Strategies and commitments Faustine Maffre University of Toulouse - - - PowerPoint PPT Presentation

Strategies and commitments

Faustine Maffre

University of Toulouse - IRIT

July 12, 2013

Context and Objectives ATL ATLEA ATELEA ATLEP Conclusion

Context and Objectives

Action logics: reasoning about actions and their effects for individual agents Example: PDL Strategic logics: reasoning about existence of strategies in multi-agent systems Example: ATL Context: multi-agent systems with states linked by transitions depending on actions done by agents Objective: explicit actions composing strategies

• extend the language of ATL with actions names
• reason about uniform strategies (epistemic extension)

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Outline

1 ATL

ATL: Strategies Language of ATL Semantics of ATL

2 ATLEA

ATLEA: Commitments Language of ATLEA Semantics of ATLEA

3 ATELEA 4 ATLEP 5 Conclusion

Context and Objectives ATL ATLEA ATELEA ATLEP Conclusion

ATL

ATL = Alternating-time Temporal Logic First introduced by Alur, Henzinger, and Kupferman between 1997 and 2002. Studies strategies of agents to ensure a property.

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Context and Objectives ATL ATLEA ATELEA ATLEP Conclusion

ATL: Strategies

Strategy for an agent a: fa: mapping every state to an action available for a Strategy for a set of agents (a coalition) A: FA: mapping every agent a to her strategy fa Introduces a “path quantifier”: Aψ = “agents in A have a strategy to ensure ψ no matter what agents outside A do”

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Context and Objectives ATL ATLEA ATELEA ATLEP Conclusion

Language of ATL

Syntax uses temporal operators and the path quantifier: ϕ ::= p | ⊥ | ¬ϕ | (ϕ ∨ ϕ) | Aϕ | A(ϕUϕ)

• temporal operators:
• ϕ: “next ϕ”
• ϕ1Uϕ2: “ϕ1 until ϕ2”

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Context and Objectives ATL ATLEA ATELEA ATLEP Conclusion

Semantics of ATL

More formally, Aψ = “agents in A have a strategy to ensure ψ no matter what agents outside A do” = there exists a strategy FA for the coalition A such that for every computation resulting from FA, ψ is true. Includes a double quantification on the strategies and computations (infinite paths in time). Does not give any information on actions composing the strategies.

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Context and Objectives ATL ATLEA ATELEA ATLEP Conclusion

ATLEA

ATLEA = Alternating-time Temporal Logic with Explicit Actions Currently developed by Andreas Herzig, Emiliano Lorini and Dirk Walther. Adds commitments on actions to ATL.

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Context and Objectives ATL ATLEA ATELEA ATLEP Conclusion

ATLEA: Commitments

Commitment on actions: a → ω = “agent a is committed to perform action ω” Commitment function ρ: finite set of action commitments dom(ρ): set of agents committed by ρ Parameter of the ATL path quantifier: Aρψ = “while agents in dom(ρ) are committed by ρ, agents in A have a strategy to ensure ψ no matter what agents outside A do” If dom(ρ) = ∅ then Aρψ is equivalent to ATL’s Aψ.

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Context and Objectives ATL ATLEA ATELEA ATLEP Conclusion

Language of ATLEA

Same as ATL except the path quantifier: ϕ ::= p | ⊥ | ¬ϕ | (ϕ ∨ ϕ) | Aρψ ψ ::= ¬ψ | ϕ | (ϕUϕ)

• action commitment function ρ
• state formulas ϕ
• path formulas ψ

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Context and Objectives ATL ATLEA ATELEA ATLEP Conclusion

Semantics of ATLEA

Study of the compatibility between actions and strategies for agents from A ∩ dom(ρ): For each agent from A ∩ dom(ρ), the action defined in the strategy fa is the same as the one defined in the commitment ρ(a). If A ∩ dom(ρ) = ∅ then any strategy is compatible with ρ. More formally, Aρψ = there exists a strategy FA for the coalition A compatible with the commitment function ρ such that for every computation resulting from FA, ψ is true.

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Context and Objectives ATL ATLEA ATELEA ATLEP Conclusion

ATELEA

ATELEA = Alternating-time Temporal Epistemic Logic with Explicit Actions Epistemic extension of ATLEA. Adds the knowledge operators to the language:

• Kaϕ: “agent a knows that ϕ”
• CAϕ: “it is common knowledge among the agents from A

that ϕ” Semantically: Relations between states meaning indistinguishability: an agent cannot distinguish two states in relation with her knowledge.

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Context and Objectives ATL ATLEA ATELEA ATLEP Conclusion

Uniform Strategies

Strategies where the same action is defined for two states linked by an indistinguishability relation. Since agents cannot distinguish states, they cannot choose different actions. Example of the Ace and the Joker cards ATELEA: reason about uniform actions (there exists an action such that the agent knows that by choosing this action, she will ensure the property).

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Context and Objectives ATL ATLEA ATELEA ATLEP Conclusion

ATLEP

ATLEP = Alternating-time Temporal Logic with Explicit Programs Currently developed. Objective: modify ATLEA commitment function to commit agents to several actions, or programs, instead of one, using PDL

• perators:
• sequences of actions
• non deterministic choices between actions
• repetitions of actions
• tests

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Context and Objectives ATL ATLEA ATELEA ATLEP Conclusion

Conclusion

ATL: reasoning about strategies ATLEA = ATL + commitment on actions: reasoning about actions and strategies ATELEA = ATLEA + epistemic: reasoning about uniform actions ATLEP = ATL + PDL: reasoning about programs and strategies To be developed: ATELEP = ATLEP + epistemic: reasoning about programs, strategies and knowledge

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