Reasoning about Resource-bounded Agents Natasha Alechina joint work - PowerPoint PPT Presentation

Reasoning about Resource-bounded Agents Natasha Alechina joint work with Brian Logan, Hoang Nga Nguyen, Franco Raimondi, Nils Bulling Agent Verification Workshop Liverpool, 11 September 2015 Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 1

Acknowledgement This work is funded by the EPSRC project(s) Verification of resource-bounded multiagent systems (joint between the University of Nottingham and Middlesex University) Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 2

Plan of the talk motivation: why reason about resources? resource logics decidability and undecidability of the model-checking problem for resource logics decidable case (RB+-ATL) feasible cases (no production, or one resource) case study (sensor network protocol) Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 3

Motivating examples sensor networks: nodes can only send and receive messages if they have sufficient energy levels mobile agents, for example patrolling robots: also need energy to move agents may need other resources for performing actions, for example money, fuel, or water (for extinguishing fires), etc. Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 4

Resource Logics variants of Alternating-Time Temporal Logic (ATL) where transitions have costs (or rewards) and the syntax can express resource requirements of a strategy, e.g.: agents A can enforce outcome ϕ if they have at most b 1 units of resource r 1 and b 2 units of resource r 2 various flavours of resource logics exist: RBCL (IJCAI 2009), RB-ATL (AAMAS 2010), RB ± ATL (ECAI 2014), RAL (Bulling & Farwer), PRB-ATL (Della Monica et al.), QATL* (Bulling & Goranko) Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 5

Model-checking resource logics model-checking problem: given a structure, a state in the structure and a formula, does the state satisfy the formula? for most resource logics the model-checking problem is undecidable: in particular, various flavours of RAL, and QATL* Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 6

Resource Agent Logic (Bulling & Farwer 2010) RAL formulae are defined by: i # i # φ ::= p | ¬ ϕ | ϕ ^ ψ | h h A i B � ϕ | h h A i i η B � ϕ | h h A i B ϕ U ψ | h h A i i η B ϕ U ψ | i # h h A i B 2 ϕ | h h A i i η B 2 ϕ where p is a proposition, A , B ✓ Agt are sets of agents, and η is a resource endowment h h A i i η B ϕ means that agents A have a strategy compatible with the endowment η to enforce ϕ whatever the opponent agents do (opponents in B also act under resource bound η ) i # h h A i B ϕ means that agents A have a strategy compatible with the current resource endowment to enforce ϕ whatever the opponent agents do (opponents in B also act under the current resource bound) Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 7

RAL fragments rfRAL in resource flat RAL , each nested ATL operator has a i # fresh assignment of resources ( h h A i B ϕ is not allowed): h h A i i η 0 A ( safe U ( h h A i i η 1 A ( visual U rescue ))) prRAL in proponent restricted RAL , only the strategy of the proponent agents is resource bounded — the opponent i # ϕ agents have no resource bound h h A i i η ϕ , h h A i rfprRAL in resource flat proponent restricted RAL is the combination of rfRAL and prRAL prRAL r positive proponent restricted RAL is the same as prRAL except that no coalition modality is under the scope of a negation Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 8

Summary of known results (IJCAI 2015) prRAL r Models RAL rfRAL prRAL rfprRAL U [ 1 ] ⇤ RBM U [1] U [1] U [1] U [1] U [ 1 ] ⇤ U [ 1 ] ⇤ D [ 2 ] ⇤ iRBM U D RBM Resource Bounded Models (infinite semantics) iRBM Resource Bounded Models with idle actions [1] Bulling & Farwer 2010 [2] Alechina et al 2014 ( ⇤ corollary) Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 9

Decidable case: RB ± ATL Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 10

RB ± ATL: syntax Agt = { a 1 , . . . , a n } a set of n agents Res = { res 1 , . . . , res r } a set of r resources, Π a set of propositions B = N r 1 a set of resource bounds, where N 1 = N [ { 1 } Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 11

RB ± ATL: syntax Formulas of RB ± ATL are defined by the following syntax h A b i h A b i h A b i ϕ ::= p | ¬ ϕ | ϕ _ ψ | h i� ϕ | h i ϕ U ψ | h i 2 ϕ where p 2 Π is a proposition, A ✓ Agt , and b 2 B is a resource bound. Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 12

RB ± ATL: meaning of formulas h A b i h i� ψ means that a coalition A can ensure that the next state satisfies ϕ under resource bound b h A b i h i ψ 1 U ψ 2 means that A has a strategy to enforce ψ while maintaining the truth of ϕ , and the cost of this strategy is at most b h A b i h i 2 ψ means that A has a strategy to make sure that ϕ is always true, and the cost of this strategy is at most b Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 13

Resource-bounded concurrent game structure A RB-CGS is a tuple M = ( Agt , Res , S , Π , π , Act , d , c , δ ) where: Agt is a non-empty set of n agents, Res is a non-empty set of r resources and S is a non-empty set of states; Π is a finite set of propositional variables and π : Π ! ℘ ( S ) is a truth assignment Act is a non-empty set of actions which includes idle , and d : S ⇥ Agt ! ℘ ( Act ) \ { ; } is a function which assigns to each s 2 S a non-empty set of actions available to each agent a 2 Agt c : S ⇥ Agt ⇥ Act ! Z r (the integer in position i indicates consumption or production of resource res i by the action a ) δ : ( s , σ ) 7! S for every s 2 S and joint action σ 2 D ( s ) gives the state resulting from executing σ in s . Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 14

Additional assumptions and notation for every s 2 S and a 2 Agt , idle 2 d ( s , a ) c ( s , a , idle ) = ¯ 0 for all s 2 S and a 2 Agt where ¯ 0 = 0 r we denote joint actions by all agents in Agt available at s by D ( s ) = d ( s , a 1 ) ⇥ · · · ⇥ d ( s , a n ) for a coalition A , D A ( s ) is the set of all joint actions by agents in A out ( s , σ ) = { s 0 2 S | 9 σ 0 2 D ( s ) : σ = σ 0 A ^ s 0 = δ ( s , σ 0 ) } cost ( s , σ ) = P a 2 A c ( s , a , σ a ) if one agent consumes 10 units of resource and another agent produces 10 units of resource, the cost of their joint action is 0 Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 15

Example: c(-,-,idle)=0, c(-,-,watch)=1, c(-,-,charge)=-1 ⟨ idle , idle , idle ⟩ s2 detect ⟨ watch, watch, idle ⟩ ⟨ idle , idle , idle ⟩ s0 s1 s3 ⟨ watch, charge/idle, idle ⟩ ⟨ – , –, bad ⟩ bad detect ⟨ charge/idle, watch, idle ⟩ ⟨ –, –, idle ⟩ ⟨ idle , idle , idle ⟩ s4 ⟨ charge/idle, charge/idle, idle ⟩ detect Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 16

Strategies and their costs a strategy for a coalition A ✓ Agt is a mapping F A : S + ! Act such that, for every λ s 2 S + , F A ( λ s ) 2 D A ( s ) a computation λ 2 S ω is consistent with a strategy F A iff, for all i � 0, λ [ i + 1 ] 2 out ( λ [ i ] , F A ( λ [ 0 , i ])) out ( s , F A ) the set of all consistent computations λ of F A that start from s given a bound b 2 B , a computation λ 2 out ( s , F A ) is b -consistent with F A iff, for every i � 0, P i j = 0 cost ( λ [ j ] , F A ( λ [ 0 , j ]))  b F A is a b -strategy if all λ 2 out ( s , F A ) are b -consistent Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 17

Truth definition h A b i M , s | = h i� φ iff 9 b -strategy F A such that for all λ 2 out ( s , F A ) : M , λ [ 1 ] | = φ h A b i M , s | = h i φ U ψ iff 9 b -strategy F A such that for all λ 2 out ( s , F A ) , 9 i � 0: M , λ [ i ] | = ψ and M , λ [ j ] | = φ for all j 2 { 0 , . . . , i � 1 } h A b i = h i 2 φ iff 9 b -strategy F A such that for all λ 2 out ( s , F A ) M , s | and i � 0: M , λ [ i ] | = φ Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 18

h { 1 , 2 } 0 i h { 1 , 2 } 0 i Example: h i 2 ( bad ! h i� detect ) ⟨ idle , idle , idle ⟩ s2 detect ⟨ watch, watch, idle ⟩ ⟨ idle , idle , idle ⟩ s0 s1 s3 ⟨ watch, charge/idle, idle ⟩ ⟨ – , –, bad ⟩ bad detect ⟨ charge/idle, watch, idle ⟩ ⟨ –, –, idle ⟩ ⟨ idle , idle , idle ⟩ s4 ⟨ charge/idle, charge/idle, idle ⟩ detect Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 19

Infinite bound versions Since the infinite resource bound version of RB-ATL modalities correspond to the standard ATL modalities, we write 1 i h h A ¯ i� φ as h h A i i� φ h A ¯ 1 i h i φ U ψ as h h A i i φ U ψ 1 i h h A ¯ i 2 φ as h h A i i 2 φ Natasha Alechina Reasoning about Resource-bounded Agents Agent Verification 2015 20