From User Preferences to Base Score Extraction Functions in Gradual Argumentation (with Appendix)
Authors: Aniol Civit, Antonio Rago, Antonio Andriella, Guillem Alenyà, Francesca Toni
Organizations: Institut de Robòtica i Informàtica Industrial, CSIC-UPC Barcelona, Spain · King’s College London London, United Kingdom · Imperial College London London, United Kingdom
Gradual argumentation is a field of symbolic AI which is attracting attention for its ability to support transparent and contestable AI systems. It is considered a useful tool in domains such as decision-making, recommendation, debate analysis, and others. The outcomes in such domains are usually dependent on the arguments' base scores, which must be selected carefully. Often, this selection process requires user expertise and may not always be straightforward. On the other hand, organising the arguments by preference could simplify the task. In this work, we introduce Base Score Extraction Functions, which provide a mapping from users' preferences over arguments to base scores. These functions can be applied to the arguments of a Bipolar Argumentation Framework (BAF), supplemented with preferences, to obtain a Quantitative Bipolar Argumentation Framework (QBAF), allowing the use of well-established computational tools in gradual argumentation. We outline the desirable properties of base score extraction functions, discuss some design choices, and provide an algorithm for base score extraction. Our method incorporates an approximation of non-linearities in human preferences to allow for better approximation of the real ones. Finally, we evaluate our approach both theoretically and experimentally in a robotics setting, and offer recommendations for selecting appropriate gradual semantics in practice.
Figures & tables
Figure 1. We introduce a methodology for converting a BAF supplemented with a preference ordering of the arguments (top), into a QBAF (bottom). A Base Score Extraction Function ν is applied to the preference ordering to obtain the arguments’ base scores τ (middle), which allow for the QBAF to be used as normal for decision-making. The output of the decision-making system is adapted to the user’s preferences. A BAF appears at the top of the image, with a preference ordering over the arguments. In the middle of the image, a base Score Extraction Function is applied to the preference ordering to obtain the base scores of the arguments. At the bottom of the image, a QBAF is generated using the base scores that were obtained. A decision-making system selects an option between two topic arguments of the QBAF.
ν
A 1
A 2
A 3
P 1
P 2
P 3
P 4
ν\refbsef:1
Δ>0δ>0
Δ>δ>0
✓
⊤=1⊥=0
⊤=1−⊥
Δ and δ constants
✓
ν\refbsef:2
Δ>0δ>0
Δ>δ>0
✓
α=β=0
α=β/2
Δ and δ constants
✓
Table 1. Summary of the conditions for satisfying the presented axioms (A) and desirable properties (P).
Preference ordering ⪰
Design Choices
QE Strengths
EB Strengths
DF Strengths
⊤
⊥
Δ/δ
σslow
σfast
σslow
σfast
σslow
σfast
a≃b≃c≃d≃e≃f
-
-
-
0.5
0.51
0.50
0.52
0.44
0.63
c≃f≻≻b≃e≻a≃d
0.9
0.1
3
0.58
0.33
0.56
0.39
0.78
0.23
0.9
0.1
5
0.57
0.32
0.55
0.39
0.79
0.2
0.75
0.25
5
0.52
0.4
0.53
0.43
0.63
0.38
b≃e≻a≃d≻≻c≃f
0.8
0.2
3
0.5
0.63
0.52
0.60
0.28
0.87
Table 2. Examples of preference orderings for the running example with different design choices for the BSEF ν1 (Eq. 1 ). The value in bold between σslow and σfast is the system output. The ( - ) symbol indicates when a design choice is not needed, which is the case when all arguments are equally preferred, and their base scores are set to 0.5.
Figure 2. Influence of an argument’s base score and its supporters or attackers on the final argument strength under different gradual semantics. Each subplot corresponds to a distinct semantics: DF-QuAD (left), Quadratic Energy (centre), and the Euler-based Semantics (right). The x-axis represents the base score of the influenced argument, and the y-axis its resulting final strength. Blue lines denote when the influencing argument is a supporter (+), while red lines denote when it is an attacker (-). Each line has assigned its aggregation ( α ), with colour intensity indicating its strength. Each subplot shows the influence of an argument's base score (x-axis), and the different aggregation strengths (lines) for that argument's final strength (y-axis) for the different gradual semantic models. The left figure is for DF-QuAD, the centre one is for Quadratic Energy, and the right is for Euler-based. The blue lines are for supports, while the red lines are for attacks. At the tip of the lines is written the base score of the supporter (+) or attacker (-). The colour intensity of the lines represents the strength of the attack or support.
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.
Yann Munro, Isabelle Bloch, Marie-Jeanne Lesot
Sorbonne Université, CNRS, LIP6, F-75005 Paris, France
Quantitative Bipolar Argumentation Frameworks (QBAFs) provide an alternative approach to computing argument acceptability in Bipolar Argumentation Frameworks (BAFs). Each argument is assigned an initial strength, which is then updated to a final strength by considering the influence of both its attackers and supporters. Over the years, several semantics have been proposed to compute argument acceptability in QBAFs, yet they often yield divergent or counterintuitive results, even for simple acyclic cases. We introduce novel gradual semantics for QBAFs that address these limitations, producing results that align more closely with intuitive expectations, while satisfying established rationality postulates from the literature. Furthermore, we study its convergence behavior, proving that it converges not only for acyclic QBAFs but also for broader classes of cyclic frameworks.
Gianvincenzo Alfano, Sergio Greco, Lucio La Cava +2
Department of Informatics, Modeling, Electronics and System Engineering University of Calabria, Italy
Preference-based argumentation frameworks (PAFs) extend Dung's approach to abstract argumentation (AAFs) by encoding preferences over arguments. Such preferences control the transformation of attacks into defeats, and different approaches to doing so result in different reductions from a PAF to an AAF. In this paper we consider a PAF inverse problem which takes an argumentation graph, a labelling and a semantics as an input, and outputs a yes" or no" as to whether there is a preference relation between the arguments which can yield the desired labelling. This inverse problem has applications in areas including preference elicitation and explainability. We consider this problem in the context of the four most widely-used preference based reductions under the complete semantics. We show that in most cases, the problem can be answered in polynomial time.
Alessio Zaninotto, Bruno Yun, Nir Oren +1
1CRIL - Université d’Artois, CNRS · 2Universite Claude Bernard Lyon 1, CNRS, Ecole Centrale de Lyon, INSA Lyon, Université Lumière Lyon 2, LIRIS, UMR5205, 69622 Villeurbanne, France · University of Aberdeen