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Stable Multi-Agent Systems

Stable Multi-Agent Systems. Andrea Bracciali, Paolo Mancarella, Kostas Stathis, Francesca Toni,. Informatica, PISA. Informatica, PISA. Computing, CITY. Computing, IMPERIAL. . ESAW’04, Toulouse 22-10-04. Motivation; I/O Agent Semantics; Stable Sets: Examples of stable MAS;

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Stable Multi-Agent Systems

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  1. Stable Multi-Agent Systems Andrea Bracciali, Paolo Mancarella, Kostas Stathis, Francesca Toni, Informatica, PISA. Informatica, PISA. Computing, CITY. Computing, IMPERIAL.  ESAW’04, Toulouse 22-10-04.

  2. Motivation; I/O Agent Semantics; Stable Sets: Examples of stable MAS; MAS Properties; Stable MAS construction; Conclusions and future work. Outline

  3. Previous work on Logic Programming (LP) to specify agents: Toni & Stathis’ ESAW’02 Access-as-you-need framework; Q: What does it take to build an abstract model of a MAS (in a way similar to the Tp op. of van Emden & Kowalski for LP)? Motivation Current work (Bracciali et al DALT’04) based on the need to model declaratively a MAS. Approach: • has formal foundations; • is abstract (language independent); • is suitable to express and verify properties.

  4. ESAW’02: Access-as-you-need Real Social Environment I must join a society to get a resource for the user Electronic Social Environment Artificial Society 1 Artificial Society n Artificial Society 2 Personal Agent

  5. ESAW’02: Access-as-you-need (cntd) Agent a: Pa: get(R, T)  request(a,b,R, T')  accept(b,a,R,T'')  T''  T'  T Aa: request(a, X, R, T), accept(X,a,R,T) ICa:  Agent b: Pb: have(r) Ab: accept(b,X,R,T), request(X, b, R, T) ICc: request(X,b,R,T)  have(R)  T'[accept(b,X,R,T')  T'  T] actions observables How do we model a MAS of this kind abstractly?

  6. Agents: 1..n; World: W, with E(W ) all possible events in W. Each agent i is equipped with; set of all possible actions A(i); set of all possible observations O(i); s.t. O(i)  A(j)  E(W ) A(i)  A(j) i  j (e.g. agent i cannot act pretending to be j). Multi-agent System Assumptions i  j

  7. agent i plan  A(i) “Mental State” (beliefs) 0 M public in out Observations  O(i) Actions  A(i) private I/O Agent Semantics

  8. Semantics for single agent i is then given as: Si(0, in) = <M, out> M may be  when: agent i is unable to plan or achieve a goal; or the observations of agent i are inconsistent with the constraints it wants to satisfy (e.g. rely on agent a1 for a resource that a1 does not posses); Inconsistent agents are required not to commit to any action. I/O Agent Semantics (cntd)

  9. A MAS = <A, W> is stable if there exists a = iouts.t. for eachiA Si(-i W i, i0) = <Mi, iout> where -i =  (j) (actions by agents other than i); (j)=   A(j) (actions by agent j); W i = W  O(i) (happened events observable by i). The set  is called astable setforMAS. Stable MAS iA jA, ij

  10. Agent 1 moves odd-numbered blocks and has goal mvToB. Agent 2 moves even-numbered blocks and has goal mvToC. Example of Stable Set 1 1 2  = {1ToB1, 2ToC2, 3ToB1} is a stable set. 2 3 1 A B C S1({2ToC2} U W 1, {1ToB1, 3ToB1}) = <M1, {1ToB1, 3ToB1}> S2({1ToB1, 3ToB1} U W 2, {2ToC2}) = <M2, {2ToC2}> with mvToB M1 and mvToC M2.

  11. Agent 1 intends to move block 1 to B. Agent 2 intends to move block 2 to B. Example of Unstable Set 2 1 1 2 A B C No stable set, as agents become inconsistent.

  12. What can we do with stable sets? • A MAS admitting stable sets is “good”/”well-behaved”; • DALT’04: properties of MAS can be specified in terms of stable sets, e.g. • A successful MAS is a stable MAS whose every agent is successful (it achieves its goals); • A robust MAS is a successful MAS such that, taking away any agent in it, the resulting MAS is still successful. • How can we guarantee the existence of stable sets for MAS? How can we construct stable sets?

  13. GivenMAS = <A, W> and , let A+be the set of all agents i in A s.t.Si(-i  W i, (i))  < , {}> A- = A - A+ Then TA(< W> A) = <Si(-i  W i, (i))>A if A = A+ = <Si(-i  W i, (i))>A+<, {}>A-otherwise Constructing Stable Sets: One Step Operator

  14. Constructing Stable Sets: concrete semantics of a MAS Given • MAS = <A, W> and • <0>A(tuple of initial plans) the concrete semantics of MAS is given by applying (possibly infinitely many times) TA,starting from <0W >A : TA (<0  W >A ), TA (TA (<0  W >A )), … Conjecture: the concrete semantics of a MAS is stable, given any tuple of initial plans.

  15. Conclusions & Future work • A language independent abstract semantics for agents. • Suitable to model and verify properties of agents & MAS. • Relies on the notion of stability to approximate well-behavedness (shown examples both positive and negative). • Initial steps towards a formal methodology. • Future work involves: • the application of the framework to more complex scenaria; • use stability to prove properties of these scenaria.

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