Aggregative Semantics for Quantitative Bipolar Argumentation Frameworks

TL;DR

This paper introduces a new family of gradual semantics called aggregative semantics for Quantitative Bipolar Argumentation Frameworks, which separately aggregate attackers and supporters to improve interpretability and flexibility.

Contribution

It proposes a novel three-stage aggregation process for bipolar argumentation, enhancing the understanding and parametrization of gradual semantics in QBAF.

Findings

Demonstrates the properties and relationships of the aggregation functions.

Provides examples illustrating the range of behaviors of aggregative semantics.

Tests and compares 500 aggregative semantics to showcase their diversity.

Abstract

Formal argumentation is being used increasingly in artificial intelligence as an effective and understandable way to model potentially conflicting pieces of information, called arguments, and identify so-called acceptable arguments depending on a chosen semantics. This paper deals with the specific context of Quantitative Bipolar Argumentation Frameworks (QBAF), where arguments have intrinsic weights and can attack or support each other. In this context, we introduce a novel family of gradual semantics, called aggregative semantics. In order to deal with situations in which attackers and supporters do not play a symmetric role, and in contrast to modular semantics, we propose to aggregate attackers and supporters separately. This leads to a three-stage computation, which consists in computing a global weight for attackers and another for supporters, before aggregating these two values with the intrinsic weight of the argument. We discuss the properties that the three aggregation functions should satisfy depending on the context, as well as their relationships with the classical principles for gradual semantics. This discussion is supported by various simple examples, as well as a final example on which five hundred aggregative semantics are tested and compared, illustrating the range of possible behaviours with aggregative semantics. Decomposing the computation into three distinct and interpretable steps leads to a more parametrisable computation: it keeps the bipolarity one step further than what is done in the literature, and it leads to more understandable gradual semantics.