The Timed Concurrent Language for Argumentation (tcla) is a framework to model concurrent interactions between communicating agents that reason and take decisions through argumentation processes, also taking into account the temporal duration of the performed actions. Time is, indeed, a crucial factor when dealing with dynamic environments in real-world applications, where agents need to act in a coordinated fashion to reach their own goals. In this paper, we discuss the syntax and the operational semantics of tcla, providing insights on how its constructs can be used to realise complex interactions between agents.

1. AI^3 2021
Concurrent
Argumentation with
Time: An Overview
Stefano Bistarelli, Maria Chiara Meo, Carlo Taticchi

2. AI^3 2021 - Concurrent Argumentation with Time: An Overview
• Argumentation Frameworks (AFs)
‣ Timed AFs
• Timed Concurrent Language for Argumentation (tcla)
‣ Syntax
‣ Operational semantics
• Modelling Timed AFs
‣ Running example
• Conclusion and Future Work
Overview
2

3. AI^3 2021 - Concurrent Argumentation with Time: An Overview
Argumentation Frameworks
3
Timed AFs

4. AI^3 2021 - Concurrent Argumentation with Time: An Overview
Argumentation Frameworks
4
Timed AFs

5. AI^3 2021 - Concurrent Argumentation with Time: An Overview
Argumentation Frameworks
4
Timed AFs

6. AI^3 2021 - Concurrent Argumentation with Time: An Overview
Argumentation Frameworks
4
Timed AFs

7. AI^3 2021 - Concurrent Argumentation with Time: An Overview
Argumentation Frameworks
4
Timed AFs

8. AI^3 2021 - Concurrent Argumentation with Time: An Overview
Argumentation Frameworks
4
Timed AFs

9. AI^3 2021 - Concurrent Argumentation with Time: An Overview
Syntax
5
Timed Concurrent Language for Argumentation
• Models concurrent processes taking place over time
• Knowledge base represented through AFs
• Bounded asynchrony and maximal parallelism
•
•
A ::= success ∣ failure ∣ add(Arg, R) → A ∣ rmv(Arg, R) → A
∣ A∥A ∣ ∃x A ∣ E ∣ p(a, l, σ, i)
E ::= testc,t(a, l, σ) → A ∣ tests,t(a, l, σ) → A ∣ checkt(Arg, R) → A
∣ E + E ∣ E +P E ∣ E∥GE

10. AI^3 2021 - Concurrent Argumentation with Time: An Overview
Timed Concurrent Language for Argumentation
Operational Semantics (1)
6
Add
Rmv

11. AI^3 2021 - Concurrent Argumentation with Time: An Overview
Timed Concurrent Language for Argumentation
7
Operational Semantics (2)

12. AI^3 2021 - Concurrent Argumentation with Time: An Overview
Timed Concurrent Language for Argumentation
8
Operational Semantics (3)

13. AI^3 2021 - Concurrent Argumentation with Time: An Overview
Timed Concurrent Language for Argumentation
9
Operational Semantics (4)

14. AI^3 2021 - Concurrent Argumentation with Time: An Overview
• Each agent handles one argument
• Agent_a:
• Agent_b:
• Agent_a || Agent_b
sleep(9) → (add({a}, {(b, a), (d, a)}) → (sleep(30) → (rmv({a}, {}) →
(sleep(18) → (add({a}, {(b, a), (d, a)}) → (sleep(15) → (rmv({a}, {}) → success)))))))
sleep(29) → (add({b}, {(b, a), (c, b)}) → (sleep(20) → (rmv({b}, {}) → success)))
Modelling Timed AFs
10
Example
is a shortcut for
sleep(t) → A
{
A if t ≤ 0
check1({}, {}) → (sleep(t − 1) → A) otherwise

15. AI^3 2021 - Concurrent Argumentation with Time: An Overview
• Each agent handles one argument
• Agent_a:
• Agent_b:
• Agent_a || Agent_b
sleep(9) → (add({a}, {(b, a), (d, a)}) → (sleep(30) → (rmv({a}, {}) →
(sleep(18) → (add({a}, {(b, a), (d, a)}) → (sleep(15) → (rmv({a}, {}) → success)))))))
sleep(29) → (add({b}, {(b, a), (c, b)}) → (sleep(20) → (rmv({b}, {}) → success)))
Modelling Timed AFs
10
Example

16. AI^3 2021 - Concurrent Argumentation with Time: An Overview
• http://conarg.dmi.unipg.it/tcla
• Run all / step-by-step execution
• Shows program output + shared memory status + Timed AF
tcla Web Interface
11

17. AI^3 2021 - Concurrent Argumentation with Time: An Overview
• tcla models concurrent argumentation processes over time
• We showed how to translate Timed AFs into tcla processes
• Working implementation available online
Conclusion
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… tcla can do more than just modelling Timed AFs!

18. AI^3 2021 - Concurrent Argumentation with Time: An Overview
• Negotiation/debating/persuasion between agents
• Use interleaving instead of maximal parallelism for time passing
(accepted at PADL 2022)
• Connections with the AGM Framework
Future Work
13

19. Concurrent Argumentation with
Time: An Overview
AI^3 2021
Stefano Bistarelli, Maria Chiara Meo, Carlo Taticchi
Thank you for your attention!