={10.1609/aaai.v37i5.25766}, abstractNote={Dung’s abstract Argumentation Framework (AF) has emerged as a central formalism in the area of knowledge representation and reasoning.
Preferences in AF allow to represent the comparative strength of arguments in a simple yet expressive way. Preference-based AF (PAF) has been proposed to extend AF with preferences of the form a > b, whose intuitive meaning is that argument a is better than b. In this paper we generalize PAF by introducing conditional preferences of the form a > b \leftarrow body that informally state that a is better than b whenever the condition expressed by body is true.
The resulting framework, namely Conditional Preference-based AF (CPAF), extends the PAF semantics under three well-known preference criteria, i.e. democratic, elitist, and KTV. After introducing CPAF, we study the complexity of the verification problem (deciding whether a set of arguments is a ``best’’ extension) as well as of the credulous and skeptical acceptance problems (deciding whether a given argument belongs to any or all ``best’’ extensions, respectively) under multiple-status semantics (that is, complete, preferred, stable, and semi-stable semantics) for the above-mentioned preference criteria.}, number={5}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Alfano, Gianvincenzo and Greco, Sergio and Parisi, Francesco and Trubitsyna, Irina}, year={2023}, month={Jun.}, pages={6218-6227} }