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) 2 / 15

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. 4 / 15

Context and Objectives ATL ATLEA ATELEA ATLEP Conclusion ATL: Strategies Strategy for an agent a : f a : mapping every state to an action available for a Strategy for a set of agents (a coalition) A : F A : mapping every agent a to her strategy f a Introduces a “path quantifier”: �� A �� ψ = “agents in A have a strategy to ensure ψ no matter what agents outside A do” 5 / 15

Context and Objectives ATL ATLEA ATELEA ATLEP Conclusion Language of ATL Syntax uses temporal operators and the path quantifier: ϕ ::= p | ⊥ | ¬ ϕ | ( ϕ ∨ ϕ ) | �� A ��� ϕ | �� A �� ( ϕ U ϕ ) • temporal operators: • � ϕ : “next ϕ ” • ϕ 1 U ϕ 2 : “ ϕ 1 until ϕ 2 ” 6 / 15

Context and Objectives ATL ATLEA ATELEA ATLEP Conclusion Semantics of ATL More formally, �� A �� ψ = “agents in A have a strategy to ensure ψ no matter what agents outside A do” = there exists a strategy F A for the coalition A such that for every computation resulting from F A , 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. 7 / 15

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. 8 / 15

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: �� A �� ρ ψ = “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 �� A �� ρ ψ is equivalent to ATL’s �� A �� ψ . 9 / 15

Context and Objectives ATL ATLEA ATELEA ATLEP Conclusion Language of ATLEA Same as ATL except the path quantifier: ϕ ::= p | ⊥ | ¬ ϕ | ( ϕ ∨ ϕ ) | �� A �� ρ ψ ψ ::= ¬ ψ | � ϕ | ( ϕ U ϕ ) • action commitment function ρ • state formulas ϕ • path formulas ψ 10 / 15

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 f a 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, �� A �� ρ ψ = there exists a strategy F A for the coalition A compatible with the commitment function ρ such that for every computation resulting from F A , ψ is true. 11 / 15

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: • K a ϕ : “agent a knows that ϕ ” • C A ϕ : “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. 12 / 15

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). 13 / 15

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 operators: • sequences of actions • non deterministic choices between actions • repetitions of actions • tests 14 / 15

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 15 / 15