Conditional Probabilistic Bipolar Argumentation Framework: Explanations, Complexity and Approximation

Recently, there has been an increasing interest in extending Dung's framework with probability theory, leading to the Probabilistic Argumentation Framework (PAF), and with supports in addition to attacks, leading to the Bipolar Argumentation Framework (BAF). In this paper, we introduce the Conditional Probabilistic Bipolar Argumentation Framework (CPBAF), which extends Probabilistic and Bipolar AF by allowing conditional probabilities on arguments, attacks, and on (possibly cyclic) supports. In this setting, we address the problem of computing the probability that a given argument is accepted. This is carried out by introducing the concept of probabilistic explanation for a given (probabilistic) extension. We show that the complexity of the problem is FP #P -hard and propose polynomial approximation algorithms with bounded additive error for CPBAF where cycles with an odd number of attacks are forbidden.

Research on rational discourse and conflict resolution has become increasingly prominent in Artificial Intelligence, prompting the development of the formal argumentation field (Bench-Capon and Dunne 2007;Simari and Rahwan 2009;Atkinson et al. 2017). A foundational model in this domain is Dung's abstract Argumentation Framework (AF) (Dung 1995), which captures conflicts among agents using a set of arguments and a binary attack relation.

To extend its expressive power, various refinements have been proposed, e.g., (Alfano et al. 2023b(Alfano et al. ,c, 2024b(Alfano et al. ,c,e, 2025d,e,c),e,c). Bipolar Argumentation Frameworks (BAFs) introduce support relations in addition to attacks (Nouioua and Risch 2011;Villata et al. 2012; Alfano et al. 2024a), allowing for cooperative and adversarial links between arguments.

Recently, increasing attention has been given to modeling uncertainty in argumentation.