Preserving Privacy in a (Timed) Concurrent Language for Argumentation

Modelling the behaviour of multiple agents concurrently interacting and reasoning in a dynamic environment is a challenging task. It necessitates tools capable of effectively capturing various forms of interaction, such as persuasion and deliberation while aiding agents in decision-making or consensus-building. In [1], we extended a language for modelling concurrent interactions between agents (tcla), which allowed us to specify agents equipped with a local argument memory and to reason with private knowledge. Furthermore, an initial formalisation of a multi-agent decision problem that preserves privacy has been provided. To illustrate the language’s capabilities, in this paper, we give a complete formalisation of a privacy-preserving multi-agent decision problem, and we demonstrate how it can be employed to define a general (correct and complete) translation function that generates a tcla program from a multi-agent decision-making process. Additionally, we present an application example that models a privacy-preserving multi-agent decision-making process to showcase an instance of our general translation function.

1. Preserving Privacy in a
(Timed) Concurrent
Language for Argumentation
Stefano Bistarelli, Maria Chiara Meo and Carlo Taticchi
CILC 2024

2. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Overview
•Abstract Argumentation Frameworks + Labelling
•Timed Concurrent Language for Argumentation
•Locality semantics
•Preserving Privacy in Multi-Agent Decision
•Conclusion & Future Work
2

3. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Abstract Argumentation
•Represent and evaluate arguments
•Abstract Argumentation Framework F=!Arg,R"
3

4. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Abstract Argumentation
•Represent and evaluate arguments
•Abstract Argumentation Framework F=!Arg,R"
3

5. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Abstract Argumentation
•Represent and evaluate arguments
•Abstract Argumentation Framework F=!Arg,R"
•Argumentation Semantics (e.g. Labelling)
3
An argument is:
•IN if it only attacked by OUT
•OUT if it is attacked by at
least one IN
•UNDEC otherwise

6. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
•Argumentation-based communication between concurrent
agents sharing a common store
•Syntax:
Timed Concurrent Language
for Argumentation (TCLA)
4

7. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
•Argumentation-based communication between concurrent
agents sharing a common store
•Syntax:
Timed Concurrent Language
for Argumentation (TCLA)
4

8. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
•Argumentation-based communication between concurrent
agents sharing a common store
•Syntax:
Timed Concurrent Language
for Argumentation (TCLA)
4

9. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
•Argumentation-based communication between concurrent
agents sharing a common store
•Syntax:
Timed Concurrent Language
for Argumentation (TCLA)
4

10. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
•Argumentation-based communication between concurrent
agents sharing a common store
•Syntax:
Timed Concurrent Language
for Argumentation (TCLA)
4

11. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
•Argumentation-based communication between concurrent
agents sharing a common store
•Syntax:
Timed Concurrent Language
for Argumentation (TCLA)
4

12. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
•Argumentation-based communication between concurrent
agents sharing a common store
•Syntax:
Timed Concurrent Language
for Argumentation (TCLA)
4

13. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
•Argumentation-based communication between concurrent
agents sharing a common store
•Syntax:
Timed Concurrent Language
for Argumentation (TCLA)
4

14. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Parallel executions
5
•True concurrency: we assume infinite processors

15. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Parallel executions
5
•True concurrency: we assume infinite processors
•Global clock for the the passing of time

16. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Parallel executions
5
•True concurrency: we assume infinite processors
•Global clock for the the passing of time
•We decrement the timeout environment T:#$%&{'}
I ((I)
Agent A 4
Agent B 1
Agent C 2

17. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
True concurrency
•With
6

18. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
True concurrency
•With
•Possible implementation
*(F,F) ,F) ) ):=(F) *F) ) )&((F) &F) ) )!F)
6

19. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
True concurrency
•With
•Possible implementation
*(F,F) ,F) ) ):=(F) *F) ) )&((F) &F) ) )!F)
•Alternative approach: interleaving
6

20. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Addition & removal
7
•Example: add({a,b},{(a,b)}) -> rmv({a},{}) -> success;

21. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Addition & removal
7
•Example: add({a,b},{(a,b)}) -> rmv({a},{}) -> success;

22. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Addition & removal
7
•Example: add({a,b},{(a,b)}) -> rmv({a},{}) -> success;

23. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Check
8

24. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Check
8

25. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Check
8

26. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
•Test semantics are similar to the check one but for the
conditions to satisfy
•Credulous test: +L,-
F
!.L(a)=l
•Sceptical test: /L,-
F
!
.L(a)=l
Test
9

27. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
•Test semantics are similar to the check one but for the
conditions to satisfy
•Credulous test: +L,-
F
!.L(a)=l
•Sceptical test: /L,-
F
!
.L(a)=l
•Example: ctest(2,{b},IN,complete) / stest(2,{s},IN,complete)
Test
9

28. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Locality semantics
•new " in # behaves like # where arguments in " are local to #
•#$%&' contains information on 0 which is hidden from the external 12
12

29. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Locality semantics
•new " in # behaves like # where arguments in " are local to #
•#$%&' contains information on 0 which is hidden from the external 12
12
AF3SS

30. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Example: Multi-Agent Decision Making
with Privacy Preserved problem
•Charlie’s, Alice’s and Bob’s beliefs
1
13
[1] Yang Gao, Francesca Toni, Hao Wang, Fanjiang Xu: Argumentation-Based Multi-Agent Decision Making with Privacy Preserved. AAMAS 2016: 1153-1161

31. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Example: Multi-Agent Decision Making
with Privacy Preserved problem
•Charlie’s, Alice’s and Bob’s beliefs
1
•Acceptable solutions:
13
[1] Yang Gao, Francesca Toni, Hao Wang, Fanjiang Xu: Argumentation-Based Multi-Agent Decision Making with Privacy Preserved. AAMAS 2016: 1153-1161

32. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
tcla for DMPP
•We can write a tcla program emulating a DMPP problem
using tcla agents in parallelN
•Each agent builds its local framework by using an add step
•The computation starts in the initial public argumentation
framework
14

33. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Example
16
…

34. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Translation
•145671 checks whether its preferred action choice is globally feasible
ctest(1,{a},IN,admissible)
a
•If this is the case, 145671 adds the 145671:8 to the public AF and checks
its partial consistency, namely ∃s ∈ 09: | ctest(1,{s},IN,admissible)
•If 14567;:8 is consistent, either continues with other agents or
terminate with success
•If 14567;:8 is not consistent, 14567; removes it from the public AF
•If no action is found which can be extended to find a solution, the
computation terminates with failure
15

35. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Conclusion
•Functionalities of the Timed Concurrent Language for
Argumentation which can be used to implement decision-
making processes
17

36. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Conclusion
•Functionalities of the Timed Concurrent Language for
Argumentation which can be used to implement decision-
making processes
•Local stores for enforcing privacy between agents
17

37. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Conclusion
•Functionalities of the Timed Concurrent Language for
Argumentation which can be used to implement decision-
making processes
•Local stores for enforcing privacy between agents
•Illustrative example demonstrating how the Timed Concurrent
Language for Argumentation can be used for modelling
DMPP problems
17

38. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Conclusion
•Functionalities of the Timed Concurrent Language for
Argumentation which can be used to implement decision-
making processes
•Local stores for enforcing privacy between agents
•Illustrative example demonstrating how the Timed Concurrent
Language for Argumentation can be used for modelling
DMPP problems
•Automatic translation from a DMPP problem to a tcla program
17

39. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Future Perspectives
•Explore other features of tcla to simplify the construction of the
models and achieve more natural interactions with the native
constructs
18

40. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Future Perspectives
•Explore other features of tcla to simplify the construction of the
models and achieve more natural interactions with the native
constructs
•Further develop illustrative examples to showcase the system’s
effectiveness and highlight limitations across various scenarios
18

41. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Future Perspectives
•Explore other features of tcla to simplify the construction of the
models and achieve more natural interactions with the native
constructs
•Further develop illustrative examples to showcase the system’s
effectiveness and highlight limitations across various scenarios
•Extend tcla to model real-world applications where agents can
coordinate autonomously and concurrently without being
bound to a fixed agent ordering
18

42. CILC 2024 Deriving Dependency Graphs from Abstract Argumentation Frameworks
Future Perspectives
•Explore other features of tcla to simplify the construction of the
models and achieve more natural interactions with the native
constructs
•Further develop illustrative examples to showcase the system’s
effectiveness and highlight limitations across various scenarios
•Extend tcla to model real-world applications where agents can
coordinate autonomously and concurrently without being
bound to a fixed agent ordering
•Endow the agents with a notion of ownership to establish
which actions can be performed on the shared arguments
18

43. Preserving Privacy in a
(Timed) Concurrent
Language for Argumentation
Stefano Bistarelli, Maria Chiara Meo and Carlo Taticchi
Thank you for your attention!