Abstract Argumentation Frameworks (AFs) are used, in the field of Artificial Intelligence, to evaluate the justification state of conflicting information, thus allowing the development of automatic reason- ing techniques and systems. Complex argumentative processes such as decision-making and negotiation, which take place over time, can be modelled through the Concurrent Language for Argumentation, a formalism for handling concurrent interactions between intelligent agents that use an AF as shared memory. In this paper, we first show how AFs can be interpreted as dependency graphs by exploiting the relation between arguments induced by the attacks. Then, we describe a methodology for obtaining a procedure that generates the given AF. Such a procedure allows to dynamically represent dialogues and other forms of interaction that brought to the instantiation of the specified AF.

1. Deriving Dependency
Graphs from Abstract
Argumentation Frameworks
Stefano Bistarelli and Carlo Taticchi

2. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Abstract Argumentation
• Represent and evaluate arguments
• Abstract Argumentation Frameworks
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3. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Abstract Argumentation
• Represent and evaluate arguments
• Abstract Argumentation Frameworks
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4. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Abstract Argumentation
• Represent and evaluate arguments
• Abstract Argumentation Frameworks
• Argumentation Semantics (e.g. Labelling)
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5. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Dependency Graphs
• Represent the dependencies of various elements
• We look for a Correct Evaluation Order
‣ if x is evaluated before y, then x must not depend on y
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6. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Dependency Graphs
• Represent the dependencies of various elements
• We look for a Correct Evaluation Order
‣ if x is evaluated before y, then x must not depend on y
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7. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
AFs as Dependency Graphs
• AFs can be interpreted as Dependency Graphs
• Finding a Correct Evaluation Order = obtain the reasoning
process that generated the graph
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8. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
AFs as Dependency Graphs
• AFs can be interpreted as Dependency Graphs
• Finding a Correct Evaluation Order = obtain the reasoning
process that generated the graph
• Issue: a Correct Evaluation Order cannot be found when the
graph has circular dependencies
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9. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
AFs as Dependency Graphs
• AFs can be interpreted as Dependency Graphs
• Finding a Correct Evaluation Order = obtain the reasoning
process that generated the graph
• Issue: a Correct Evaluation Order cannot be found when the
graph has circular dependencies
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10. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Feasible Evaluation Order
• Treat any cycle as an agglomeration of nodes whose
evaluation order is not in
fl
uential
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For all arguments x and y not in circular dependencies between them, if x is
evaluated before y, then x and all arguments in circular dependences with x
must not depend on y and all arguments in circular dependences with y

11. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Feasible Evaluation Order
• Treat any cycle as an agglomeration of nodes whose
evaluation order is not in
fl
uential
5
2
3
4
For all arguments x and y not in circular dependencies between them, if x is
evaluated before y, then x and all arguments in circular dependences with x
must not depend on y and all arguments in circular dependences with y
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12. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Feasible Evaluation Order
• Treat any cycle as an agglomeration of nodes whose
evaluation order is not in
fl
uential
• A Feasible Evaluation Order for an acyclic graph is also a
Correct Evaluation Order
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For all arguments x and y not in circular dependencies between them, if x is
evaluated before y, then x and all arguments in circular dependences with x
must not depend on y and all arguments in circular dependences with y

13. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Feasible Evaluation Order
• Treat any cycle as an agglomeration of nodes whose
evaluation order is not in
fl
uential
• A Feasible Evaluation Order for an acyclic graph is also a
Correct Evaluation Order
• How to compute a Feasible Evaluation Order?
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For all arguments x and y not in circular dependencies between them, if x is
evaluated before y, then x and all arguments in circular dependences with x
must not depend on y and all arguments in circular dependences with y

14. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Concurrent Language for
Argumentation
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15. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Example
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16. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Example
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17. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Example
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Example
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19. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Automated Construction
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20. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Automated Construction
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21. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Automated Construction
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22. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Some properties
1. The program terminates
2. The shared store obtained at the end of the execution
corresponds to the desired AF
3. Arguments are added into the store following a feasible
evaluation order
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23. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Conclusion
• AFs from the perspective of dependency between arguments
• Dependency can be derived from the attack relation
• Feasible Evaluation Order to understand the evolution of
AFs and determine the order in which arguments are
presented
• Automatic AFs generation through the Concurrent Language
for Argumentation
‣ Arguments are added in a Feasible Evaluation Order
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24. AIxIA 2023 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Future Perspectives
1. Model multiparties dialogues (debate, persuasion games)
2. Study the AF’s evolution, explain why a speci
fi
c argument is
introduced
3. Working implementation (prototype available)
4. Consider hidden attacks (explicitly added only between
visible arguments)
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25. Deriving Dependency Graphs from
Abstract Argumentation Frameworks
Stefano Bistarelli and Carlo Taticchi
Thank you for your attention!